Dr. Indranil Ghosh

University of North Carolina at Wilmington | UNCW · Department of Mathematics and Statistics

There are various ways to characterize a bivariate distribution based on given distributional information. For example, information on both families of conditional densities, i.e., of XX given YY and of YY given XX, is sufficient to characterize the bivariate distribution. On the other hand, knowledge of both regression functions, i.e., E(X|Y=y)E(X...

Consider a two-dimensional discrete random variable (X, Y) with possible values 1, 2, …, I for X and 1, 2, …, J for Y. For specifying the distribution of (X, Y), suppose both conditional distributions, of X given Y and of Y given X, are provided. Under this setting, we present here different ways of measuring discrepancy between incompatible condit...

The Pareto distribution is a simple model for non-negative data with a power law probability tail. Income and wealth data is typically modeled using some variant of the classical Pareto distribution. In practice, it is frequently likely that the observed data has been truncated with respect to some unobserved covariable. In this paper a hidden trun...

The concept of weighted distributions is well-known in the literature concerning observational studies and surveys in research related to forestry, ecology, bio-medicine and many other areas. This paper proposes a new bivariate and multivariate exponential distribution. Several structural properties of the proposed bivariate exponential distributio...

The univariate Burr distribution and its properties and applications have been studied quite exten- sively in the literature. Some generalizations, as well as multivariate extensions of it, have also been proposed for greater flexibility in modeling univariate and multivariate data. In this paper, we construct generalized bivariate Burr (Type VII)...

A finite mixture of exponentiated Kumaraswamy Gompertz and exponentiated Kumaraswamy Fréchet is developed and discussed as a novel probability model. We study some useful structural properties of the proposed model. To estimate the model parameters under the classical method, we use maximum likelihood estimation using a progressive type II censorin...

The stop-loss moments have generally used as useful summary measures for analyzing the data which exceeds specific threshold levels. In many scientific studies the investigator cannot record the sampling units with equal probability, and in such a scenario the selected sample units appear with unequal probability, in other words with different weig...

In this article, we discuss a bivariate geometric distribution whose conditionals are geometric distributions and the marginals are not geometric and exhibits negative correlation. Several useful structural properties of the bivariate geometric distribution namely marginals, moments, generating functions, stochastic ordering are investigated. Simpl...

The usefulness of a hidden truncated Pareto (type II) model along with its’ inference under both the classical and Bayesian paradigm have been discussed in the literature in great details. In the multivariate set-up, some discussions are made that are primarily based on constructing a multivariate hidden truncated Pareto (type II) models with — sin...

Exponentiated exponential (EE) model has been used effectively in reliability, engineering, biomedical, social sciences, and other applications. In this study, we introduce a new bivariate mixture EE model with two parameters assuming two cases, independent and dependent random variables. We develop a bivariate mixture starting from two EE models a...

Recently, there seems to be an increasing amount of interest in the use of the tail conditional expectation (TCE) as a useful measure of risk associated with a production process, for example, in the measurement of risk associated with stock returns corresponding to the manufacturing industry, such as the production of electric bulbs, investment in...

In health related studies, we sometimes come across left-skewed heavy-tailed survival data and vary often the probability distributions proposed in the literature to fit the model of such survival data is not adequate. In this article, we explore a new probability density function with bounded domain. The new distribution arises from the Lomax dist...

Conditional specification of distributions is a developing area with several applications. In the finite discrete case, a variety of compatible conditions can be derived. In this paper, we revisit a rank–based criterion for identifying compatible distributions corresponding to complete conditional specification, including the case with zeros under...

In this follow up article of Arnold & Ghosh (2013), we re-visit and study in details one of the two special cases of multivariate hidden truncation -(a) single variable truncation from above in a trivariate scenario where the component random variables follow an appropriate Pareto (type II) distribution. The case with single variable truncation was...

Conditional specification of distributions is a developing area with several applications. In the finite discrete case, a variety of compatible conditions can be derived. In this paper, we revisit a rank–based criterion for identifying compatible distributions corresponding to complete conditional specification, including the case with zeros under...

This edited collection brings together internationally recognized experts in a range of areas of statistical science to honor the contributions of the distinguished statistician, Barry C. Arnold. A pioneering scholar and professor of statistics at the University of California, Riverside, Dr. Arnold has made exceptional advancements in different are...

In the bivariate case, we illustrate the situations where the normalizing constant is in a closed form and situations where the normalizing constant is not in a closed form. Distributional properties of such models are investigated. Discussions on some conjectures related to hidden truncation paradigm for non-normal models are also provided.

In this work, approximations for the distribution of the product of independent Beta random variables, based on mixtures of generalized Gamma distributions, are proposed. These mixtures are finite, and the parameters involved are determined using a two-step moment matching technique. A numerical study is conducted in order to assess the precision o...

In this paper, we try to supplement the distribution theory literature by incorporating a new bounded distribution, called the bounded weighted exponential (BWE) distribution in the (0, 1) intervals by transformation method. The proposed distribution exhibits decreasing and left-skewed unimodal density while the hazard rate can have increasing and...

We present some counterexamples of the classical and non-classical bivariate and multivariate normal distributions to widen our knowledge of these distributions. We hope that this paper will provide practitioners and users of bivariate and multivariate normal distributions of better view on the necessary and sufficient conditions leading to bivaria...

We introduce a new family of univariate continuous distributions called the Marshal-Olkin transmuted G family which extends the transmuted-G family pioneered by Shaw and Buckley (2007). Special models for the new family are provided. Some of its mathematical properties including quantile measure, explicit expressions for the ordinary and incomplete...

Discrete analog of a continuous distribution (especially in the univariate domain) is not new in the literature. The work of discretizing continuous distributions begun with the paper by Nakagawa and Osaki in 1975 to the best of the knowledge of the author. Since then several authors proposed discrete analogs of known continuous models. In this pap...

Following Arnold and Beaver (2000, Sankhy¯a A, 62, 23–35), we re-visit the hidden truncation paradigm for non-normal models with a feature that the resulting hidden truncated distribution arises from two different families of distributions with the same support set as well as from the same family. In the bivariate case, we illustrate the situations...

In this article, we discuss a bivariate Poisson distribution whose conditionals are univariate Poisson distributions and the marginals are not Poisson which exhibits negative correlation. Some useful structural properties of this distribution namely marginals, moments, generating functions, stochastic ordering are investigated. Simple proofs of neg...

In this work, approximations for the distribution of the product of independent Beta random variables, based on mixtures of generalized Gamma distributions, are proposed. These mixtures are finite and the parameters involved are determined using a two-step moment matching technique. A numerical study is conducted in order to assess the precision of...

In this paper, we consider observations arising out from a hidden truncation Pareto (IV) distribution and to be used to make inferences about the inequality, precision, shape, and truncation parameter(s). Two different types of dependent prior analyses are reviewed and compared with each other. We conjecture that mathematical tractability should be...

We study a new family of distributions defined by the minimum of the Poisson random number of independent identically distributed random variables having a general Weibull-G distribution (see Bourguignon et al. (2014)). Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean...

The exponentiated half logistic (EHL) distribution can be mostly and effectively used in modeling lifetime data. It is very similar to the gamma and exponentiated exponential distributions with two parameters. The major advantage of EHL distribution over the gamma distribution is that its cumulative distribution has a closed form. In this research,...

Several variants of the classical bivariate and multivariate generalized Pareto distributions have been discussed and studied in the literature (see Arnold (1983, 1993, 2015), Arnold and Laguna (1977), Ali and Nadarajah (2007), Rootzen and Tajvidi (2006) and the references cited therein). Ali and Nadarajah (2007) studied a truncated version of the...

The Lindley distribution has been generalized by many authors in recent years. A new two-parameter distribution with decreasing failure rate is introduced, called Alpha Power Transformed Lindley (�PTL) distribution that provides better fits than the Lindley distribution and some of its known generalizations. The new model includes the Lindley distr...

Conditional specification of distributions is a developing area with many applications. In the finite discrete case, a variety of compatible conditions can be derived. In this paper, we propose an alternative approach to study the compatibility of two conditional probability distributions under the finite discrete set up. A technique based on rank-...

Weighted distributions (univariate and bivariate) have received widespread attention over the last two decades because of their flexibility for analyzing skewed data. In this paper, we derive the bivariate and multivariate weighted Kumaraswamy distributions via the construction method as discussed in B.C. Arnold, I. Ghosh, A. Alzaatreh, Commun. Sta...

Recently, Alzaatreh et al. (2013a, 2013b) introduced a new method for generating new distributions. They used the method to propose a new distribution, called, the Weibull‐Pareto distribution (WPD). It is observed that the proposed distribution can be used quite effectively to model skewed data. They also proposed a modification of the maximum like...

Recently, Alzaatreh et al. (2013a, 2013b) introduced a new method for generating new distributions. They used the method to propose a new distribution, called, the Weibull-Pareto distribution (WPD). It is observed that the proposed distribution can be used quite effectively to model skewed data. They also proposed a modification of the maximum like...

Copulas are useful tools for modeling the dependence structure between two or more variables. Copulas are becoming a quite flexible tool in modeling dependence among the components of a multivariate vector, in particular to predict losses in insurance and finance. In this article, we study the dependence structure of some well-known real life insur...

In this paper a new probability density function with bounded domain is presented. This distri- bution arises from the Marshall-Olkin extended exponential distribution proposed by Marshall and Olkin (1997). It depends on two parameters and can be considered as an alternative to the classical beta and Kumaraswamy distributions. It presents the advan...

In the area of stress-strength models, there has been a large amount of work as regards estimation of the reliability R = Pr(X < Y ): The algebraic form for R = Pr(X < Y ) has been worked out for the vast majority of the well-known distributions when X and Y are independent random variables belonging to the same univariate family. In this paper, fo...

In this work, we introduce a new class of continuous distributions called the generalized poissonfamily which extends the quadratic rank transmutation map. We provide some special models for thenew family. Some of its mathematical properties including Rényi and q-entropies, order statistics andcharacterizations are derived. The estimations of the m...

In this paper, we provide some new results for the Weibull-R family of distributions (Alzaghal, Ghosh and Alzaatreh (2016)). We derive some new structural properties of the Weibull-R family of distributions. We provide various characterizations of the family via conditional moments, some functions of order statistics and via record values.

In this chapter, we focus on exploring some basic ideas on Bayesian and Markov networks and associated inferential procedures under both the classical and Bayesian paradigm. This chapter draws heavily on the article by Friedman et al. (2007). At the end of this chapter some conceptual as well as hands-on-exercises are provided for a better understa...

In this paper, we focus on the moderate to large sample inference for a particular family of the Generalized Transmuted Poisson-G (henceforth GTPG in short) for a baseline G distribution, when G follows a Weibull distribution with suitable parameters. We also consider some useful characterizations for generalized transmuted Poisson-Weibull (hencefo...

It is well known that joint bivariate densities cannot always be characterized by the corresponding two conditional densities. Hence, additional requirements have to be imposed. In the form of a conjecture, Arnold et al. (J Multivar Anal 99:1383–1392, 2008) suggested using any one of the two conditional densities and replacing the other one by the...

The Lindley distribution has been generalized by many authors in recent years. A new two-parameter distribution is introduced, called Alpha Power Transformed Lindley (αP T L) distribution that provides better fit than the Lindley distribution and some of the well known distributions. The new model includes the Lindley distribution as a special case...

In environmental studies, many data are typically skewed and it is desired to have a flexible statistical model for this kind of data. In this paper, we study a class of skewed distributions by invoking arguments as described by Ferreira and Steel (2006, Journal of the American Statistical Association, 101: 823--829). In particular, we consider usi...

This paper introduces a new four-parameter lifetime model called the odd log-logistic Dagum distribution. The new model has the advantage of being capable of modeling various shapes of aging and failure criteria. We derive some structural properties of the model odd log-logistic Dagum such as order statistics and incomplete moments. The maximum lik...

Over the last few decades, a significant development has been made towards the augmentation of some well-known lifetime distributions by various strategies. These newly developed models have enjoyed a considerable amount of success in modeling various real life phenomena. Motivated by this, Ristic & Balakrishnan (2012) developed a special class of...

A copula is a useful tool for constructing bivariate and/or multivariate distributions. In this article, we consider a new modified class of (Farlie-Gumbel-Morgenstern) FGM bivariate copula for constructing several different bivariate Kumaraswamy type copulas and discuss their structural properties, including dependence structures. It is establishe...

Traditional statistical approaches for estimating the parameters of the Kumaraswamy distribution have dealt with precise information. However, in real world situations, some information about an underlying experimental process might be imprecise and might be represented in the form of fuzzy information. In this paper, we consider the problem of est...

In this paper, we introduce a new family of continuous distributions called the transmuted Topp-Leone G family which extends the transmuted class pioneered by Shaw and Buckley (2007). Some of its mathematical properties including probability weighted moments, moments, generating functions, order statistics, incomplete moments, mean deviations, stre...

It is also shown that our proposed skew-normal model subsumes many other well-known skew-normal model that exists in the literature. Recent work on a new two-parameter generalized skew-normal model has received a lot of attention. This paper presents a new generalized Balakrishnan type skew–normal distribution by introducing two shape parameters. W...

We introduce a new class of distributions called the generalized odd generalized exponential family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, quantile and generating functions, R´enyi, Shannon and q-entropies, order statistics and probability weighted moments are derived. We also pr...

We propose and study a new class of continuous distributions called the beta Weibull-G family which extends the Weibull-G family introduced by Bourguignon et al. (2014). Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, order statistics and probability weighted moments a...

Explicit expressions for the densities of the Sum, S=X_{1}+X_{2} , Difference, D=X_{1}-X_{2} , Product, P=X_{1}X_{2} and the Ratio, R=X_{1}/X_{2} are derived when X_{1} and X_{2} are independent or sub-independent Kumaraswamy random variables. The expressions appear to involve the incomplete gamma functions. Some possible real life scenarios are me...

In this article, we introduce a new three-parameter odd log-logistic power Lindley distribution and discuss some of its properties. These include the shapes of the density and hazard rate functions, mixture representation, the moments, the quantile function, and order statistics. Maximum likelihood estimation of the parameters and their estimated a...

We introduce and study a new distribution called the odd log-logistic modified Weibull (OLLMW) distribution. Various of its structural properties are obtained in terms of Meijer’s G-function, such as the moments, generating function, conditional moments, mean deviations, order statistics and maximum likelihood estimators. The distribution exhibits...

In this paper we explore some mechanisms for constructing bivariate and multivariate beta and Kumaraswamy distributions. Specifically, we focus our attention on the Arnold-Ng (2011) eight parameter bivariate beta model. Several models in the literature are identified as special cases of this distribution including the Jones-Olkin- Liu-Libby-Novick...

We define and study a new generalization of the Fréchet distribution called the beta exponential Fréchet distribution. The new model includes thirty two special models. Some of its mathematical properties, including explicit expressions for the ordinary and incomplete moments, quantile and generating functions, mean residual life, mean inactivity t...

div class="page" title="Page 1"> Over the last few decades, a significant development has been made towards the augmen- tation of some well-known lifetime distributions by various strategies. These newly developed models have enjoyed a sizable amount of success in modeling various types of observed phe- nomena. In this paper we consider a new life...

Income and wealth data are typically modeled by some variant of the classical Pareto distribution. Often, in practice, the observed data are truncated with respect to some unobserved covariate. In this paper, a hidden truncation formulation of this scenario is proposed and analyzed. For this purpose, a bivariate Pareto (IV) distribution is assumed...

We introduce and study some general mathematical properties of a new generator of continuous distributions with two extra parameters called the Gompertz-G generator. We present some special models. We investigate the shapes of the density and hazard functions and derive explicit expressions for the ordinary and incomplete moments, quantile and gene...

In this chapter, a new generalization of the Kumaraswamy distribution, namely the gamma-Kumaraswamy distribution is defined and studied. Several distributional properties of the distribution are discussed in this chapter, which includes limiting behavior, mode, quantiles, moments, skewness, kurtosis, Shannon’s entropy, and order statistics. Under t...

A family of generalized Cauchy distributions, T-Cauchy{Y} family, is proposed using the T-R{Y} framework. The family of distributions is generated using the quantile functions of uniform, exponential, log-logistic, logistic, extreme value, and Fréchet distributions. Several general properties of the T-Cauchy{Y} family are studied in detail includin...

In this paper we discuss various strategies for constructing bivariate Kumaraswamy distributions via copula approach. The copula methods and construction studied here is different than those briefly discussed in Arnold & Ghosh (2016). Here, we consider here few different type of copula generators, which subsumes Clayton copula type generators. Vari...

The Lomax distribution, known as Pareto (type II) distribution, is a heavy tail probability distribution used extensively in business, economics and in actuarial modeling. The Weibull-Pareto distribution defined by Alzaatreh et al. (2013a) has shown high bias and standard error for the ML estimates when the parameter $c>>1$. In this paper we use th...

The univariate logistic distribution and its properties and applications have been studied quite extensively in the literature. Some generalizations as well as multivariate extensions of it have also been proposed for greater flexibility in modeling univariate and multivariate data. In this paper, we construct three different types of generalized b...

In this paper we discuss various strategies for constructing bivariate Kumaraswamy distributions. As alternatives to the Nadarajah, Cordeiro and Ortega (2011) bivariate model, four different models are introduced utilizing a conditional specification approach, a conditional survival function approach, an Arnold-Ng bivariate beta distribution constr...

Weighted distributions (univariate and bivariate) have received widespread attention over the last two decades because of their flexibility for analyzing skewed data. In this paper, we propose an alternative method to construct a new family of bivariate and multivariate weighted distributions. For illustrative purposes, some examples of the propose...

In this article we discuss Bayesian estimation of Kumaraswamy distributions based on three different types of censored samples. We obtain Bayes estimates of the model parameters using two different types of loss functions (LINEX and Quadratic) under each censoring scheme (left censoring, singly type-II censoring, and doubly type-II censoring) using...

Finite mixture models have provided a reasonable tool to model various type of observed phenomena , specially those which are random in nature. In this paper, a finite mixture of Weibull and Pareto (IV) distribution is considered and studied. Some structural properties of the resulting model are discussed including estimation of the model parameter...