Browsing by Author "Bhaswati Mukherjee"

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A bayes comparison of weibull extension and modified weibull models for data showing bathtub hazard rate
(Taylor and Francis Ltd., 2013) S.K. Upadhyay; Ashutosh Gupta; Bhaswati Mukherjee; Ankit Khokhar
A number of models have been proposed in the literature to model data reflecting bathtub-shaped hazard rate functions. Mixture distributions provide the obvious choice for modelling such data sets but these contain too many parameters and hamper the accuracy of the inferential procedures particularly when the data are meagre. Recently, a few distributions have been proposed which are simply generalizations of the two-parameterWeibull model and are capable of producing bathtub behaviour of the hazard rate function. The Weibull extension and the modified Weibull models are two such families. This study focuses on comparing these two distributions for data sets exhibiting bathtub shape of the hazard rate. Bayesian tools are preferred due to their wide range of applicability in various nested and non-nested model comparison problems. Real data illustrations are provided so that a particular model can be recommended based on various tools of model comparison discussed in the paper. © 2013 Taylor & Francis.
A Bayesian study for the comparison of generalized gamma model with its components
(Springer India, 2010) Bhaswati Mukherjee; Ashutosh Gupta; S.K. Upadhyay
Generalized gamma distribution offers a flexible family and many of the important lifetime models are obtained as component models by setting its shape parameters to unity. The flexibility of the generalized gamma model, however, occurs at the cost of its increased complexity. The present paper makes a simulation based Bayesian study to have a thorough comparison of the generalized gamma with its components in situations where the given data appear compatible with this family. Of course, if a component model is recommended the latter inferences are quite easy to deal with. The study has been conducted in two stages. First, the generalized gamma family with a scale and two shape parameters is examined to see if one or both of its shape parameters can be set to unity in order that the component models can be looked upon as possible candidates. Second, a threshold parameter added in to the family selected at the first stage is tested against zero to see if there is any desirability of threshold in the model(s). A real data set is considered for the purpose of illustration. The paper proceeds by checking compatibility of the various component models with the given data set and finally compares the models to select the one that is most pertinent with the data. © 2011, Indian Statistical Institute.
A Bayesian study for the comparison of generalized gamma model with its components
(Indian Statistical Institute, 2010) Bhaswati Mukherjee; Ashutosh Gupta; S.K. Upadhyay
Generalized gamma distribution offers a flexible family and many of the important lifetime models are obtained as component models by setting its shape parameters to unity. The flexibility of the generalized gamma model, however, occurs at the cost of its increased complexity. The present paper makes a simulation based Bayesian study to have a thorough comparison of the generalized gamma with its components in situations where the given data appear compatible with this family. Of course, if a component model is recommended the latter inferences are quite easy to deal with. The study has been conducted in two stages. First, the generalized gamma family with a scale and two shape parameters is examined to see if one or both of its shape parameters can be set to unity in order that the component models can be looked upon as possible candidates. Second, a threshold parameter added in to the family selected at the first stage is tested against zero to see if there is any desirability of threshold in the model(s). A real data set is considered for the purpose of illustration. The paper proceeds by checking compatibility of the various component models with the given data set and finally compares the models to select the one that is most pertinent with the data. © Indian Statistical Institute 2011.
Accelerated test system strength models based on Birnbaum-Saunders distribution: A complete Bayesian analysis and comparison
(2009) S.K. Upadhyay; Bhaswati Mukherjee; Ashutosh Gupta
Several models for studies related to tensile strength of materials are proposed in the literature where the size or length component has been taken to be an important factor for studying the specimens' failure behaviour. An important model, developed on the basis of cumulative damage approach, is the three-parameter extension of the Birnbaum-Saunders fatigue model that incorporates size of the specimen as an additional variable. This model is a strong competitor of the commonly used Weibull model and stands better than the traditional models, which do not incorporate the size effect. The paper considers two such cumulative damage models, checks their compatibility with a real dataset, compares them with some of the recent toolkits, and finally recommends a model, which appears an appropriate one. Throughout the study is Bayesian based on Markov chain Monte Carlo simulation. © 2009 Springer Science+Business Media, LLC.
Assessing the value of the threshold parameter in the Weibull distribution using Bayes paradigm
(2008) S.K. Upadhyay; Bhaswati Mukherjee
The Weibull distribution represents a wide variety of situations. Usually, the distribution is considered as a two-parameter family with a scale, and a shape parameter. If, however, the given data reflect additional information in the form of a minimum guarantee, a positive value away from zero, it is better to go for a three-parameter model with the additional parameter known as the threshold. The threshold parameter is often very important, but increases the complexity of the model. Arbitrarily going for the three-parameter form is not advisable unless it is really required by the data. This article attempts to make a simulation-based Bayesian study for checking if the threshold parameter can be taken to be zero or positive in situations representing the two models. We study the compatibility of the models for the given data set. We conduct the posterior simulation in each case using Gibbs sampling. © 2008 IEEE.
Bayes analysis and comparison of accelerated weibull and accelerated birnbaum-saunders models
(2010) S.K. Upadhyay; Bhaswati Mukherjee
Several models are proposed in the literature for modeling fatigue data resulting from materials subject to cyclic stress and strain. Accelerated Weibull and accelerated Birnbaum-Saunders distributions are most commonly used models. Whereas the accelerated Weibull model is easier compared to accelerated Birnbaum-Saunders, it fails to represent the situation equally well. The present article focuses on Bayes analysis of the two models and provides a comparison based on some important Bayesian tools. Model compatibility study using predictive simulation ideas is preceded by the said comparison. Throughout, the posterior simulations are carried out by Markov chain Monte Carlo procedure.
Weibull extension model: A Bayes study using Markov chain Monte Carlo simulation
(2008) Ashutosh Gupta; Bhaswati Mukherjee; S.K. Upadhyay
Several generalizations of the two-parameter Weibull model have been proposed to model data sets that exhibit complex non-monotone shapes of hazard rate function. The present paper focuses on one such generalization referred to as the Weibull extension model in the literature. Complete Bayesian analysis of the model has been provided using Markov chain Monte Carlo simulation. Finally, a thorough study has been conducted for checking the adequacy of the model for a given data set using some of the graphical and numerical methods based on predictive simulation ideas. A real data set is considered for illustration. © 2007 Elsevier Ltd. All rights reserved.