Search results for: negative binomial model

Authors: Mohd Asrul Affedi, Nyi Nyi Naing

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Overdispersion is present in count data, and basically when a phenomenon happened, a Negative Binomial (NB) is commonly used to replace a standard Poisson model. Analysis of count data event, such as mortality cases basically Poisson regression model is appropriate. Hence, the model is not appropriate when existing a zero values. The zero-inflated negative binomial model is appropriate. In this article, we modelled the mortality cases as a dependent variable by age categorical. The objective of this study to determine existing overdispersion in mortality data of AIDS co-infection patients in Kelantan.

Keywords: negative binomial death rate, overdispersion, zero-inflation negative binomial death rate, AIDS

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Authors: Rafid Saeed Abdulrazak Alshkaki

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In this paper, zero-one inflated negative binomial distribution is considered, along with some of its structural properties, then its parameters were estimated using the method of moments. It is found that the method of moments to estimate the parameters of the zero-one inflated negative binomial models is not a proper method and may give incorrect conclusions.

Keywords: zero one inflated models, negative binomial distribution, moments estimator, non negative integer sampling

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Authors: Mohd Asrul Affendi Bi Abdullah, Nyi Nyi Naing

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The purpose of this study was to identify comparable manner between negative binomial death rate (NBDR) and zero inflated negative binomial death rate (ZINBDR) with died patients with (HIV + T B+) and (HIV + T B−). HIV and TB is a serious world wide problem in the developing country. Data were analyzed with applying NBDR and ZINBDR to make comparison which a favorable model is better to used. The ZINBDR model is able to account for the disproportionately large number of zero within the data and is shown to be a consistently better fit than the NBDR model. Hence, as a results ZINBDR model is a superior fit to the data than the NBDR model and provides additional information regarding the died mechanisms HIV+TB. The ZINBDR model is shown to be a use tool for analysis death rate according age categorical.

Keywords: zero inflated negative binomial death rate, HIV and TB, AIC and BIC, death rate

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Authors: Prashant Verma, Prafulla K. Swain, K. K. Singh, Mukti Khetan

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Objective: In India, around 20,000 women die every year due to abortion-related complications. In the modelling of count variables, there is sometimes a preponderance of zero counts. This article concerns the estimation of various count regression models to predict the average number of spontaneous abortion among women in the Punjab state of India. It also assesses the factors associated with the number of spontaneous abortions. Materials and methods: The study included 27,173 married women of Punjab obtained from the DLHS-4 survey (2012-13). Poisson regression (PR), Negative binomial (NB) regression, zero hurdle negative binomial (ZHNB), and zero-inflated negative binomial (ZINB) models were employed to predict the average number of spontaneous abortions and to identify the determinants affecting the number of spontaneous abortions. Results: Statistical comparisons among four estimation methods revealed that the ZINB model provides the best prediction for the number of spontaneous abortions. Antenatal care (ANC) place, place of residence, total children born to a woman, woman's education and economic status were found to be the most significant factors affecting the occurrence of spontaneous abortion. Conclusions: The study offers a practical demonstration of techniques designed to handle count variables. Statistical comparisons among four estimation models revealed that the ZINB model provided the best prediction for the number of spontaneous abortions and is recommended to be used to predict the number of spontaneous abortions. The study suggests that women receive institutional Antenatal care to attain limited parity. It also advocates promoting higher education among women in Punjab, India.

Keywords: count data, spontaneous abortion, Poisson model, negative binomial model, zero hurdle negative binomial, zero-inflated negative binomial, regression

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Authors: Mokhtar Kouki Inès Rekik

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This paper focuses on the assessment of the air pollution and morbidity relationship in Tunisia. Air pollution is measured by ozone air concentration and the morbidity is measured by the number of respiratory-related restricted activity days during the 2-week period prior to the interview. Socioeconomic data are also collected in order to adjust for any confounding covariates. Our sample is composed by 407 Tunisian respondents; 44.7% are women, the average age is 35.2, near 69% are living in a house built after the 1980, and 27.8% have reported at least one day of respiratory-related restricted activity. The model consists on the regression of the number of respiratory-related restricted activity days on the air quality measure and the socioeconomic covariates. In order to correct for zero-inflation and heterogeneity, we estimate several models (Poisson, Negative binomial, Zero inflated Poisson, Poisson hurdle, Negative binomial hurdle and finite mixture Poisson models). Bootstrapping and post-stratification techniques are used in order to correct for any sample bias. According to the Akaike information criteria, the hurdle negative binomial model has the greatest goodness of fit. The main result indicates that, after adjusting for socioeconomic data, the ozone concentration increases the probability of positive number of restricted activity days.

Keywords: bootstrapping, hurdle negbin model, overdispersion, ozone concentration, respiratory-related restricted activity days

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Authors: W. Sriwattanapongse, S. Prasitwattanaseree, S. Wongtrangan

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The transportation accidents mortality is a major problem that leads to loss of human lives, and economic. The objective was to identify patterns of statistical modeling for estimating mortality rates due to transportation accidents in Thailand by using data from 2000 to 2009. The data was taken from the death certificate, vital registration database. The number of deaths and mortality rates were computed classifying by gender, age, year and region. There were 114,790 cases of transportation accidents deaths. The highest average age-specific transport accident mortality rate is 3.11 per 100,000 per year in males, Southern region and the lowest average age-specific transport accident mortality rate is 1.79 per 100,000 per year in females, North-East region. Linear, poisson and negative binomial models were chosen for fitting statistical model. Among the models fitted, the best was chosen based on the analysis of deviance and AIC. The negative binomial model was clearly appropriate fitted.

Keywords: transportation accidents, mortality, modeling, analysis of deviance

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Authors: Oluwayemisi O. Alaba, John O. Olaomi

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The 2013 Nigerian Demographic Health Survey (NDHS) data was used to investigate the determinants of family size in Nigeria using the geo-additive model. The fixed effect of categorical covariates were modelled using the diffuse prior, P-spline with second-order random walk for the nonlinear effect of continuous variable, spatial effects followed Markov random field priors while the exchangeable normal priors were used for the random effects of the community and household. The Negative Binomial distribution was used to handle overdispersion of the dependent variable. Inference was fully Bayesian approach. Results showed a declining effect of secondary and higher education of mother, Yoruba tribe, Christianity, family planning, mother giving birth by caesarean section and having a partner who has secondary education on family size. Big family size is positively associated with age at first birth, number of daughters in a household, being gainfully employed, married and living with partner, community and household effects.

Keywords: Bayesian analysis, family size, geo-additive model, negative binomial

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Authors: Atheer Al-Nuaimi, Harry Evdorides

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Every day many people die or get disabled or injured on roads around the world, which necessitates more specific treatments for transportation safety issues. International road assessment program (iRAP) model is one of the comprehensive road safety models which accounting for many factors that affect road safety in a cost-effective way in low and middle income countries. In iRAP model road safety has been divided into five star ratings from 1 star (the lowest level) to 5 star (the highest level). These star ratings are based on star rating score which is calculated by iRAP methodology depending on road attributes, traffic volumes and operating speeds. The outcome of iRAP methodology are the treatments that can be used to improve road safety and reduce fatalities and serious injuries (FSI) numbers. These countermeasures can be used separately as a single countermeasure or mix as multiple countermeasures for a location. There is general agreement that the adequacy of a countermeasure is liable to consistent losses when it is utilized as a part of mix with different countermeasures. That is, accident diminishment appraisals of individual countermeasures cannot be easily added together. The iRAP model philosophy makes utilization of a multiple countermeasure adjustment factors to predict diminishments in the effectiveness of road safety countermeasures when more than one countermeasure is chosen. A multiple countermeasure correction factors are figured for every 100-meter segment and for every accident type. However, restrictions of this methodology incorporate a presumable over-estimation in the predicted crash reduction. This study aims to adjust this correction factor by developing new models to calculate the effect of using multiple countermeasures on the number of fatalities for a location or an entire road. Regression models have been used to establish relationships between crash frequencies and the factors that affect their rates. Multiple linear regression, negative binomial regression, and Poisson regression techniques were used to develop models that can address the effectiveness of using multiple countermeasures. Analyses are conducted using The R Project for Statistical Computing showed that a model developed by negative binomial regression technique could give more reliable results of the predicted number of fatalities after the implementation of road safety multiple countermeasures than the results from iRAP model. The results also showed that the negative binomial regression approach gives more precise results in comparison with multiple linear and Poisson regression techniques because of the overdispersion and standard error issues.

Keywords: international road assessment program, negative binomial, road multiple countermeasures, road safety

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Authors: Mounia El Hafyani, Khalid El Himdi

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Precipitation is one of the key variables in water resource planning. The importance of modeling wet and dry durations is a crucial pointer in engineering hydrology. The objective of this study is to model and analyze the distribution of wet and dry durations. For this purpose, the daily rainfall data from 1967 to 2017 of the Moroccan city of Kenitra’s station are used. Three models are implemented for the distribution of wet and dry durations, namely the first-order Markov chain, the second-order Markov chain, and the truncated negative binomial law. The adherence of the data to the proposed models is evaluated using Chi-square and Kolmogorov-Smirnov tests. The Akaike information criterion is applied to assess the most effective model distribution. We go further and study the law of the number of wet and dry days among k consecutive days. The calculation of this law is done through an algorithm that we have implemented based on conditional laws. We complete our work by comparing the observed moments of the numbers of wet/dry days among k consecutive days to the calculated moment of the three estimated models. The study shows the effectiveness of our approach in modeling wet and dry durations of daily precipitation.

Keywords: Markov chain, rainfall, truncated negative binomial law, wet and dry durations

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Authors: Norm Josephy, Lucy Kimball, Victoria Steblovskaya

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Hedging of a portfolio of European options under proportional transaction costs is considered. Our discrete time financial market model extends the binomial market model with transaction costs to the case where the underlying stock price ratios are distributed over a bounded interval rather than over a two-point set. An optimal hedging strategy is chosen from a set of admissible non-self-financing hedging strategies. Our approach to optimal hedging of a portfolio of options is based on theoretical foundation that includes determination of a no-arbitrage option price interval as well as on properties of the non-self-financing strategies and their residuals. A computational algorithm for optimizing an investor relevant criterion over the set of admissible non-self-financing hedging strategies is developed. Applicability of our approach is demonstrated using both simulated data and real market data.

Keywords: extended binomial model, non-self-financing hedging, optimization, proportional transaction costs

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Authors: Ishapathik Das, Sumen Sen, N. Rao Chaganty, Pooja Sengupta

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Dependent multivariate count data occur in several research studies. These data can be modeled by a multivariate Poisson or Negative binomial distribution constructed using copulas. However, when some of the counts are inflated, that is, the number of observations in some cells are much larger than other cells, then the copula based multivariate Poisson (or Negative binomial) distribution may not fit well and it is not an appropriate statistical model for the data. There is a need to modify or adjust the multivariate distribution to account for the inflated frequencies. In this article, we consider the situation where the frequencies of two cells are higher compared to the other cells, and develop a doubly inflated multivariate Poisson distribution function using multivariate Gaussian copula. We also discuss procedures for regression on covariates for the doubly inflated multivariate count data. For illustrating the proposed methodologies, we present a real data containing bivariate count observations with inflations in two cells. Several models and linear predictors with log link functions are considered, and we discuss maximum likelihood estimation to estimate unknown parameters of the models.

Keywords: copula, Gaussian copula, multivariate distributions, inflated distributios

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Authors: Bohsiu Wu

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Among serious crimes, child homicide is a rather rare event. However, the killing of children stirs up a special type of emotion in society that pales other criminal acts. This study examines the relevancy of three possible community-level explanations for child homicide: social deprivation, female empowerment, and social isolation. The social deprivation hypothesis posits that child homicide results from lack of resources in communities. The female empowerment hypothesis argues that a higher female status translates into a higher level of capability to prevent child homicide. Finally, the social isolation hypothesis regards child homicide as a result of lack of social connectivity. Child homicide data, aggregated by US postal ZIP codes in California from 1990 to 1999, were analyzed with a negative binomial regression. The results of the negative binomial analysis demonstrate that social deprivation is the most salient and consistent predictor among all other factors in explaining child homicide victimization at the ZIP-code level. Both social isolation and female labor force participation are weak predictors of child homicide victimization across communities. Further, results from the negative binomial regression show that it is the communities with a higher, not lower, degree of female labor force participation that are associated with a higher count of child homicide. It is possible that poor communities with a higher level of female employment have a lesser capacity to provide the necessary care and protection for the children. Policies aiming at reducing social deprivation and strengthening female empowerment possess the potential to reduce child homicide in the community.

Keywords: child homicide, deprivation, empowerment, isolation

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Authors: Benjamin Lee Warren

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Many problems exist in additive number theory which is essential to determine the primes that are the sum of two elements from a given single-variable polynomial sequence, and most of them are unattackable in the present day. Here, we determine solutions for this problem to a few certain sequences (certain binomial coefficients and power sums) using only elementary algebra and some algebraic factoring methods (as well as Euclid’s Lemma and Faulhaber’s Formula). In particular, we show that there are finitely many primes as sums of two of these types of elements. Several cases are fully illustrated, and bounds are presented for the cases not fully illustrated.

Keywords: binomial coefficients, power sums, primes, algebra

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Authors: Rajesh Singh, Kailash Kale

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In this paper, the Binomial process type occurrence of software failures is considered and failure intensity has been characterized by one parameter Rayleigh class Software Reliability Growth Model (SRGM). The proposed SRGM is mathematical function of parameters namely; total number of failures i.e. η-0 and scale parameter i.e. η-1. It is assumed that very little or no information is available about both these parameters and then considering non-informative priors for both these parameters, the Bayes estimators for the parameters η-0 and η-1 have been obtained under square error loss function. The proposed Bayes estimators are compared with their corresponding maximum likelihood estimators on the basis of risk efficiencies obtained by Monte Carlo simulation technique. It is concluded that both the proposed Bayes estimators of total number of failures and scale parameter perform well for proper choice of execution time.

Keywords: binomial process, non-informative prior, maximum likelihood estimator (MLE), rayleigh class, software reliability growth model (SRGM)

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Authors: Shourav Ahmed, M. Gulam Kibria, Kais Zaman

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Control charts graphically verify variation in quality parameters. Attribute type control charts deal with quality parameters that can only hold two states, e.g., good or bad, yes or no, etc. At present, p-control chart is most commonly used to deal with attribute type data. In construction of p-control chart using binomial distribution, the value of proportion non-conforming must be known or estimated from limited sample information. As the probability distribution of fraction non-conforming (p) is considered in hyperbinomial distribution unlike a constant value in case of binomial distribution, it reduces the risk of false detection. In this study, a statistical control chart is proposed based on hyperbinomial distribution when prior estimate of proportion non-conforming is unavailable and is estimated from limited sample information. We developed the control limits of the proposed modified p-chart using the mean and variance of hyperbinomial distribution. The proposed modified p-chart can also utilize additional sample information when they are available. The study also validates the use of modified p-chart by comparing with the result obtained using cumulative distribution function of hyperbinomial distribution. The study clearly indicates that the use of hyperbinomial distribution in construction of p-control chart yields much accurate estimate of quality parameters than using binomial distribution.

Keywords: binomial distribution, control charts, cumulative distribution function, hyper binomial distribution

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Authors: Debarati Bhaumik, Diptish Dey

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Multilevel models, increasingly deployed in industries such as insurance, food production, and entertainment within functions such as marketing and supply chain management, need to be transparent and ethical. Applications usually result in binary classification within groups or hierarchies based on a set of input features. Using open-source datasets, we demonstrate that popular explainability methods, such as SHAP and LIME, consistently underperform inaccuracy when interpreting these models. They fail to predict the order of feature importance, the magnitudes, and occasionally even the nature of the feature contribution (negative versus positive contribution to the outcome). Besides accuracy, the computational intractability of SHAP for binomial classification is a cause of concern. For transparent and ethical applications of these hierarchical statistical models, sound audit frameworks need to be developed. In this paper, we propose an audit framework for technical assessment of multilevel regression models focusing on three aspects: (i) model assumptions & statistical properties, (ii) model transparency using different explainability methods, and (iii) discrimination assessment. To this end, we undertake a quantitative approach and compare intrinsic model methods with SHAP and LIME. The framework comprises a shortlist of KPIs, such as PoCE (Percentage of Correct Explanations) and MDG (Mean Discriminatory Gap) per feature, for each of these three aspects. A traffic light risk assessment method is furthermore coupled to these KPIs. The audit framework will assist regulatory bodies in performing conformity assessments of AI systems using multilevel binomial classification models at businesses. It will also benefit businesses deploying multilevel models to be future-proof and aligned with the European Commission’s proposed Regulation on Artificial Intelligence.

Keywords: audit, multilevel model, model transparency, model explainability, discrimination, ethics

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Authors: Syed Afrozuddin Ahmed, Junaid Saghir Siddiqi, Sabah Quaiser

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Various studies have reported that global warming causes unstable climate and many serious impact to physical environment and public health. The increasing incidence of dengue incidence is now a priority health issue and become a health burden of Pakistan. In this study it has been investigated that spatial pattern of environment causes the emergence or increasing rate of dengue fever incidence that effects the population and its health. The climatic or environmental structure data and the Dengue Fever (DF) data was processed by coding, editing, tabulating, recoding, restructuring in terms of re-tabulating was carried out, and finally applying different statistical methods, techniques, and procedures for the evaluation. Five climatic variables which we have studied are precipitation (P), Maximum temperature (Mx), Minimum temperature (Mn), Humidity (H) and Wind speed (W) collected from 1980-2012. The dengue cases in Karachi from 2010 to 2012 are reported on weekly basis. Principal component analysis is applied to explore the climatic variables and/or the climatic (structure) which may influence in the increase or decrease in the number of dengue fever cases in Karachi. PC1 for all the period is General atmospheric condition. PC2 for dengue period is contrast between precipitation and wind speed. PC3 is the weighted difference between maximum temperature and wind speed. PC4 for dengue period contrast between maximum and wind speed. Negative binomial and Poisson regression model are used to correlate the dengue fever incidence to climatic variable and principal component score. Relative humidity is estimated to positively influence on the chances of dengue occurrence by 1.71% times. Maximum temperature positively influence on the chances dengue occurrence by 19.48% times. Minimum temperature affects positively on the chances of dengue occurrence by 11.51% times. Wind speed is effecting negatively on the weekly occurrence of dengue fever by 7.41% times.

Keywords: principal component analysis, dengue fever, negative binomial regression model, poisson regression model

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Authors: Laraib Niaz

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This paper analyzes the ways in which education and economic deprivation are linked to terrorism in Pakistan using data for terrorist incidents from the Global Terrorism Database (GTD). It employs the technique of negative binomial regression for the years between 1990 and 2013, presenting evidence for a positive association between education and terrorism. Conversely, a negative correlation with economic deprivation is signified in the results. The study highlights the element of radicalization as witnessed in the curriculum and textbooks of public schools as a possible reason for extremism, which in turn may lead to terrorism.

Keywords: education, Pakistan, terrorism, poverty

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Authors: Y. N. Phang, E. F. Loh

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Many researchers have suggested the use of zero inflated Poisson (ZIP) and zero inflated negative binomial (ZINB) models in modeling over-dispersed medical count data with extra variations caused by extra zeros and unobserved heterogeneity. The studies indicate that ZIP and ZINB always provide better fit than using the normal Poisson and negative binomial models in modeling over-dispersed medical count data. In this study, we proposed the use of Zero Inflated Inverse Trinomial (ZIIT), Zero Inflated Poisson Inverse Gaussian (ZIPIG) and zero inflated strict arcsine models in modeling over-dispersed medical count data. These proposed models are not widely used by many researchers especially in the medical field. The results show that these three suggested models can serve as alternative models in modeling over-dispersed medical count data. This is supported by the application of these suggested models to a real life medical data set. Inverse trinomial, Poisson inverse Gaussian, and strict arcsine are discrete distributions with cubic variance function of mean. Therefore, ZIIT, ZIPIG and ZISA are able to accommodate data with excess zeros and very heavy tailed. They are recommended to be used in modeling over-dispersed medical count data when ZIP and ZINB are inadequate.

Keywords: zero inflated, inverse trinomial distribution, Poisson inverse Gaussian distribution, strict arcsine distribution, Pearson’s goodness of fit

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Authors: Akalu Banbeta, Emmanuel Lesaffre, Reynaldo Martina, Joost Van Rosmalen

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Including data from previous studies (historical data) in the analysis of the current study may reduce the sample size requirement and/or increase the power of analysis. The most common example is incorporating historical control data in the analysis of a current clinical trial. However, this only applies when the historical control dataare similar enough to the current control data. Recently, several Bayesian approaches for incorporating historical data have been proposed, such as the meta-analytic-predictive (MAP) prior and the modified power prior (MPP) both for single control as well as for multiple historical control arms. Here, we examine the performance of the MAP and the MPP approaches for the analysis of (over-dispersed) count data. To this end, we propose a computational method for the MPP approach for the Poisson and the negative binomial models. We conducted an extensive simulation study to assess the performance of Bayesian approaches. Additionally, we illustrate our approaches on an overactive bladder data set. For similar data across the control arms, the MPP approach outperformed the MAP approach with respect to thestatistical power. When the means across the control arms are different, the MPP yielded a slightly inflated type I error (TIE) rate, whereas the MAP did not. In contrast, when the dispersion parameters are different, the MAP gave an inflated TIE rate, whereas the MPP did not.We conclude that the MPP approach is more promising than the MAP approach for incorporating historical count data.

Keywords: count data, meta-analytic prior, negative binomial, poisson

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Authors: Jacqueline Y. Thompson, Sam Watson, Lee Middleton, Karla Hemming

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Introduction: The odds ratio (estimated via logistic regression) is a well-established and common approach for estimating covariate-adjusted binary treatment effects when comparing a treatment and control group with dichotomous outcomes. Its popularity is primarily because of its stability and robustness to model misspecification. However, the situation is different for the relative risk and risk difference, which are arguably easier to interpret and better suited to specific designs such as non-inferiority studies. So far, there is no equivalent, widely acceptable approach to estimate an adjusted relative risk and risk difference when conducting clinical trials. This is partly due to the lack of a comprehensive evaluation of available candidate methods. Methods/Approach: A simulation study is designed to evaluate the performance of relevant candidate methods to estimate relative risks to represent conditional and marginal estimation approaches. We consider the log-binomial, generalised linear models (GLM) with iteratively weighted least-squares (IWLS) and model-based standard errors (SE); log-binomial GLM with convex optimisation and model-based SEs; log-binomial GLM with convex optimisation and permutation tests; modified-Poisson GLM IWLS and robust SEs; log-binomial generalised estimation equations (GEE) and robust SEs; marginal standardisation and delta method SEs; and marginal standardisation and permutation test SEs. Independent and identically distributed datasets are simulated from a randomised controlled trial to evaluate these candidate methods. Simulations are replicated 10000 times for each scenario across all possible combinations of sample sizes (200, 1000, and 5000), outcomes (10%, 50%, and 80%), and covariates (ranging from -0.05 to 0.7) representing weak, moderate or strong relationships. Treatment effects (ranging from 0, -0.5, 1; on the log-scale) will consider null (H0) and alternative (H1) hypotheses to evaluate coverage and power in realistic scenarios. Performance measures (bias, mean square error (MSE), relative efficiency, and convergence rates) are evaluated across scenarios covering a range of sample sizes, event rates, covariate prognostic strength, and model misspecifications. Potential Results, Relevance & Impact: There are several methods for estimating unadjusted and adjusted relative risks. However, it is unclear which method(s) is the most efficient, preserves type-I error rate, is robust to model misspecification, or is the most powerful when adjusting for non-prognostic and prognostic covariates. GEE estimations may be biased when the outcome distributions are not from marginal binary data. Also, it seems that marginal standardisation and convex optimisation may perform better than GLM IWLS log-binomial.

Keywords: binary outcomes, statistical methods, clinical trials, simulation study

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Authors: Praveen Vayalamkuzhi, Veeraragavan Amirthalingam

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Studies on safety on highways are becoming the need of the hour as over 400 lives are lost every day in India due to road crashes. In order to evaluate the factors that lead to different levels of crash severity, it is necessary to investigate the level of safety of highways and their relation to crashes. In the present study, an attempt is made to identify the factors that contribute to road crashes and to quantify their effect on the severity of road crashes. The study was carried out on a four-lane divided rural highway in India. The variables considered in the analysis includes components of horizontal alignment of highway, viz., straight or curve section; time of day, driveway density, presence of median; median opening; gradient; operating speed; and annual average daily traffic. These variables were considered after a preliminary analysis. The major complexities in the study are the heterogeneous traffic and the speed variation between different classes of vehicles along the highway. To quantify the impact of each of these factors, statistical analyses were carried out using Logit model and also negative binomial regression. The output from the statistical models proved that the variables viz., horizontal components of the highway alignment; driveway density; time of day; operating speed as well as annual average daily traffic show significant relation with the severity of crashes viz., fatal as well as injury crashes. Further, the annual average daily traffic has significant effect on the severity compared to other variables. The contribution of highway horizontal components on crash severity is also significant. Logit models can predict crashes better than the negative binomial regression models. The results of the study will help the transport planners to look into these aspects at the planning stage itself in the case of highways operated under heterogeneous traffic flow condition.

Keywords: geometric design, heterogeneous traffic, road crash, statistical analysis, level of safety

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Authors: Manuel Urueña Palomo

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In this paper, we introduce the study of a new solution to gravitational singularities by violating the energy conditions of the Penrose Hawking singularity theorems. We consider that a shift to negative energies, and thus, to negative masses, takes place at the event horizon of a black hole, justified by the original, singular and exact Schwarzschild solution. These negative energies are supported by relativistic particle physics considering the negative energy solutions of the Dirac equation, which states that a time transformation shifts to a negative energy particle. In either general relativity or full Newtonian mechanics, these negative masses are predicted to be repulsive. It is demonstrated that the model fits actual observations, and could possibly clarify the size of observed and unexplained supermassive black holes, when considering the inflation that would take place inside the event horizon where massive particles interact antigravitationally. An approximated solution of the model proposed could be simulated in order to compare it with these observations.

Keywords: black holes, CPT symmetry, negative mass, time transformation

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Authors: Showkat Ahmad Lone, Ahmadur Rahman, Ariful Islam

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The major assumption in accelerated life tests (ALT) is that the mathematical model relating the lifetime of a test unit and the stress are known or can be assumed. In some cases, such life–stress relationships are not known and cannot be assumed, i.e. ALT data cannot be extrapolated to use condition. So, in such cases, partially accelerated life test (PALT) is a more suitable test to be performed for which tested units are subjected to both normal and accelerated conditions. This study deals with estimating information about failure times of items under step-stress partially accelerated life tests using progressive failure-censored hybrid data with random removals. The life data of the units under test is considered to follow exponential life distribution. The removals from the test are assumed to have binomial distributions. The point and interval maximum likelihood estimations are obtained for unknown distribution parameters and tampering coefficient. An optimum test plan is developed using the D-optimality criterion. The performances of the resulting estimators of the developed model parameters are evaluated and investigated by using a simulation algorithm.

Keywords: binomial distribution, d-optimality, multiple censoring, optimal design, partially accelerated life testing, simulation study

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Authors: Mohd Asrul Affendi Bin Abdullah

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Sample size calculation is especially important for zero inflated models because a large sample size is required to detect a significant effect with this model. This paper verify how to present percentage of power approximation for categorical and then extended to zero inflated models. Wald test was chosen to determine power sample size of AIDS death rate because it is frequently used due to its approachability and its natural for several major recent contribution in sample size calculation for this test. Power calculation can be conducted when covariates are used in the modeling ‘excessing zero’ data and assist categorical covariate. Analysis of AIDS death rate study is used for this paper. Aims of this study to determine the power of sample size (N = 945) categorical death rate based on parameter estimate in the simulation of the study.

Keywords: power sample size, Wald test, standardize rate, ZINBDR

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Authors: Y. S. Yusoff, G. Streftaris, H. R Waters

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Death within 30 days is an important factor to be looked into, as there is a significant risk of deaths immediately following or soon after, Myocardial Infarction (MI) or stroke. In this paper, we will model the deaths within 30 days following a Myocardial Infarction (MI) or stroke in the UK. We will see how the probabilities of sudden deaths from MI or stroke have changed over the period 1981-2000. We will model the sudden deaths using a Generalized Linear Model (GLM), fitted using the R statistical package, under a Binomial distribution for the number of sudden deaths. We parameterize our model using the extensive and detailed data from the Framingham Heart Study, adjusted to match UK rates. The results show that there is a reduction for the sudden deaths following a MI over time but no significant improvement for sudden deaths following a stroke.

Keywords: sudden deaths, myocardial infarction, stroke, ischemic heart disease

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Authors: Vijay Kumar Singh, Pooja Kushwaha, Prabhat Ranjan, Krishna Kumar Ojha, Jitendra Kumar

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Present day high-throughput genomic technologies, NGS/microarrays, are producing large volume of data that require improved analysis methods to make sense of the data. The correlation between genes and samples has been regularly used to gain insight into many biological phenomena including, but not limited to, co-expression/co-regulation, gene regulatory networks, clustering and pattern identification. However, presence of outliers and violation of assumptions underlying Pearson correlation is frequent and may distort the actual correlation between the genes and lead to spurious conclusions. Here, we report a method to measure the strength of association between genes. The method assumes that the expression values of a gene are Bernoulli random variables whose outcome depends on the sample being probed. The method considers the two genes as uncorrelated if the number of sample with same outcome for both the genes (Ns) is equal to certainly expected number (Es). The extent of correlation depends on how far Ns can deviate from the Es. The method does not assume normality for the parent population, fairly unaffected by the presence of outliers, can be applied to qualitative data and it uses the binomial distribution to assess the significance of association. At this stage, we would not claim about the superiority of the method over other existing correlation methods, but our method could be another way of calculating correlation in addition to existing methods. The method uses binomial distribution, which has not been used until yet, to assess the significance of association between two variables. We are evaluating the performance of our method on NGS/microarray data, which is noisy and pierce by the outliers, to see if our method can differentiate between spurious and actual correlation. While working with the method, it has not escaped our notice that the method could also be generalized to measure the association of more than two variables which has been proven difficult with the existing methods.

Keywords: binomial distribution, correlation, microarray, outliers, transcriptome

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Authors: Mohammad Tahir Yousafzai, Amna Rehana Siddiqui, Naveed Zafar Janjua

Abstract:

We assessed the frequency and predictors of sharp injuries (SIs) among health care workers (HCWs) at first level care facilities (FLCF) in rural Pakistan. HCWs working at public clinic (PC), privately owned licensed practitioners’ clinic (LPC) and non-licensed practitioners’ clinic (NLC) were interviewed on universal precautions (UPs) and constructs of health belief model (HBM) to assess their association with SIs through negative-binomial regression. From 365 clinics, 485 HCWs were interviewed. Overall annual rate of Sis was 192/100 HCWs/year; 78/100 HCWs among licensed prescribers, 191/100 HCWs among non-licensed prescribers, 248/100 HCWs among qualified assistants, and 321/100 HCWs among non-qualified assistants. Increasing knowledge score about bloodborne pathogens (BBPs) transmission (rate-ratio (RR): 0.93; 95%CI: 0.89–0.96), fewer years of work experience, being a non-licensed prescriber (RR: 2.02; 95%CI: 1.36–2.98) licensed (RR: 2.86; 9%CI: 1.81–4.51) or non-licensed assistant (RR: 2.78; 95%CI: 1.72–4.47) compared to a licensed prescriber, perceived barriers (RR: 1.06;95%CI: 1.03–1.08), and compliance with UPs scores (RR: 0.93; 95%CI: 0.87–0.97) were significant predictors of SIs. Improved knowledge about BBPs, compliance with UPs and reduced barriers to follow UPs could reduce SIs to HCWs.

Keywords: health belief model, sharp injuries, needle stick injuries, healthcare workers

Procedia PDF Downloads 310

Authors: Rodrigo Costa, Thomas Mazzuchi, Shahram Sarkani

Abstract:

This study analyzes the evolution of Bitcoin Improvement Proposals (BIPs), the self-governing mechanism that enables updates to the Bitcoin protocol. By modeling BIP submission frequencies with a Negative Binomial distribution and detecting change points with the Pelt Rupture model, we identify three distinct intervals of proposal activity, suggesting shifts in development priorities over time. Long-term growth patterns, captured by Gompertz and Weibull models, indicate an S-shaped trend in cumulative BIP counts, pointing toward a maturation phase in Bitcoin’s protocol. Our findings suggest that Bitcoin may be entering a stable stage, with fewer fundamental changes and more incremental enhancements. This trend highlights the need for further research into BIP content and more studies into its dynamics to better understand decentralized protocol governance and maturation.

Keywords: bitcoin improvement proposals, innovation management, change point detection, systems modeling, simulation

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Authors: Saowanit Sukparungsee

Abstract:

Generally, the traditional Shewhart p chart has been developed by for charting the binomial data. This chart has been developed using the normal approximation with condition as low defect level and the small to moderate sample size. In real applications, however, are away from these assumptions due to skewness in the exact distribution. In this paper, a modified Exponentially Weighted Moving Average (EWMA) control chat for detecting a change in binomial data by improving square root transformations, namely ISRT p EWMA control chart. The numerical results show that ISRT p EWMA chart is superior to ISRT p chart for small to moderate shifts, otherwise, the latter is better for large shifts.

Keywords: number of defects, exponentially weighted moving average, average run length, square root transformations

Procedia PDF Downloads 440