Search results for: truncated negative binomial law

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 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: 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: 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: Liyana Zahid, Mohd Fareq Abd Malek, Ee Meng Cheng, Wei Wen Liu, Yeng Seng Lee, Muhammad Nadeem Iqbal, Fwen Hoon Wee

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One of the parameters that affect the performance of microwave absorbers is the shape of the absorbers. This paper shows the performance (reflection loss) of truncated pyramidal and truncated wedge microwave absorbers in the range frequency between 8.2 to 12.4 GHz (X-Band) in simulation. The material used is sugarcane bagasse (SCB) which is one of the new materials that used to fabricate the microwave absorber. The complex permittivity was measured using Agilent dielectric probe technique. The designs were simulated using CST Microwave Studio Software. The reflection losses between these two shapes were compared.

Keywords: microwave absorber, reflection loss, sugarcane bagasse (SCB), X-Band

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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: Kornelius Ronald Demu, Dewi Retno Sari Saputro, Purnami Widyaningsih

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Human Development Index (HDI) is a standard measurement for a country's human development. Several factors may have influenced it, such as life expectancy, gross domestic product (GDP) based on the province's annual expenditure, the number of poor people, and the percentage of an illiterate people. The scatter plot between HDI and the influenced factors show that the plot does not follow a specific pattern or form. Therefore, the HDI's data in Indonesia can be applied with a nonparametric regression model. The estimation of the regression curve in the nonparametric regression model is flexible because it follows the shape of the data pattern. One of the nonparametric regression's method is a truncated spline. Truncated spline regression is one of the nonparametric approach, which is a modification of the segmented polynomial functions. The estimator of a truncated spline regression model was affected by the selection of the optimal knots point. Knot points is a focus point of spline truncated functions. The optimal knots point was determined by the minimum value of generalized cross validation (GCV). In this article were applied the data of Human Development Index with a truncated spline nonparametric regression model. The results of this research were obtained the best-truncated spline regression model to the HDI's data in Indonesia with the combination of optimal knots point 5-5-5-4. Life expectancy and the percentage of an illiterate people were the significant factors depend to the HDI in Indonesia. The coefficient of determination is 94.54%. This means the regression model is good enough to applied on the data of HDI in Indonesia.

Keywords: generalized cross validation (GCV), Human Development Index (HDI), knots point, nonparametric regression, truncated spline

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Authors: Shunpu Zhang

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We propose a new multiple test called the minPOP test for testing multiple hypotheses simultaneously. Under the assumption that the test statistics are independent, we show that the minPOP test has higher global power than the existing multiple testing methods. We further propose a stepwise multiple-testing procedure based on the minPOP test and two of its modified versions (the Double Truncated and Left Truncated minPOP tests). We show that these multiple tests have strong control of the family-wise error rate (FWER). A method for finding the p-values of the proposed tests after adjusting for multiplicity is also developed. Simulation results show that the Double Truncated and Left Truncated minPOP tests, in general, have a higher number of rejections than the existing multiple testing procedures.

Keywords: multiple test, single-step procedure, stepwise procedure, p-value for multiple testing

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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: 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: 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: B. Mahfoud, A. Bendjaghlouli

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Natural convection is simulated in a truncated cone filled with nanofluid. Inclined and top walls have constant temperature where the heat source is located on the bottom wall of the conical container which is thermally insulated. A finite volume approach is used to solve the governing equations using the SIMPLE algorithm for different parameters such as Rayleigh number, inclination angle of inclined walls of the enclosure and heat source length. The results showed an enhancement in cooling system by using a nanofluid, when conduction regime is assisted. The inclination angle of inclined sidewall and heat source length affect the heat transfer rate and the maximum temperature.

Keywords: heat source, truncated cone, nanofluid, natural convection

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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: Srinivasa Rao Gadde

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In this article, we considered a group acceptance sampling plans for exponentiated half logistic distribution when the life-test is truncated at a pre-specified time. It is assumed that the index parameter of the exponentiated half logistic distribution is known. The design parameters such as the number of groups and the acceptance number are obtained by satisfying the producer’s and consumer’s risks at the specified quality levels in terms of medians and 10th percentiles under the assumption that the termination time and the number of items in each group are pre-fixed. Finally, an example is given to illustration the methodology.

Keywords: group acceptance sampling plan, operating characteristic, consumer and producer’s risks, truncated life-test

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Authors: Saif Akram, E. Rathakrishnan

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The mixing promoting efficiency of two identical sharp and truncated vertex triangular tabs offering geometrical blockage of 2.5% each, placed at the exit of a Mach 1.5 elliptic nozzle was studied experimentally. The effectiveness of both the tabs in enhancing the mixing of jets with the ambient air are determined by measuring the Pitot pressure along the jet axis and the jet spread in both the minor and major axes of the elliptic nozzle, covering marginally overexpanded to moderately underexpanded levels at the nozzle exit. The results reveal that both the tabs enhance mixing characteristics of the uncontrolled elliptic jet when placed at minor axis. A core length reduction of 67% is achieved at NPR 3 which is the overexpanded state. Similarly, the core length is reduced by about 67%, 50% and 57% at NPRs of 4, 5 and 6 (underexpanded states) respectively. However, unlike the considerable increment in mixing promoting efficiency by the use of truncated vertex tabs for axisymmetric jets, the effect is not much pronounced for the case of supersonic elliptic jets. The CPD plots for both the cases almost overlap, especially when tabs are placed at minor axis, at all the pressure conditions. While, when the tabs are used at major axis, in the case of overexpanded condition, the sharp vertex triangular tabs act as a better mixing enhancer for the supersonic elliptic jets. For the jet controlled with truncated vertex triangular tabs, the core length reductions are of the same order as those for the sharp vertex triangular tabs. The jet mixing is hardly influenced by the tip effect in case of supersonic elliptic jet.

Keywords: elliptic jet, tabs, truncated, triangular

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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: Qijiao He, Lin Ye

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To evaluate the effect of the ribs on internal structure in film hole and the film cooling performance on outer surface, the numerical study investigates on the effects of rib configuration on the film cooling performance with ribbed cross-flow coolant channel. The base smooth case and three ribbed cases, including the continuous rib case and two cross-truncated rib cases with different arrangement, are studied. The distributions of adiabatic film cooling effectiveness and heat transfer coefficient are obtained under the blowing ratios with the value of 0.5 and 1.0, respectively. A commercial steady RANS (Reynolds-averaged Navier-Stokes) code with realizable k-ε turbulence model and enhanced wall treatment were performed for numerical simulations. The numerical model is validated against available experimental data. The two cross-truncated rib cases produce approximately identical cooling effectiveness compared with the smooth case under lower blowing ratio. The continuous rib case significantly outperforms the other cases. With the increase of blowing ratio, the cases with ribs are inferior to the smooth case, especially in the upstream region. The cross-truncated rib I case produces the highest cooling effectiveness among the studied the ribbed channel case. It is found that film cooling effectiveness deteriorates with the increase of spiral intensity of the cross-flow inside the film hole. Lower spiral intensity leads to a better film coverage and thus results in better cooling effectiveness. The distinct relative merits among the cases at different blowing ratios are explored based on the aforementioned dominant mechanism. With regard to the heat transfer coefficient, the smooth case has higher heat transfer intensity than the ribbed cases under the studied blowing ratios. The laterally-averaged heat transfer coefficient of the cross-truncated rib I case is higher than the cross-truncated rib II case.

Keywords: cross-flow, cross-truncated rib, film cooling, numerical simulation

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Authors: O. Anan, D. Böhning, A. Maruotti

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The purpose of the study is to estimate the elusive target population size under a truncated count model that accounts for heterogeneity. The purposed estimator is based on the generalized Poisson distribution (GPD), which extends the Poisson distribution by adding a dispersion parameter. Thus, it becomes an useful model for capture-recapture data where concurrent events are not homogeneous. In addition, it can account for over-dispersion and under-dispersion. The ratios of neighboring frequency counts are used as a tool for investigating the validity of whether generalized Poisson or Poisson distribution. Since capture-recapture approaches do not provide the zero counts, the estimated parameters can be achieved by modifying the EM-algorithm technique for the zero-truncated generalized Poisson distribution. The properties and the comparative performance of proposed estimator were investigated through simulation studies. Furthermore, some empirical examples are represented insights on the behavior of the estimators.

Keywords: capture, recapture methods, ratio plot, heterogeneous population, zero-truncated count

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Authors: A. D. Abdellatif, A. N. Ahmed, M. E. Abdelaziz

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The main purpose of this paper is to design a double acceptance sampling plan under the time truncated life test when the product lifetime follows an exponentiated transmuted Weibull distribution. Here, the motive is to meet both the consumer’s risk and producer’s risk simultaneously at the specified quality levels, while the termination time is specified. A comparison between the results of the double and single acceptance sampling plans is conducted. We demonstrate the applicability of our results to real data sets.

Keywords: double sampling plan, single sampling plan, producer’s risk, consumer’s risk, exponentiated transmuted weibull distribution, time truncated experiment, single, double, Marshal-Olkin

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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: 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: 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: M. Z. Raqab, Debasis Kundu, M. A. Meraou

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In this paper, we have analyzed maximum precipitation data during a particular period of time obtained from different stations in the Global Historical Climatological Network of the USA. One important point to mention is that some stations are shut down on certain days for some reason or the other. Hence, the maximum values are recorded by excluding those readings. It is assumed that the number of stations that operate follows zero-truncated Poisson random variables, and the daily precipitation follows a lognormal random variable. We call this model a compound truncated Poisson lognormal model. The proposed model has three unknown parameters, and it can take a variety of shapes. The maximum likelihood estimators can be obtained quite conveniently using Expectation-Maximization (EM) algorithm. Approximate maximum likelihood estimators are also derived. The associated confidence intervals also can be obtained from the observed Fisher information matrix. Simulation results have been performed to check the performance of the EM algorithm, and it is observed that the EM algorithm works quite well in this case. When we analyze the precipitation data set using the proposed model, it is observed that the proposed model provides a better fit than some of the existing models.

Keywords: compound Poisson lognormal distribution, EM algorithm, maximum likelihood estimation, approximate maximum likelihood estimation, Fisher information, skew distribution

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Authors: Jean-Philippe Amat, Timothée Vergne, Aymeric Hans, Bénédicte Ferry, Pascal Hendrikx, Jackie Tapprest, Barbara Dufour, Agnès Leblond

Abstract:

The surveillance of infectious diseases is necessary to describe their occurrence and help the planning, implementation and evaluation of risk mitigation activities. However, the exact number of detected cases may remain unknown whether surveillance is based on serological tests because identifying seroconversion may be difficult. Moreover, incomplete detection of cases or outbreaks is a recurrent issue in the field of disease surveillance. This study addresses these two issues. Using a viral animal disease as an example (equine viral arteritis), the goals were to establish suitable rules for identifying seroconversion in order to estimate the number of cases and outbreaks detected by a surveillance system in France between 2006 and 2013, and to assess the sensitivity of this system by estimating the total number of outbreaks that occurred during this period (including unreported outbreaks) using a capture-recapture model. Data from horses which exhibited at least one positive result in serology using viral neutralization test between 2006 and 2013 were used for analysis (n=1,645). Data consisted of the annual antibody titers and the location of the subjects (towns). A consensus among multidisciplinary experts (specialists in the disease and its laboratory diagnosis, epidemiologists) was reached to consider seroconversion as a change in antibody titer from negative to at least 32 or as a three-fold or greater increase. The number of seroconversions was counted for each town and modeled using a unilist zero-truncated binomial (ZTB) capture-recapture model with R software. The binomial denominator was the number of horses tested in each infected town. Using the defined rules, 239 cases located in 177 towns (outbreaks) were identified from 2006 to 2013. Subsequently, the sensitivity of the surveillance system was estimated as the ratio of the number of detected outbreaks to the total number of outbreaks that occurred (including unreported outbreaks) estimated using the ZTB model. The total number of outbreaks was estimated at 215 (95% credible interval CrI95%: 195-249) and the surveillance sensitivity at 82% (CrI95%: 71-91). The rules proposed for identifying seroconversion may serve future research. Such rules, adjusted to the local environment, could conceivably be applied in other countries with surveillance programs dedicated to this disease. More generally, defining ad hoc algorithms for interpreting the antibody titer could be useful regarding other human and animal diseases and zoonosis when there is a lack of accurate information in the literature about the serological response in naturally infected subjects. This study shows how capture-recapture methods may help to estimate the sensitivity of an imperfect surveillance system and to valorize surveillance data. The sensitivity of the surveillance system of equine viral arteritis is relatively high and supports its relevance to prevent the disease spreading.

Keywords: Bayesian inference, capture-recapture, epidemiology, equine viral arteritis, infectious disease, seroconversion, surveillance

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

Abstract:

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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