Ramesh Gupta - Academia.edu (original) (raw)

Papers by Ramesh Gupta

Research paper thumbnail of Weighted inverse Gaussian – a versatile lifetime model

Journal of Applied Statistics, 2011

Jorgensen, Seshadri and Whitmore (1991, Scandinavian Journal of Statistics, 77-89) introduced a t... more Jorgensen, Seshadri and Whitmore (1991, Scandinavian Journal of Statistics, 77-89) introduced a three-parameter generalized inverse Gaussian distribution, which is a mixture of the inverse Gaussian distribution and length biased inverse Gaussian distribution. Also Birnbaum-Saunders distribution is a special case for p = 1/2, where p is the mixing parameter. It is observed that the estimators of the unknown parameters can be obtained by solving a three-dimensional optimization process, which may not be a trivial issue. Most of the iterative algorithms are quite sensitive to the initial guesses. In this paper we propose to use the EM algorithm to estimate the unknown parameters for complete and censored samples. In the proposed EM algorithm, at the M-step the optimization problem can be solved analytically, and the observed Fisher information matrix can be obtained. These can be used to construct asymptotic confidence intervals of the unknown parameters. Some simulation experiments are conducted to examine the performance of the proposed EM algorithm, and it is observed that the performances are quite satisfactory. The methodology proposed here is illustrated by three data sets.

Research paper thumbnail of On Bivariate Birnbaum–Saunders Distribution

American Journal of Mathematical and Management Sciences, 2016

Univariate Birnbaum-Saunders distribution has been used quite effectively to analyze positively s... more Univariate Birnbaum-Saunders distribution has been used quite effectively to analyze positively skewed lifetime data. It has received considerable amount of attention in the last few years. In this paper, we study the bivariate Birnbaum-Saunders distribution from a reliability and dependence point of view. It is observed that the bivariate Birnbaum-Saunders distribution can be obtained as a Gaussian copula. It helps in deriving several dependency properties and also to compute several dependency measures of the bivariate Birnbaum-Saunders distribution. Further, we consider the estimation of the unknown parameters based on copula, and study their performances using Monte Carlo simulations. One data set has been analyzed for illustrative purposes. Finally we extend some of the results for multivariate Birnbaum-Saunders distribution also.

Research paper thumbnail of Bivariate Conway–Maxwell–Poisson distribution: Formulation, properties, and inference

Journal of Multivariate Analysis, 2016

The bivariate Poisson distribution is a popular distribution for modeling bivariate count data. I... more The bivariate Poisson distribution is a popular distribution for modeling bivariate count data. Its basic assumptions and marginal equi-dispersion, however, may prove limiting in some contexts. To allow for data dispersion, we develop here a bivariate Conway-Maxwell-Poisson (COM-Poisson) distribution that includes the bivariate Poisson, bivariate Bernoulli, and bivariate geometric distributions all as special cases. As a result, the bivariate COM-Poisson distribution serves as a flexible alternative and unifying framework for modeling bivariate count data, especially in the presence of data dispersion. Published by Elsevier Inc.

Research paper thumbnail of On some association measures in bivariate distributions and their relationships

Journal of Statistical Planning and Inference, 2003

In this paper, we study three time dependent measures of association, viz. the odds ratio, condit... more In this paper, we study three time dependent measures of association, viz. the odds ratio, conditional mean residual life and the conditional probability. We examine conditions under which these measures exceed unity. We also obtain a class of distributions for which the components of the hazard gradient (mean residual lives) are proportional. Finally, some examples are provided to illustrate the results.

Research paper thumbnail of A new generalization of the negative binomial distribution

Computational Statistics & Data Analysis, 2004

Research paper thumbnail of Entropy and Residual Entropy Functions and Some Characterization Results

Pakistan Journal of Statistics and Operation Research, 2012

In this paper, we have developed conditions under which the entropy function and the residual ent... more In this paper, we have developed conditions under which the entropy function and the residual entropy function characterize the distribution. We have also studied some stochastic comparisons based on the entropy measure and established relations between entropy comparisons and comparisons with respect to other measures in reliability. Conditions for decreasing (increasing) uncertainty in a residual life distribution are obtained. Some relations between the classes of distribution in reliability and the classes of distribution, based on the monotonic properties of uncertainty, in a residual life distribution are obtained.

Research paper thumbnail of On the Multivariate Normal Hazard

Journal of Multivariate Analysis, 1997

It is well known that the hazard rate of a univariate normal distribution is increasing. In this ... more It is well known that the hazard rate of a univariate normal distribution is increasing. In this paper, we prove that the hazard gradient, in the case of general multivariate normal distribution, is increasing in the sense of Johnson and Kotz. 1997 Academic Press 1. Definition 1. The joint multivariate hazard rate of m jointly absolutely continuous random variables X 1 , X 2 , ..., X m is defined as the vector h(x)= \ & \ x 1 + } } } & \ x m ++ ln G(x)= &grad ln G(x) where G(x)=P(X i >x i , i=1, 2, ..., m) is the joint survival function. For convenience, we shall write &(Â x j) ln G(x)=h j (x). Note that h j (x) is the article no. MV971675 64 0047-259XÂ97 25.00

Research paper thumbnail of The monotonicity of the reliability measures of the beta distribution

Applied Mathematics Letters, 2000

In this paper, we investigate the monotonic properties of the hazard (failure) rate and mean resi... more In this paper, we investigate the monotonic properties of the hazard (failure) rate and mean residual life function (life expectancy) of the beta distribution. The monotonic properties are sometimes very useful in identifying an appropriate model.

Research paper thumbnail of Bayes estimation in a mixture inverse Gaussian model

Annals of the Institute of Statistical Mathematics

In this paper a mixture model involving the inverse Gaussian distribution and its length biased v... more In this paper a mixture model involving the inverse Gaussian distribution and its length biased version is studied from a Bayesian viewpoint. Using proper priors, the Bayes estimates of the parameters of the model are derived and the results are applied on the aircraft data of Proschan (1963, Technometrics, 5,375-383). The posterior distributions of the parameters are expressed in terms of the confluent-hypergeometric function and the modified Bessel function of the third kind. The integral involved in the expression of the estimate of the mean is evaluated by numerical techniques.

Research paper thumbnail of Analysis of survival data by a Weibull-generalized Poisson distribution

Journal of Applied Statistics, 2014

In life-testing and survival analysis, sometimes the components are arranged in series or paralle... more In life-testing and survival analysis, sometimes the components are arranged in series or parallel system and the number of components is initially unknown. Thus, the number of components, say Z, is considered as random with an appropriate probability mass function. In this paper, we model the survival data with baseline distribution as Weibull and the distribution of Z as generalized Poisson, giving rise to four parameters in the model: increasing, decreasing, bathtub and upside bathtub failure rates. Two examples are provided and the maximum-likelihood estimation of the parameters is studied. Rao's score test is developed to compare the results with the exponential Poisson model studied by Kus [17] and the exponential-generalized Poisson distribution with baseline distribution as exponential and the distribution of Z as generalized Poisson. Simulation studies are carried out to examine the performance of the estimates.

Research paper thumbnail of Reliability Studies of the Skew-Normal Distribution and Its Application to a Strength-Stress Model

Communications in Statistics: Theory and Methods, 2001

The skew-normal distribution proposed by Azzalini [1] is suitable for the analysis of data exhibi... more The skew-normal distribution proposed by Azzalini [1] is suitable for the analysis of data exhibiting a unimodal empirical distribution function but having some skewness present, a structure often occurring in data analysis. In this paper we study the skew-normal ...

Research paper thumbnail of Association Measures in the Bivariate Correlated Frailty Model

• This paper deals with a general bivariate correlated frailty model. This includes the multiplic... more • This paper deals with a general bivariate correlated frailty model. This includes the multiplicative as well as the additive frailty effect. The association parameter is studied for the shared as well as the general correlated model. The results for the gamma, the inverse Gaussian and the stable frailty models are derived.

Research paper thumbnail of Limiting Behaviour of the Mean Residual Life

In survival or reliability studies, the mean residual life or life expectancy is an important cha... more In survival or reliability studies, the mean residual life or life expectancy is an important characteristic of the model. Here, we study the limiting behaviour of the mean residual life, and derive an asymptotic expansion which can be used to obtain a good approximation for large values of the time variable. The asymptotic expansion is valid for a quite general class of failure rate distributions--perhaps the largest class that can be expected given that the terms depend only on the failure rate and its derivatives.

Research paper thumbnail of Generalized Sichel Distribution and Associated Inference

Journal of Statistical Theory and Applications, 2017

In this paper, we propose a generalized form of Sichel distribution which is obtained by mixing t... more In this paper, we propose a generalized form of Sichel distribution which is obtained by mixing the Poisson distribution with the extended generalized inverse Gaussian distribution. This distribution models over dispersed, zero-inflated and heavy-tailed count data sets. These characteristics are examined with respect to the dispersion, zero-inflation and the third central moment inflation indices. Examples are provided to compare the extension with several other existing models including the Poisson-inverse Gaussian and the Sichel distributions.

Research paper thumbnail of Discussion of Birnbaum-Saunders distribution: A review of models, analysis, and applications

Applied Stochastic Models in Business and Industry, 2018

Research paper thumbnail of Representing the mean residual life in terms of the failure rate

Mathematical and Computer Modelling, 2003

Research paper thumbnail of On some mixture models based on the Birnbaum–Saunders distribution and associated inference

Journal of Statistical Planning and Inference, 2011

Research paper thumbnail of Random effect bivariate survival models and stochastic comparisons

Journal of Applied Probability, 2010

In this paper we propose a general bivariate random effect model with special emphasis on frailty... more In this paper we propose a general bivariate random effect model with special emphasis on frailty models and environmental effect models, and present some stochastic comparisons. The relationship between the conditional and the unconditional hazard gradients are derived and some examples are provided. We investigate how the well-known stochastic orderings between the distributions of two frailties translate into the orderings between the corresponding survival functions. These results are used to obtain the properties of the bivariate multiplicative model and the shared frailty model.

Research paper thumbnail of Score Test for Zero Inflated Generalized Poisson Regression Model

Communications in Statistics - Theory and Methods, 2005

In certain applications involving count data, it is sometimes found that zeros are observed with ... more In certain applications involving count data, it is sometimes found that zeros are observed with a frequency significantly higher (lower) than predicted by the assumed model. Examples of such applications are cited in the literature from engineering, manufacturing, economics, public health, epidemiology, psychology, sociology, political science, agriculture, road safety, species abundance, use of recreational facilities, horticulture and criminology. In this article, a zero adjusted generalized Poisson distribution is studied and a score test is developed, with and without covariates, to determine whether such

Research paper thumbnail of Proportional odds frailty model and stochastic comparisons

Annals of the Institute of Statistical Mathematics, 2013

In this paper, we present some distributional properties of the survival and frailty distribution... more In this paper, we present some distributional properties of the survival and frailty distribution involved in the proportional odds (PO) frailty model. Stochastic orderings are studied for this proportional odds frailty model. It is showed that negative dependence arises in the PO frailty model as opposed to the proportional hazard frailty model.

Research paper thumbnail of Weighted inverse Gaussian – a versatile lifetime model

Journal of Applied Statistics, 2011

Jorgensen, Seshadri and Whitmore (1991, Scandinavian Journal of Statistics, 77-89) introduced a t... more Jorgensen, Seshadri and Whitmore (1991, Scandinavian Journal of Statistics, 77-89) introduced a three-parameter generalized inverse Gaussian distribution, which is a mixture of the inverse Gaussian distribution and length biased inverse Gaussian distribution. Also Birnbaum-Saunders distribution is a special case for p = 1/2, where p is the mixing parameter. It is observed that the estimators of the unknown parameters can be obtained by solving a three-dimensional optimization process, which may not be a trivial issue. Most of the iterative algorithms are quite sensitive to the initial guesses. In this paper we propose to use the EM algorithm to estimate the unknown parameters for complete and censored samples. In the proposed EM algorithm, at the M-step the optimization problem can be solved analytically, and the observed Fisher information matrix can be obtained. These can be used to construct asymptotic confidence intervals of the unknown parameters. Some simulation experiments are conducted to examine the performance of the proposed EM algorithm, and it is observed that the performances are quite satisfactory. The methodology proposed here is illustrated by three data sets.

Research paper thumbnail of On Bivariate Birnbaum–Saunders Distribution

American Journal of Mathematical and Management Sciences, 2016

Univariate Birnbaum-Saunders distribution has been used quite effectively to analyze positively s... more Univariate Birnbaum-Saunders distribution has been used quite effectively to analyze positively skewed lifetime data. It has received considerable amount of attention in the last few years. In this paper, we study the bivariate Birnbaum-Saunders distribution from a reliability and dependence point of view. It is observed that the bivariate Birnbaum-Saunders distribution can be obtained as a Gaussian copula. It helps in deriving several dependency properties and also to compute several dependency measures of the bivariate Birnbaum-Saunders distribution. Further, we consider the estimation of the unknown parameters based on copula, and study their performances using Monte Carlo simulations. One data set has been analyzed for illustrative purposes. Finally we extend some of the results for multivariate Birnbaum-Saunders distribution also.

Research paper thumbnail of Bivariate Conway–Maxwell–Poisson distribution: Formulation, properties, and inference

Journal of Multivariate Analysis, 2016

The bivariate Poisson distribution is a popular distribution for modeling bivariate count data. I... more The bivariate Poisson distribution is a popular distribution for modeling bivariate count data. Its basic assumptions and marginal equi-dispersion, however, may prove limiting in some contexts. To allow for data dispersion, we develop here a bivariate Conway-Maxwell-Poisson (COM-Poisson) distribution that includes the bivariate Poisson, bivariate Bernoulli, and bivariate geometric distributions all as special cases. As a result, the bivariate COM-Poisson distribution serves as a flexible alternative and unifying framework for modeling bivariate count data, especially in the presence of data dispersion. Published by Elsevier Inc.

Research paper thumbnail of On some association measures in bivariate distributions and their relationships

Journal of Statistical Planning and Inference, 2003

In this paper, we study three time dependent measures of association, viz. the odds ratio, condit... more In this paper, we study three time dependent measures of association, viz. the odds ratio, conditional mean residual life and the conditional probability. We examine conditions under which these measures exceed unity. We also obtain a class of distributions for which the components of the hazard gradient (mean residual lives) are proportional. Finally, some examples are provided to illustrate the results.

Research paper thumbnail of A new generalization of the negative binomial distribution

Computational Statistics & Data Analysis, 2004

Research paper thumbnail of Entropy and Residual Entropy Functions and Some Characterization Results

Pakistan Journal of Statistics and Operation Research, 2012

In this paper, we have developed conditions under which the entropy function and the residual ent... more In this paper, we have developed conditions under which the entropy function and the residual entropy function characterize the distribution. We have also studied some stochastic comparisons based on the entropy measure and established relations between entropy comparisons and comparisons with respect to other measures in reliability. Conditions for decreasing (increasing) uncertainty in a residual life distribution are obtained. Some relations between the classes of distribution in reliability and the classes of distribution, based on the monotonic properties of uncertainty, in a residual life distribution are obtained.

Research paper thumbnail of On the Multivariate Normal Hazard

Journal of Multivariate Analysis, 1997

It is well known that the hazard rate of a univariate normal distribution is increasing. In this ... more It is well known that the hazard rate of a univariate normal distribution is increasing. In this paper, we prove that the hazard gradient, in the case of general multivariate normal distribution, is increasing in the sense of Johnson and Kotz. 1997 Academic Press 1. Definition 1. The joint multivariate hazard rate of m jointly absolutely continuous random variables X 1 , X 2 , ..., X m is defined as the vector h(x)= \ & \ x 1 + } } } & \ x m ++ ln G(x)= &grad ln G(x) where G(x)=P(X i >x i , i=1, 2, ..., m) is the joint survival function. For convenience, we shall write &(Â x j) ln G(x)=h j (x). Note that h j (x) is the article no. MV971675 64 0047-259XÂ97 25.00

Research paper thumbnail of The monotonicity of the reliability measures of the beta distribution

Applied Mathematics Letters, 2000

In this paper, we investigate the monotonic properties of the hazard (failure) rate and mean resi... more In this paper, we investigate the monotonic properties of the hazard (failure) rate and mean residual life function (life expectancy) of the beta distribution. The monotonic properties are sometimes very useful in identifying an appropriate model.

Research paper thumbnail of Bayes estimation in a mixture inverse Gaussian model

Annals of the Institute of Statistical Mathematics

In this paper a mixture model involving the inverse Gaussian distribution and its length biased v... more In this paper a mixture model involving the inverse Gaussian distribution and its length biased version is studied from a Bayesian viewpoint. Using proper priors, the Bayes estimates of the parameters of the model are derived and the results are applied on the aircraft data of Proschan (1963, Technometrics, 5,375-383). The posterior distributions of the parameters are expressed in terms of the confluent-hypergeometric function and the modified Bessel function of the third kind. The integral involved in the expression of the estimate of the mean is evaluated by numerical techniques.

Research paper thumbnail of Analysis of survival data by a Weibull-generalized Poisson distribution

Journal of Applied Statistics, 2014

In life-testing and survival analysis, sometimes the components are arranged in series or paralle... more In life-testing and survival analysis, sometimes the components are arranged in series or parallel system and the number of components is initially unknown. Thus, the number of components, say Z, is considered as random with an appropriate probability mass function. In this paper, we model the survival data with baseline distribution as Weibull and the distribution of Z as generalized Poisson, giving rise to four parameters in the model: increasing, decreasing, bathtub and upside bathtub failure rates. Two examples are provided and the maximum-likelihood estimation of the parameters is studied. Rao's score test is developed to compare the results with the exponential Poisson model studied by Kus [17] and the exponential-generalized Poisson distribution with baseline distribution as exponential and the distribution of Z as generalized Poisson. Simulation studies are carried out to examine the performance of the estimates.

Research paper thumbnail of Reliability Studies of the Skew-Normal Distribution and Its Application to a Strength-Stress Model

Communications in Statistics: Theory and Methods, 2001

The skew-normal distribution proposed by Azzalini [1] is suitable for the analysis of data exhibi... more The skew-normal distribution proposed by Azzalini [1] is suitable for the analysis of data exhibiting a unimodal empirical distribution function but having some skewness present, a structure often occurring in data analysis. In this paper we study the skew-normal ...

Research paper thumbnail of Association Measures in the Bivariate Correlated Frailty Model

• This paper deals with a general bivariate correlated frailty model. This includes the multiplic... more • This paper deals with a general bivariate correlated frailty model. This includes the multiplicative as well as the additive frailty effect. The association parameter is studied for the shared as well as the general correlated model. The results for the gamma, the inverse Gaussian and the stable frailty models are derived.

Research paper thumbnail of Limiting Behaviour of the Mean Residual Life

In survival or reliability studies, the mean residual life or life expectancy is an important cha... more In survival or reliability studies, the mean residual life or life expectancy is an important characteristic of the model. Here, we study the limiting behaviour of the mean residual life, and derive an asymptotic expansion which can be used to obtain a good approximation for large values of the time variable. The asymptotic expansion is valid for a quite general class of failure rate distributions--perhaps the largest class that can be expected given that the terms depend only on the failure rate and its derivatives.

Research paper thumbnail of Generalized Sichel Distribution and Associated Inference

Journal of Statistical Theory and Applications, 2017

In this paper, we propose a generalized form of Sichel distribution which is obtained by mixing t... more In this paper, we propose a generalized form of Sichel distribution which is obtained by mixing the Poisson distribution with the extended generalized inverse Gaussian distribution. This distribution models over dispersed, zero-inflated and heavy-tailed count data sets. These characteristics are examined with respect to the dispersion, zero-inflation and the third central moment inflation indices. Examples are provided to compare the extension with several other existing models including the Poisson-inverse Gaussian and the Sichel distributions.

Research paper thumbnail of Discussion of Birnbaum-Saunders distribution: A review of models, analysis, and applications

Applied Stochastic Models in Business and Industry, 2018

Research paper thumbnail of Representing the mean residual life in terms of the failure rate

Mathematical and Computer Modelling, 2003

Research paper thumbnail of On some mixture models based on the Birnbaum–Saunders distribution and associated inference

Journal of Statistical Planning and Inference, 2011

Research paper thumbnail of Random effect bivariate survival models and stochastic comparisons

Journal of Applied Probability, 2010

In this paper we propose a general bivariate random effect model with special emphasis on frailty... more In this paper we propose a general bivariate random effect model with special emphasis on frailty models and environmental effect models, and present some stochastic comparisons. The relationship between the conditional and the unconditional hazard gradients are derived and some examples are provided. We investigate how the well-known stochastic orderings between the distributions of two frailties translate into the orderings between the corresponding survival functions. These results are used to obtain the properties of the bivariate multiplicative model and the shared frailty model.

Research paper thumbnail of Score Test for Zero Inflated Generalized Poisson Regression Model

Communications in Statistics - Theory and Methods, 2005

In certain applications involving count data, it is sometimes found that zeros are observed with ... more In certain applications involving count data, it is sometimes found that zeros are observed with a frequency significantly higher (lower) than predicted by the assumed model. Examples of such applications are cited in the literature from engineering, manufacturing, economics, public health, epidemiology, psychology, sociology, political science, agriculture, road safety, species abundance, use of recreational facilities, horticulture and criminology. In this article, a zero adjusted generalized Poisson distribution is studied and a score test is developed, with and without covariates, to determine whether such

Research paper thumbnail of Proportional odds frailty model and stochastic comparisons

Annals of the Institute of Statistical Mathematics, 2013

In this paper, we present some distributional properties of the survival and frailty distribution... more In this paper, we present some distributional properties of the survival and frailty distribution involved in the proportional odds (PO) frailty model. Stochastic orderings are studied for this proportional odds frailty model. It is showed that negative dependence arises in the PO frailty model as opposed to the proportional hazard frailty model.