Search results for: maximum likelihood estimates

Authors: Jiahao Tian, Michael D. Porter

Abstract:

Law enforcement agencies are tasked with crime prevention and crime reduction under limited resources. Having an accurate temporal estimate of the crime rate would be valuable to achieve such a goal. However, estimation is usually complicated by the interval-censored nature of crime data. We cast the problem of intensity estimation as a Poisson regression using an EM algorithm to estimate the parameters. Two special penalties are added that provide smoothness over the time of day and day of the week. This approach presented here provides accurate intensity estimates and can also uncover day-of-week clusters that share the same intensity patterns. Anticipating where and when crimes might occur is a key element to successful policing strategies. However, this task is complicated by the presence of interval-censored data. The censored data refers to the type of data that the event time is only known to lie within an interval instead of being observed exactly. This type of data is prevailing in the field of criminology because of the absence of victims for certain types of crime. Despite its importance, the research in temporal analysis of crime has lagged behind the spatial component. Inspired by the success of solving crime-related problems with a statistical approach, we propose a statistical model for the temporal intensity estimation of crime with censored data. The model is built on Poisson regression and has special penalty terms added to the likelihood. An EM algorithm was derived to obtain maximum likelihood estimates, and the resulting model shows superior performance to the competing model. Our research is in line with the smart policing initiative (SPI) proposed by the Bureau Justice of Assistance (BJA) as an effort to support law enforcement agencies in building evidence-based, data-driven law enforcement tactics. The goal is to identify strategic approaches that are effective in crime prevention and reduction. In our case, we allow agencies to deploy their resources for a relatively short period of time to achieve the maximum level of crime reduction. By analyzing a particular area within cities where data are available, our proposed approach could not only provide an accurate estimate of intensities for the time unit considered but a time-variation crime incidence pattern. Both will be helpful in the allocation of limited resources by either improving the existing patrol plan with the understanding of the discovery of the day of week cluster or supporting extra resources available.

Keywords: cluster detection, EM algorithm, interval censoring, intensity estimation

Procedia PDF Downloads 42

Authors: Keunhong Chae, Seokho Yoon

Abstract:

In this paper, frequency offset (FO) estimation schemes robust to the non-Gaussian noise environments are proposed for orthogonal frequency division multiplexing (OFDM) systems. First, a maximum-likelihood (ML) estimation scheme in non-Gaussian noise environments is proposed, and then, the complexity of the ML estimation scheme is reduced by employing a reduced set of candidate values. In numerical results, it is demonstrated that the proposed schemes provide a significant performance improvement over the conventional estimation scheme in non-Gaussian noise environments while maintaining the performance similar to the estimation performance in Gaussian noise environments.

Keywords: frequency offset estimation, maximum-likelihood, non-Gaussian noise environment, OFDM, training symbol

Procedia PDF Downloads 323

Authors: Chen Li-Ching

Abstract:

The multinomial logistic regression model is used popularly for inferring the relationship of risk factors and disease with multiple categories. This study based on the discrepancy between the nonparametric maximum likelihood estimator and semiparametric maximum likelihood estimator of the cumulative distribution function to propose a Kolmogorov-Smirnov type test statistic to assess adequacy of the multinomial logistic regression model for case-control data. A bootstrap procedure is presented to calculate the critical value of the proposed test statistic. Empirical type I error rates and powers of the test are performed by simulation studies. Some examples will be illustrated the implementation of the test.

Keywords: case-control studies, goodness-of-fit test, Kolmogorov-Smirnov test, multinomial logistic regression

Procedia PDF Downloads 427

Authors: Rana Rimawi, Ayman Baklizi

Abstract:

Skewed distributions are important models that are frequently used in applications. Generalized distributions form a class of skewed distributions and gain widespread use in applications because of their flexibility in data analysis. More specifically, the Generalized Logistic Distribution with its different types has received considerable attention recently. In this study, based on progressively type-II censored data, we will consider point estimation in type II Generalized Logistic Distribution (Type II GLD). We will develop several estimators for its unknown parameters, including maximum likelihood estimators (MLE), Bayes estimators and linear estimators (BLUE). The estimators will be compared using simulation based on the criteria of bias and Mean square error (MSE). An illustrative example of a real data set will be given.

Keywords: point estimation, type II generalized logistic distribution, progressive censoring, maximum likelihood estimation

Procedia PDF Downloads 167

Authors: Dongxu Chen, Yipeng Li

Abstract:

This paper presents an information geometry NonlocalMeans(NLM) algorithm for Poisson denoising. NLM estimates a noise-free pixel as a weighted average of image pixels, where each pixel is weighted according to the similarity between image patches in Euclidean space. In this work, every pixel is a Poisson distribution locally estimated by Maximum Likelihood (ML), all distributions consist of a statistical manifold. A NLM denoising algorithm is conducted on the statistical manifold where Fisher information matrix can be used for computing distribution geodesics referenced as the similarity between patches. This approach was demonstrated to be competitive with related state-of-the-art methods.

Keywords: image denoising, Poisson noise, information geometry, nonlocal-means

Procedia PDF Downloads 262

Authors: A. M. Abd-Elfattah, M. H. Abu-Moussa

Abstract:

In this paper, the estimation of stress-strength parameter R = P(Y < X) is considered when X; Y the strength and stress respectively are two independent random variables of Burr Type XII distribution. The samples taken for X and Y are progressively censoring of type II. The maximum likelihood estimator (MLE) of R is obtained when the common parameter is unknown. But when the common parameter is known the MLE, uniformly minimum variance unbiased estimator (UMVUE) and the Bayes estimator of R = P(Y < X) are obtained. The exact condence interval of R based on MLE is obtained. The performance of the proposed estimators is compared using the computer simulation.

Keywords: Burr Type XII distribution, progressive type-II censoring, stress-strength model, unbiased estimator, maximum-likelihood estimator, uniformly minimum variance unbiased estimator, confidence intervals, Bayes estimator

Procedia PDF Downloads 427

Authors: Lamyaa Gamal El-Deen Taha, Ashraf Sharawi

Abstract:

Planet image is a new data source from planet lab. This research is concerned with the assessment of Planet image for land cover mapping. Two pixel based classifiers and one subpixel based classifier were compared. Firstly, rectification of Planet image was performed. Secondly, a comparison between minimum distance, maximum likelihood and neural network classifications for classification of Planet image was performed. Thirdly, the overall accuracy of classification and kappa coefficient were calculated. Results indicate that neural network classification is best followed by maximum likelihood classifier then minimum distance classification for land cover mapping.

Keywords: planet image, land cover mapping, rectification, neural network classification, multilayer perceptron, soft classifiers, hard classifiers

Procedia PDF Downloads 151

Authors: Ahmed Shaik

Abstract:

Estimates are very critical in accounting and Financial Reporting cannot be complete without these estimates. There is a long list of accounting estimates that are required to be made to compute Net Income and to determine the value of assets and liabilities. To name a few, valuation of inventory, depreciation, valuation of goodwill, provision for bad debts and estimated warranties, etc. require the use of different valuation models and forecasts. Different business entities under the same industry may use different approaches to measure the value of financial items being reported in Income Statement and Balance Sheet. The disclosure notes do not provide enough details of the approach used by a business entity to arrive at the value of a financial item. Lack of details in the disclosure notes makes it difficult to compare the financial performance of one business entity with the other in the same industry. This paper is an attempt to identify the lack of enough information about accounting estimates in disclosure notes, the impact of the absence of details of accounting estimates on the comparability of financial data and financial analysis. An attempt is made to suggest the detailed disclosure while taking care of the cost and benefit of making such disclosure.

Keywords: accounting estimates, disclosure notes, financial reporting, transparency

Procedia PDF Downloads 176

Authors: Md Al Masum Bhuiyan, Maria C. Mariani, Osei K. Tweneboah

Abstract:

In the present work, we develop a technique for estimating the volatility of financial time series by using stochastic differential equation. Taking the daily closing prices from developed and emergent stock markets as the basis, we argue that the incorporation of stochastic volatility into the time-varying parameter estimation significantly improves the forecasting performance via Maximum Likelihood Estimation. While using the technique, we see the long-memory behavior of data sets and one-step-ahead-predicted log-volatility with ±2 standard errors despite the variation of the observed noise from a Normal mixture distribution, because the financial data studied is not fully Gaussian. Also, the Ornstein-Uhlenbeck process followed in this work simulates well the financial time series, which aligns our estimation algorithm with large data sets due to the fact that this algorithm has good convergence properties.

Keywords: financial time series, maximum likelihood estimation, Ornstein-Uhlenbeck type models, stochastic volatility model

Procedia PDF Downloads 212

Authors: Mesut BALIBEY, Serpil TÜRKYILMAZ

Abstract:

A popular topic in the econometrics and time series area is the cointegrating relationships among the components of a nonstationary time series. Engle and Granger’s least squares method and Johansen’s conditional maximum likelihood method are the most widely-used methods to determine the relationships among variables. Furthermore, a method proposed to test a unit root based on the periodogram ordinates has certain advantages over conventional tests. Periodograms can be calculated without any model specification and the exact distribution under the assumption of a unit root is obtained. For higher order processes the distribution remains the same asymptotically. In this study, in order to indicate advantages over conventional test of periodograms, we are going to examine a possible relationship between tourism and economic growth during the period 1999:01-2010:12 for Turkey by using periodogram method, Johansen’s conditional maximum likelihood method, Engle and Granger’s ordinary least square method.

Keywords: cointegration, economic growth, periodogram ordinate, tourism

Procedia PDF Downloads 242

Authors: Dewi Retno Sari Saputro, Purnami Widyaningsih, Hendrika Handayani

Abstract:

Extreme data on an observation can occur due to unusual circumstances in the observation. The data can provide important information that can’t be provided by other data so that its existence needs to be further investigated. The method for obtaining extreme data is one of them using maxima block method. The distribution of extreme data sets taken with the maxima block method is called the distribution of extreme values. Distribution of extreme values is Gumbel distribution with two parameters. The parameter estimation of Gumbel distribution with maximum likelihood method (ML) is difficult to determine its exact value so that it is necessary to solve the approach. The purpose of this study was to determine the parameter estimation of Gumbel distribution with quasi-Newton BFGS method. The quasi-Newton BFGS method is a numerical method used for nonlinear function optimization without constraint so that the method can be used for parameter estimation from Gumbel distribution whose distribution function is in the form of exponential doubel function. The quasi-New BFGS method is a development of the Newton method. The Newton method uses the second derivative to calculate the parameter value changes on each iteration. Newton's method is then modified with the addition of a step length to provide a guarantee of convergence when the second derivative requires complex calculations. In the quasi-Newton BFGS method, Newton's method is modified by updating both derivatives on each iteration. The parameter estimation of the Gumbel distribution by a numerical approach using the quasi-Newton BFGS method is done by calculating the parameter values that make the distribution function maximum. In this method, we need gradient vector and hessian matrix. This research is a theory research and application by studying several journals and textbooks. The results of this study obtained the quasi-Newton BFGS algorithm and estimation of Gumbel distribution parameters. The estimation method is then applied to daily rainfall data in Purworejo District to estimate the distribution parameters. This indicates that the high rainfall that occurred in Purworejo District decreased its intensity and the range of rainfall that occurred decreased.

Keywords: parameter estimation, Gumbel distribution, maximum likelihood, broyden fletcher goldfarb shanno (BFGS)quasi newton

Procedia PDF Downloads 297

Authors: Mohamed Raouf Benmakrelouf, Joseph Rynkiewicz

Abstract:

Targeted maximum likelihood estimation (TMLE) is well-established method for causal effect estimation with desirable statistical properties. TMLE is a doubly robust maximum likelihood based approach that includes a secondary targeting step that optimizes the target statistical parameter. A causal interpretation of the statistical parameter requires assumptions of the Rubin causal framework. The causal effect of binary variable, E, on outcomes, Y, is defined in terms of comparisons between two potential outcomes as E[YE=1 − YE=0]. Our aim in this paper is to present an adaptation of TMLE methodology to estimate the causal effect of a non-binary categorical variable, providing a large application. We propose coding on the initial data in order to operate a binarization of the interest variable. For each category, we get a transformation of the non-binary interest variable into a binary variable, taking value 1 to indicate the presence of category (or group of categories) for an individual, 0 otherwise. Such a dummy variable makes it possible to have a pair of potential outcomes and oppose a category (or a group of categories) to another category (or a group of categories). Let E be a non-binary interest variable. We propose a complete disjunctive coding of our variable E. We transform the initial variable to obtain a set of binary vectors (dummy variables), E = (Ee : e ∈ {1, ..., |E|}), where each vector (variable), Ee, takes the value of 0 when its category is not present, and the value of 1 when its category is present, which allows to compute a pairwise-TMLE comparing difference in the outcome between one category and all remaining categories. In order to illustrate the application of our strategy, first, we present the implementation of TMLE to estimate the causal effect of non-binary variable on outcome using simulated data. Secondly, we apply our TMLE adaptation to survey data from the French Political Barometer (CEVIPOF), to estimate the causal effect of education level (A five-level variable) on a potential vote in favor of the French extreme right candidate Jean-Marie Le Pen. Counterfactual reasoning requires us to consider some causal questions (additional causal assumptions). Leading to different coding of E, as a set of binary vectors, E = (Ee : e ∈ {2, ..., |E|}), where each vector (variable), Ee, takes the value of 0 when the first category (reference category) is present, and the value of 1 when its category is present, which allows to apply a pairwise-TMLE comparing difference in the outcome between the first level (fixed) and each remaining level. We confirmed that the increase in the level of education decreases the voting rate for the extreme right party.

Keywords: statistical inference, causal inference, super learning, targeted maximum likelihood estimation

Procedia PDF Downloads 69

Authors: Md. Rashidul Hasan, Atikur Rahman Baizid

Abstract:

The Bayesian estimation approach is a non-classical estimation technique in statistical inference and is very useful in real world situation. The aim of this paper is to study the Bayes estimators of the parameter of exponential distribution under different loss functions and then compared among them as well as with the classical estimator named maximum likelihood estimator (MLE). In our real life, we always try to minimize the loss and we also want to gather some prior information (distribution) about the problem to solve it accurately. Here the gamma prior is used as the prior distribution of exponential distribution for finding the Bayes estimator. In our study, we also used different symmetric and asymmetric loss functions such as squared error loss function, quadratic loss function, modified linear exponential (MLINEX) loss function and non-linear exponential (NLINEX) loss function. Finally, mean square error (MSE) of the estimators are obtained and then presented graphically.

Keywords: Bayes estimator, maximum likelihood estimator (MLE), modified linear exponential (MLINEX) loss function, Squared Error (SE) loss function, non-linear exponential (NLINEX) loss function

Procedia PDF Downloads 355

Authors: Rajesh Singh, Kailash Kale

Abstract:

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)

Procedia PDF Downloads 362

Authors: A. Y. Mukhtar, J. B. Munyakazi, R. Ouifki

Abstract:

Over the past few decades, the unprecedented increase in mobility has raised considerable concern about the relationship between mobility and vector-borne diseases and malaria in particular. Thus, one can claim that human mobility is one of the contributing factors to the resurgence of malaria. To assess human mobility on malaria burden among hosts, we formulate a movement-based model on a network of patches. We then extend human multi-group SEIAR deterministic epidemic models into a system of stochastic differential equations (SDEs). Our quantitative stochastic model which is expressed in terms of average rates of movement between compartments is fitted to time-series data (weekly malaria data of 2011 for each patch) using the maximum likelihood approach. Using the metapopulation (multi-group) model, we compute and analyze the basic reproduction number. The result shows that human movement is sufficient to preserve malaria disease firmness in the patches with the low transmission. With these results, we concluded that the sensitivity of malaria to the human mobility is turning to be greatly important over the implications of future malaria control in South Sudan.

Keywords: basic reproduction number, malaria, maximum likelihood, movement, stochastic model

Procedia PDF Downloads 111

Authors: Fatemah A. Alqallaf, Debasis Kundu

Abstract:

The aim of this paper is to introduce a bivariate inverse generalized exponential distribution which has a singular component. The proposed bivariate distribution can be used when the marginals have heavy-tailed distributions, and they have non-monotone hazard functions. Due to the presence of the singular component, it can be used quite effectively when there are ties in the data. Since it has four parameters, it is a very flexible bivariate distribution, and it can be used quite effectively for analyzing various bivariate data sets. Several dependency properties and dependency measures have been obtained. The maximum likelihood estimators cannot be obtained in closed form, and it involves solving a four-dimensional optimization problem. To avoid that, we have proposed to use an EM algorithm, and it involves solving only one non-linear equation at each `E'-step. Hence, the implementation of the proposed EM algorithm is very straight forward in practice. Extensive simulation experiments and the analysis of one data set have been performed. We have observed that the proposed bivariate inverse generalized exponential distribution can be used for modeling dependent competing risks data. One data set has been analyzed to show the effectiveness of the proposed model.

Keywords: Block and Basu bivariate distributions, competing risks, EM algorithm, Marshall-Olkin bivariate exponential distribution, maximum likelihood estimators

Procedia PDF Downloads 110

Authors: Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa

Abstract:

A generalized log-logistic distribution with variable shapes of the hazard rate was introduced and studied, extending the log-logistic distribution by adding an extra parameter to the classical distribution, leading to greater flexibility in analysing and modeling various data types. The proposed distribution has a large number of well-known lifetime special sub-models such as; Weibull, log-logistic, exponential, and Burr XII distributions. Its basic mathematical and statistical properties were derived. The method of maximum likelihood was adopted for estimating the unknown parameters of the proposed distribution, and a Monte Carlo simulation study is carried out to assess the behavior of the estimators. The importance of this distribution is that its tendency to model both monotone (increasing and decreasing) and non-monotone (unimodal and bathtub shape) or reversed “bathtub” shape hazard rate functions which are quite common in survival and reliability data analysis. Furthermore, the flexibility and usefulness of the proposed distribution are illustrated in a real-life data set and compared to its sub-models; Weibull, log-logistic, and BurrXII distributions and other parametric survival distributions with 3-parmaeters; like the exponentiated Weibull distribution, the 3-parameter lognormal distribution, the 3- parameter gamma distribution, the 3-parameter Weibull distribution, and the 3-parameter log-logistic (also known as shifted log-logistic) distribution. The proposed distribution provided a better fit than all of the competitive distributions based on the goodness-of-fit tests, the log-likelihood, and information criterion values. Finally, Bayesian analysis and performance of Gibbs sampling for the data set are also carried out.

Keywords: hazard rate function, log-logistic distribution, maximum likelihood estimation, generalized log-logistic distribution, survival data, Monte Carlo simulation

Procedia PDF Downloads 167

Authors: Safa A. Mohammed Ali, Ammar S. Ahamed, Mohammed Khair Abdalla

Abstract:

The objectives of this study were to estimate the means and genetic parameters of birth and weaning weight of calves of pure Holstein-Friesian cows raised in Sudan. The traits studied were:*Weight at birth *Weight at weaning. The study also included some of the important factors that affected these traits. The data were analyzed using Harvey’s Least Squares and Maximum Likelihood programme. The results obtained showed that the overall mean weight at birth of the calves under study was 34.36±0.94kg. Male calves were found to be heavier than females; the difference between the sexes was highly significant (P<0.001). The mean weight at birth of male calves was 34.27±1.17 kg while that of females was 32.51±1.14kg. The effect of sex of calves, sire and parity of dam were highly significant (P<0.001). The overall mean of weight at weaning was 67.10 ± 5.05 kg, weight at weaning was significantly (p<0.001) effected by sex of calves, sire, year and season of birth have highly significant (P<0.001) effect on either trait. Also estimates heritabilities of birth weight was (0.033±0.015) lower than heritabilities of weaning weight (0.224±0.039), and genetic correlation was 0.563, the phenotypic correlation 0.281, and the environmental correlation 0.268.

Keywords: birth, weaning, weight, friesian

Procedia PDF Downloads 629

Authors: Mahmut Yildirim

Abstract:

This paper proposed the bidirectional long short-term memory (Bi-LSTM) network-aided deep learning (DL)-based signal detection for Orthogonal frequency division multiplexing with all index modulation (OFDM-AIM), namely Bi-DeepAIM. OFDM-AIM is developed to increase the spectral efficiency of OFDM with index modulation (OFDM-IM), a promising multi-carrier technique for communication systems beyond 5G. In this paper, due to its strong classification ability, Bi-LSTM is considered an alternative to the maximum likelihood (ML) algorithm, which is used for signal detection in the classical OFDM-AIM scheme. The performance of the Bi-DeepAIM is compared with LSTM network-aided DL-based OFDM-AIM (DeepAIM) and classic OFDM-AIM that uses (ML)-based signal detection via BER performance and computational time criteria. Simulation results show that Bi-DeepAIM obtains better bit error rate (BER) performance than DeepAIM and lower computation time in signal detection than ML-AIM.

Keywords: bidirectional long short-term memory, deep learning, maximum likelihood, OFDM with all index modulation, signal detection

Procedia PDF Downloads 28

Authors: Ariful Islam, Showkat Ahmad Lone

Abstract:

The Mukherjee-Islam Model is commonly used as a simple life time distribution to assess system reliability. The model exhibits a better fit for failure information and provides more appropriate information about hazard rate and other reliability measures as shown by various authors. It is possible to introduce a location parameter at a time (i.e., a time before which failure cannot occur) which makes it a more useful failure distribution than the existing ones. Even after shifting the location of the distribution, it represents a decreasing, constant and increasing failure rate. It has been shown to represent the appropriate lower tail of the distribution of random variables having fixed lower bound. This study presents the reliability computations and probability weighted moment estimation of three parameter model. A comparative analysis is carried out between three parameters finite range model and some existing bathtub shaped curve fitting models. Since probability weighted moment method is used, the results obtained can also be applied on small sample cases. Maximum likelihood estimation method is also applied in this study.

Keywords: comparative analysis, maximum likelihood estimation, Mukherjee-Islam failure model, probability weighted moment estimation, reliability

Procedia PDF Downloads 244

Authors: Yogita Mishra, Arijit Roy, Dhruval Bhavsar

Abstract:

The study estimates the nitrogen concentration in selected vegetation community’s i.e. chir pine (pinusroxburghii) by using hyperspectral satellite data and also identified the appropriate spectral bands and nitrogen indices. The Short Wave InfraRed reflectance spectrum at 1790 nm and 1680 nm shows the maximum possible absorption by nitrogen in selected species. Among the nitrogen indices, log normalized nitrogen index performed positively and negatively too. The strong positive correlation is taken out from 1510 nm and 760 nm for the pinusroxburghii for leaf nitrogen concentration and leaf nitrogen mass while using NDNI. The regression value of R² developed by using linear equation achieved maximum at 0.7525 for the analysis of satellite image data and R² is maximum at 0.547 for ground truth data for pinusroxburghii respectively.

Keywords: hyperspectral, NDNI, nitrogen concentration, regression value

Procedia PDF Downloads 265

Authors: Ceren Vardar Acar, Mine Caglar

Abstract:

In finance, the price of a volatile asset can be modeled using fractional Brownian motion (fBm) with Hurst parameter H>1/2. The Black-Scholes model for the values of returns of an asset using fBm is given as, 〖Y_t=Y_0 e^((r+μ)t+σB)〗_t^H, 0≤t≤T where Y_0 is the initial value, r is constant interest rate, μ is constant drift and σ is constant diffusion coefficient of fBm, which is denoted by B_t^H where t≥0. Black-Scholes model can be constructed with some Markov processes such as Brownian motion. The advantage of modeling with fBm to Markov processes is its capability of exposing the dependence between returns. The real life data for a volatile asset display long-range dependence property. For this reason, using fBm is a more realistic model compared to Markov processes. Investors would be interested in any kind of information on the risk in order to manage it or hedge it. The maximum possible loss is one way to measure highest possible risk. Therefore, it is an important variable for investors. In our study, we give some theoretical bounds on the distribution of maximum possible loss of fBm. We provide both asymptotical and strong estimates for the tail probability of maximum loss of standard fBm and fBm with drift and diffusion coefficients. In the investment point of view, these results explain, how large values of possible loss behave and its bounds.

Keywords: maximum drawdown, maximum loss, fractional brownian motion, large deviation, Gaussian process

Procedia PDF Downloads 460

Authors: Altaf H. Khan, Frank Stenger, Mohammed A. Hussein, Reaz A. Chaudhuri, Sameera Asif

Abstract:

This paper discusses a novel approach to approximate quadrature integrals that arise in the estimation of likelihood parameters for the generalized linear mixed models (GLMM) as well as Bayesian methodology also requires computation of multidimensional integrals with respect to the posterior distributions in which computation are not only tedious and cumbersome rather in some situations impossible to find solutions because of singularities, irregular domains, etc. An attempt has been made in this work to apply Sinc function based quadrature rules to approximate intractable integrals, as there are several advantages of using Sinc based methods, for example: order of convergence is exponential, works very well in the neighborhood of singularities, in general quite stable and provide high accurate and double precisions estimates. The Sinc function based approach seems to be utilized first time in statistical domain to our knowledge, and it's viability and future scopes have been discussed to apply in the estimation of parameters for GLMM models as well as some other statistical areas.

Keywords: generalized linear mixed model, likelihood parameters, qudarature, Sinc function

Procedia PDF Downloads 371

Authors: Jayanta Pokharel, Gokarna Aryal, Netra Kanaal, Chris Tsokos

Abstract:

Investment in stocks and shares aims to seek potential gains while weighing the risk of future needs, such as retirement, children's education etc. Analysis of the behavior of the stock market returns and making prediction is important for investors to mitigate risk on investment. Historically, the normal variance models have been used to describe the behavior of stock market returns. However, the returns of the financial assets are actually skewed with higher kurtosis, heavier tails, and a higher center than the normal distribution. The Laplace distribution and its family are natural candidates for modeling stock returns. The Variance-Gamma (VG) distribution is the most sought-after distributions for modeling asset returns and has been extensively discussed in financial literatures. In this paper, it explore the other Laplace family, such as Asymmetric Laplace, Skewed Laplace, Kumaraswamy Laplace (KS) together with Variance-Gamma to model the weekly returns of the S&P 500 Index and it's eleven business sector indices. The method of maximum likelihood is employed to estimate the parameters of the distributions and our empirical inquiry shows that the Kumaraswamy Laplace distribution performs much better for stock returns modeling among the choice of distributions used in this study and in practice, KS can be used as a strong alternative to VG distribution.

Keywords: stock returns, variance-gamma, kumaraswamy laplace, maximum likelihood

Procedia PDF Downloads 41

Authors: Khandoker Akib Mohammad

Abstract:

While analyzing time-to-event data, it is possible that a certain fraction of subjects will never experience the event of interest, and they are said to be cured. When this feature of survival models is taken into account, the models are commonly referred to as cure models. In the presence of covariates, the conditional survival function of the population can be modelled by using the cure model, which depends on the probability of being uncured (incidence) and the conditional survival function of the uncured subjects (latency), and a combination of logistic regression and Cox proportional hazards (PH) regression is used to model the incidence and latency respectively. In this paper, we have shown the asymptotic normality of the profile likelihood estimator via asymptotic expansion of the profile likelihood and obtain the explicit form of the variance estimator with an implicit function in the profile likelihood. We have also shown the efficient score function based on projection theory and the profile likelihood score function are equal. Our contribution in this paper is that we have expressed the efficient information matrix as the variance of the profile likelihood score function. A simulation study suggests that the estimated standard errors from bootstrap samples (SMCURE package) and the profile likelihood score function (our approach) are providing similar and comparable results. The numerical result of our proposed method is also shown by using the melanoma data from SMCURE R-package, and we compare the results with the output obtained from the SMCURE package.

Keywords: Cox PH model, cure model, efficient score function, EM algorithm, implicit function, profile likelihood

Procedia PDF Downloads 111

Authors: Ashutosh Saxena, Kumar Pallav, Ramji Dwivedi

Abstract:

The present study estimates the seismicity parameter 'b' and maximum possible magnitude of an earthquake (Mmax) for Gujarat region with three well-established methods viz. Kijiko parametric model (KP), Kijiko-Sellevol-Bayern (KSB) and Tapered Gutenberg-Richter (TGR), as a combined seismic source regime. The earthquake catalogue is prepared for a period of 1330 to 2013 in the region Latitudes 20o N to 250 N and Longitudinally extending from 680 to 750 E for earthquake moment magnitude (Mw) ≥4.0. The ’a’ and 'b' value estimated for the region as 4.68 and 0.58. Further, Mmax estimated as 8.54 (± 0.29), 8.69 (± 0.48), and 8.12 with KP, KSB, and TGR, respectively.

Keywords: Mmax, seismicity parameter, Gujarat, Tapered Gutenberg-Richter

Procedia PDF Downloads 510

Authors: Kajingulu Malandala, Ranganai Edmore

Abstract:

The asymmetric Laplace distribution (ADL) is commonly used as the likelihood function of the Bayesian quantile regression, and it offers different families of likelihood method for quantile regression. Notwithstanding their popularity and practicality, ADL is not smooth and thus making it difficult to maximize its likelihood. Furthermore, Bayesian inference is time consuming and the selection of likelihood may mislead the inference, as the Bayes theorem does not automatically establish the posterior inference. Furthermore, ADL does not account for greater skewness and Kurtosis. This paper develops a new aspect of quantile regression approach for count data based on inverse of the cumulative density function of the Poisson, binomial and Delaporte distributions using the integrated nested Laplace Approximations. Our result validates the benefit of using the integrated nested Laplace Approximations and support the approach for count data.

Keywords: quantile regression, Delaporte distribution, count data, integrated nested Laplace approximation

Procedia PDF Downloads 134

Authors: Fariba Azizi, Firoozeh Haghighi, Viliam Makis

Abstract:

In this paper, we propose a method to model the relationship between failure time and degradation for a simple step stress test where underlying degradation path is linear and different causes of failure are possible. It is assumed that the intensity function depends only on the degradation value. No assumptions are made about the distribution of the failure times. A simple step-stress test is used to shorten failure time of products and a tampered failure rate (TFR) model is proposed to describe the effect of the changing stress on the intensities. We assume that some of the products that fail during the test have a cause of failure that is only known to belong to a certain subset of all possible failures. This case is known as masking. In the presence of masking, the maximum likelihood estimates (MLEs) of the model parameters are obtained through an expectation-maximization (EM) algorithm by treating the causes of failure as missing values. The effect of incomplete information on the estimation of parameters is studied through a Monte-Carlo simulation. Finally, a real example is analyzed to illustrate the application of the proposed methods.

Keywords: cause of failure, linear degradation path, reliability function, expectation-maximization algorithm, intensity, masked data

Procedia PDF Downloads 307

Authors: Neda Orak, Mostafa Zarei

Abstract:

Environmental assessment is an important session in environment management. Since various methods and techniques have been produces and implemented. Remote sensing (RS) is widely used in many scientific and research fields such as geology, cartography, geography, agriculture, forestry, land use planning, environment, etc. It can show earth surface objects cyclical changes. Also, it can show earth phenomena limits on basis of electromagnetic reflectance changes and deviations records. The research has been done on mangrove forests assessment by RS techniques. Mangrove forests quantitative analysis in Basatin and Bidkhoon estuaries was the aim of this research. It has been done by Landsat satellite images from 1975- 2013 and match to ground control points. This part of mangroves are the last distribution in northern hemisphere. It can provide a good background to improve better management on this important ecosystem. Landsat has provided valuable images to earth changes detection to researchers. This research has used MSS, TM, +ETM, OLI sensors from 1975, 1990, 2000, 2003-2013. Changes had been studied after essential corrections such as fix errors, bands combination, georeferencing on 2012 images as basic image, by maximum likelihood and IPVI Index. It was done by supervised classification. 2004 google earth image and ground points by GPS (2010-2012) was used to compare satellite images obtained changes. Results showed mangrove area in bidkhoon was 1119072 m2 by GPS and 1231200 m2 by maximum likelihood supervised classification and 1317600 m2 by IPVI in 2012. Basatin areas is respectively: 466644 m2, 88200 m2, 63000 m2. Final results show forests have been declined naturally. It is due to human activities in Basatin. The defect was offset by planting in many years. Although the trend has been declining in recent years again. So, it mentioned satellite images have high ability to estimation all environmental processes. This research showed high correlation between images and indexes such as IPVI and NDVI with ground control points.

Keywords: IPVI index, Landsat sensor, maximum likelihood supervised classification, Nayband National Park

Procedia PDF Downloads 267

Authors: N. R. N. Idris, S. Baharom

Abstract:

A meta-analysis may be performed using aggregate data (AD) or an individual patient data (IPD). In practice, studies may be available at both IPD and AD level. In this situation, both the IPD and AD should be utilised in order to maximize the available information. Statistical advantages of combining the studies from different level have not been fully explored. This study aims to quantify the statistical benefits of including available IPD when conducting a conventional summary-level meta-analysis. Simulated meta-analysis were used to assess the influence of the levels of data on overall meta-analysis estimates based on IPD-only, AD-only and the combination of IPD and AD (mixed data, MD), under different study scenario. The percentage relative bias (PRB), root mean-square-error (RMSE) and coverage probability were used to assess the efficiency of the overall estimates. The results demonstrate that available IPD should always be included in a conventional meta-analysis using summary level data as they would significantly increased the accuracy of the estimates. On the other hand, if more than 80% of the available data are at IPD level, including the AD does not provide significant differences in terms of accuracy of the estimates. Additionally, combining the IPD and AD has moderating effects on the biasness of the estimates of the treatment effects as the IPD tends to overestimate the treatment effects, while the AD has the tendency to produce underestimated effect estimates. These results may provide some guide in deciding if significant benefit is gained by pooling the two levels of data when conducting meta-analysis.

Keywords: aggregate data, combined-level data, individual patient data, meta-analysis

Procedia PDF Downloads 350