Rameshwar D. Gupta

University of New Brunswick, Fredericton, New Brunswick, Canada

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Publications (54)32.23 Total impact

  • Source
    Debasis Kundu, Rameshwar D. Gupta
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    ABSTRACT: Recently, Gupta and Gupta [Analyzing skewed data by power-normal model, Test 17 (2008), pp. 197–210] proposed the power-normal distribution for which normal distribution is a special case. The power-normal distribution is a skewed distribution, whose support is the whole real line. Our main aim of this paper is to consider bivariate power-normal distribution, whose marginals are power-normal distributions. We obtain the proposed bivariate power-normal distribution from Clayton copula, and by making a suitable transformation in both the marginals. Lindley–Singpurwalla distribution also can be used to obtain the same distribution. Different properties of this new distribution have been investigated in detail. Two different estimators are proposed. One data analysis has been performed for illustrative purposes. Finally, we propose some generalizations to multivariate case also along the same line and discuss some of its properties.
    Statistics: A Journal of Theoretical and Applied Statistics 05/2011; iFirst(2011). · 1.26 Impact Factor
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    Debasis Kundu, Rameshwar D. Gupta
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    ABSTRACT: Generalized exponential distribution has been used quite effectively to model positively skewed lifetime data as an alternative to the well known Weibull or gamma distributions. In this paper we introduce an absolute continuous bivariate generalized exponential distribution by using a simple transformation from a well known bivariate exchangeable distribution. The marginal distributions of the proposed bivariate generalized exponential distributions are generalized exponential distributions. The joint probability density function and the joint cumulative distribution function can be expressed in closed forms. It is observed that the proposed bivariate distribution can be obtained using Clayton copula with generalized exponential distribution as marginals. We derive different properties of this new distribution. It is a five-parameter distribution, and the maximum likelihood estimators of the unknown parameters cannot be obtained in closed forms. We propose some alternative estimators, which can be obtained quite easily, and they can be used as initial guesses to compute the maximum likelihood estimates. One data set has been analyzed for illustrative purposes. Finally we propose some generalization of the proposed model. KeywordsBivariate exchangeable distribution–Dependence properties–Clayton copula–Hazard rate–Maximum likelihood estimators–Pseudo generator
    AStA Advances in Statistical Analysis 01/2011; 95(2):169-185. · 0.96 Impact Factor
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    Debasis Kundu, Rameshwar D. Gupta
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    ABSTRACT: The two-parameter generalized exponential distribution has been used recently quite extensively to analyze lifetime data. In this paper the two-parameter generalized exponential distribution has been embedded in a larger class of distributions obtained by introducing another shape parameter. Because of the additional shape parameter, more flexibility has been introduced in the family. It is observed that the new family is positively skewed, and has increasing, decreasing, unimodal and bathtub shaped hazard functions. It can be observed as a proportional reversed hazard family of distributions. This new family of distributions is analytically quite tractable and it can be used quite effectively to analyze censored data also. Analyses of two data sets are performed and the results are quite satisfactory.
    Statistical Methodology. 01/2011; 8(6):485-496.
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    Debasis Kundu, Rameshwar D. Gupta
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    ABSTRACT: Recently the proportional reversed hazard model has received a considerable amount of attention in the statistical literature. The main aim of this paper is to introduce a bivariate proportional reversed hazard model and discuss its different properties. In most of the cases the joint probability distribution function can be expressed in compact forms. The maximum likelihood estimators cannot be expressed in explicit forms in most of the cases. EM algorithm has been proposed to compute the maximum likelihood estimators of the unknown parameters. For illustrative purposes two data sets have been analyzed and the performances are quite satisfactory. KeywordsJoint probability density function–Conditional probability density function–Maximum likelihood estimators–EM algorithm
    01/2010; 72(2):236-253.
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    Debasis Kundu, Rameshwar D Gupta
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    ABSTRACT: Block and Basu bivariate exponential distribution is one of the most popular abso-lutely continuous bivariate distribution. Extensive work has been done on the Block and Basu bivariate exponential model over the past several decades. Interestingly it is observed that the Block and Basu bivariate exponential model can be extended to the Weibull model also. We call this new model as the Block and Basu bivariate Weibull model. We consider different properties of the Block and Basu bivariate Weibull model. The Block and Basu bivariate Weibull model has four unknown parameters and the maximum likelihood estimators cannot be obtained in closed form. To compute the the maximum likelihood estimators directly, one needs to solve a four dimensional op-timization problem. We propose to use the EM algorithm for computing the maximum likelihood estimators of the unknown parameters. The proposed EM algorithm can be carried out by solving one non-linear equation at each EM step. Our method can be used to compute the maximum likelihood estimators for the Block and Basu bivariate exponential model also. One data analysis has been preformed for illustrative purpose.
    Statistical Methodology. 01/2010; 7(4).
  • Ramesh C. Gupta, Rameshwar D. Gupta
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    ABSTRACT: 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.
    Journal of Applied Probability 01/2010; 47(2010). · 0.55 Impact Factor
  • Source
    Rameshwar D Gupta, Debasis Kundu
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    ABSTRACT: In this paper we discuss different properties of the two generalizations of the logistic distributions, which can be used to model the data exhibiting a unimodal density having some skewness present. The first generalization is carried out using the basic idea of Azzalini [2] and we call it as the skew logistic distribution. It is observed that the density function of the skew logistic distribution is always unimodal and log-concave in nature. But the distribution function, failure rate function and different moments can not be obtained in explicit forms and therefore it becomes quite difficult to use it in practice. The second generalization we propose as a proportional reversed hazard family with the base line distribution as the logistic distribution. It is also known in the literature as the Type-I generalized logistic distribution. The density function of the proportional reversed hazard logistic distribution may be asymmetric but it is always unimodal and log-concave. The distribution function, hazard function are in compact forms and the different moments can be obtained in terms of the ψ function and its derivatives. We have proposed different estimators and performed one data analysis for illustrative purposes.
    01/2010;
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    Debasis Kundu, Rameshwar D. Gupta
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    ABSTRACT: Recently Sarhan and Balakrishnan [2007. A new class of bivariate distribution and its mixture. Journal of Multivariate Analysis 98, 1508–1527] introduced a new bivariate distribution using generalized exponential and exponential distributions. They discussed several interesting properties of this new distribution. Unfortunately, they did not discuss any estimation procedure of the unknown parameters. In this paper using the similar idea as of Sarhan and Balakrishnan [2007. A new class of bivariate distribution and its mixture. Journal of Multivariate Analysis 98, 1508–1527], we have proposed a singular bivariate distribution, which has an extra shape parameter. It is observed that the marginal distributions of the proposed bivariate distribution are more flexible than the corresponding marginal distributions of the Marshall–Olkin bivariate exponential distribution, Sarhan–Balakrishnan's bivariate distribution or the bivariate generalized exponential distribution. Different properties of this new distribution have been discussed. We provide the maximum likelihood estimators of the unknown parameters using EM algorithm. We reported some simulation results and performed two data analysis for illustrative purposes. Finally we propose some generalizations of this bivariate model.
    Journal of Statistical Planning and Inference 01/2010; 140(2):526-538. · 0.71 Impact Factor
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    Wan-Ying Chang, Rameshwar D. Gupta, P. Richards
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    ABSTRACT: We study the general structure of the generalized Dirichlet distri- butions, deriving general formulas for the marginal and conditional probability density functions of those distributions. We develop the multivariate reverse rule properties of these distributions, apply those properties to derive proba- bility inequalities, and derive stochastic representations and orderings for the distributions. Further, we study approaches for estimating the parameters of these distributions and recommend that parameter estimation be carried out by the maximum likelihood method.
    01/2010;
  • Rameshwar D. Gupta, Debasis Kundu
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    ABSTRACT: Introducing a shape parameter to an exponential model is nothing new. There are many ways to introduce a shape parameter to an exponential distribution. The different methods may result in variety of weighted exponential (WE) distributions. In this article, we have introduced a shape parameter to an exponential model using the idea of Azzalini, which results in a new class of WE distributions. This new WE model has the probability density function (PDF) whose shape is very close to the shape of the PDFS of Weibull, gamma or generalized exponential distributions. Therefore, this model can be used as an alternative to any of these distributions. It is observed that this model can also be obtained as a hidden truncation model. Different properties of this new model have been discussed and compared with the corresponding properties of well-known distributions. Two data sets have been analysed for illustrative purposes and it is observed that in both the cases it fits better than Weibull, gamma or generalized exponential distributions.
    Statistics: A Journal of Theoretical and Applied Statistics 12/2009; 43(6):621-634. · 1.26 Impact Factor
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    Neeraj Misra, Nitin Gupta, Rameshwar D. Gupta
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    ABSTRACT: A multivariate frailty model in which survival function depends on baseline distributions of components and the frailty random variable is considered. Since misspecification in choice of frailty distribution and/or baseline distribution may affect the distribution of multivariate frailty model, using theory of stochastic orders, we compare multivariate frailty models arising from different choices of frailty distribution.
    Journal of Statistical Planning and Inference 01/2009; · 0.71 Impact Factor
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    Debasis Kundu, Rameshwar D. Gupta
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    ABSTRACT: Recently it has been observed that the generalized exponential distribution can be used quite effectively to analyze lifetime data in one dimension. The main aim of this paper is to define a bivariate generalized exponential distribution so that the marginals have generalized exponential distributions. It is observed that the joint probability density function, the joint cumulative distribution function and the joint survival distribution function can be expressed in compact forms. Several properties of this distribution have been discussed. We suggest to use the EM algorithm to compute the maximum likelihood estimators of the unknown parameters and also obtain the observed and expected Fisher information matrices. One data set has been re-analyzed and it is observed that the bivariate generalized exponential distribution provides a better fit than the bivariate exponential distribution.
    Journal of Multivariate Analysis 01/2009; 100(4):581-593. · 1.06 Impact Factor
  • Ravindra Khattree, Rameshwar D. Gupta
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    ABSTRACT: Consider the case of classifying an incoming message as one of two known p-dimension signals or as a pure noise. Let the noise co-variance matrix (assumed to be same in all the three cases) be unknown. We consider the problem of estimation of “realized signal to noise ratio matrix”, which is an index of discriminatory power, under various loss functions. Optimum estimators are obtained under these loss functions. Finally, an attempt is made to provide a lower confidence bound for the realized signal to noise ratio matrix. In the process, the probability distribution of the smaller eigenvalue of a 2 × 2 confluent hypergeometric random matrix is obtained.
    Australian &amp New Zealand Journal of Statistics 06/2008; 32(2):239 - 246. · 0.53 Impact Factor
  • Rameshwar D. Gupta, Harshinder Singh
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    ABSTRACT: Maximum likelihood estimates of ordered means of two normal distributions having common variance have been shown to be better than the usual maximum likelihood estimates (i.e. corresponding sample means) with respect to Pitman Nearness criterion. The maximum likelihood estimate of common variance taking into consideration the order restriction of the means is shown to have smaller mean square error than the unrestricted maximum likelihood estimate of the common variance. These two estimators have also been compared with respect to Pitman Nearness criterion.
    Australian &amp New Zealand Journal of Statistics 06/2008; 34(3):407 - 414. · 0.53 Impact Factor
  • Rameshwar D. Gupta, Donald St P. Richards
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    ABSTRACT: SummaryA series expansion is obtained for the confluent hypergeometric function of the second kind when the argument is a 2 times 2 positive definite matrix. Applications are made to the distributions of Hotelling's generalized T02 statistic, and the smallest latent root of the covariance matrix.
    Australian &amp New Zealand Journal of Statistics 06/2008; 24(2):216 - 220. · 0.53 Impact Factor
  • Source
    Debasis Kundu, Rameshwar D. Gupta
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    ABSTRACT: Recently two-parameter generalized exponential distribution has been introduced by the authors. In this paper we consider the Bayes estimators of the unknown parameters under the assumptions of gamma priors on both the shape and scale parameters. The Bayes estimators cannot be obtained in explicit forms. Approximate Bayes estimators are computed using the idea of Lindley. We also propose Gibbs sampling procedure to generate samples from the posterior distributions and in turn computing the Bayes estimators. The approximate Bayes estimators obtained under the assumptions of non-informative priors, are compared with the maximum likelihood estimators using Monte Carlo simulations. One real data set has been analyzed for illustrative purposes.
    Computational Statistics & Data Analysis 02/2008; · 1.30 Impact Factor
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    Ramesh C. Gupta, Rameshwar D. Gupta
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    ABSTRACT: The purpose of this paper is to study the structure and properties of the proportional reversed hazard rate model (PRHRM) in contrast to the celebrated proportional hazard model (PHM). The monotonicity of the hazard rate and the reversed hazard rate of the model is investigated. Some criteria of aging are presented and the inheritance of the aging notions (of the base distribution) by the PRHRM is studied. Characterizations of the model involving Fisher information are presented and the statistical inference of the parameters is discussed. Finally, it is shown that several members of the proportional reversed hazard rate class have been found to be useful and flexible in real data analysis.
    Journal of Statistical Planning and Inference 11/2007; · 0.71 Impact Factor
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    Debasis Kundu, Rameshwar D. Gupta
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    ABSTRACT: In this paper we propose a very convenient way to generate gamma random variables using generalized exponential distribution, when the shape parameter lies between 0 and 1. The new method is compared with the most popular Ahrens and Dieter method and the method proposed by Best. Like Ahrens and Dieter and Best methods our method also uses the acceptance–rejection principle. But it is observed that our method has greater acceptance proportion than Ahrens and Dieter or Best methods.
    Computational Statistics & Data Analysis 02/2007; · 1.30 Impact Factor
  • Source
    Rameshwar D. Gupta
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    ABSTRACT: Mudholkar and Srivastava [1993. Exponentiated Weibull family for analyzing bathtub failure data. IEEE Trans. Reliability 42, 299–302] introduced three-parameter exponentiated Weibull distribution. Two-parameter exponentiated exponential or generalized exponential distribution is a particular member of the exponentiated Weibull distribution. Generalized exponential distribution has a right skewed unimodal density function and monotone hazard function similar to the density functions and hazard functions of the gamma and Weibull distributions. It is observed that it can be used quite effectively to analyze lifetime data in place of gamma, Weibull and log-normal distributions. The genesis of this model, several properties, different estimation procedures and their properties, estimation of the stress-strength parameter, closeness of this distribution to some of the well-known distribution functions are discussed in this article.
    Journal of Statistical Planning and Inference 01/2007; · 0.71 Impact Factor
  • Source
    Debasis Kundu, Rameshwar D Gupta
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    ABSTRACT: This paper deals with the estimation of R = P [Y < X] when X and Y are two independent Weibull distributions with different scale parameters but having the same shape parameter. The maximum likelihood estimator and the approximate maximum likelihood estimator of R are proposed. We obtain the asymptotic distribution of the maximum likelihood estimator of R. Based on the asymptotic distribution, the confidence interval of R can be obtained. We also propose two bootstrap confidence intervals. We consider the Bayesian estimate of R and propose the corresponding credible interval for R. Monte Carlo simulations are performed to compare the different proposed methods. Analysis of a real data set has also been presented for illustrative purposes.
    IEEE Transactions on Reliability 07/2006; 55(2). · 2.29 Impact Factor

Publication Stats

886 Citations
32.23 Total Impact Points

Institutions

  • 1987–2011
    • University of New Brunswick
      • • Department of Computer Science & Applied Statistics
      • • Department of Mathematics and Statistics
      Fredericton, New Brunswick, Canada
  • 2009–2010
    • Indian Institute of Technology Kanpur
      • Department of Mathematics and Statistics
      Kānpur, Uttar Pradesh, India
  • 1990–1997
    • University of Virginia
      • Department of Statistics
      Charlottesville, VA, United States
  • 1993
    • University of Rochester
      Rochester, New York, United States