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The bivariate Poisson distribution is a natural choice for modeling bivariate count data. Its constraining assumption, however, limits model flexibility in some contexts. This work considers the tr...

For two vast families of mixture distributions and a given prior, we provide unified representations of posterior and predictive distributions. Model applications presented include bivariate mixtur...

In this article, we study the concomitants of m-generalized order statistics (m-GOS) from iterated Farlie–Gumbel–Morgenstern bivariate distributions, denoted by IFGM ( λ , η ) , as an extension of ...

Anisotropic functional deconvolution model is investigated in the bivariate case when the design points ti , i = 1 , 2 , ⋯ , N , and xl , l = 1 , 2 , ⋯ , M , are irregular and follow known densitie...

Consider a discrete-time risk model with dependence structures, where claim sizes are assumed to follow a one-sided linear process whose innovations further obey a so-called bivariate upper tail in...

We propose families of bivariate copulas based on the Kumaraswamy distortion of existing copulas. With the additional two parameters in the Kumaraswamy distribution, the induced copulas permit more...

There are many well-known bivariate distributions, such as the normal distribution, for which the question of whether they are max- or min-infinite divisible was settled a long time ago. However, d...

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...

In this work, we study semiparametric copula models under bivariate censoring. Basing on divergences theory, we propose new estimates for the parameter of the considered model and we establish thei...

A bivariate zero-inflated Poisson control chart for rare events in an industrial process was presented in the paper of Fatahi et al. (2012). They used a specific copula to address the dependency between the bivariate counts. The copula that they provided did not satisfy the criteria for a copula when the correlation parameter is negative and they did not calculate the upper control limit for the sum of events correctly. We provide proper copula’s and upper control limits and also discuss their choice of parameter estimators. We illustrate our results with simulations.

Under the dependent structure of bivariate Eyraud-Farlie-Gumbel-Morgenstern copula, we present the asymptotics of expected shortfall for portfolio loss as the confidence level tends to one. Additio...

In this article, we study multivariate monitoring systems based on a bivariate integer-valued autoregressive process of order 1, BINAR(1). The charting procedures are evaluated using extensive simu...

Birnbaum-Saunders models have been widely used to describe data following positive-skew distributions. In this article, we introduce a bivariate Birnbaum-Saunders distribution which has the mean as...

The Farlie-Gumbel-Morgensten (FGM) family of bivariate distributions with given marginals, is frequently used in theory and applications and has been generalized in many ways. With the help of two ...

In this paper, two bivariate models based on the proposed methods of Marshall and Olkin are introduced. In the first model, the new bivariate distribution is presented based on the proposed method ...

We construct a new bivariate mixture of negative binomial distributions which represents over-dispersed data more efficiently. This is an extension of a univariate mixture of beta and negative bino...

We consider simple n− variate distributions, which are the special cases of general elliptically contoured and Kotz type distributions. In particular, we analyze the distributions having jo...

Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyze the bivariate data on related survival time...

In this paper we study some characteristic properties of higher-degree bivariate stop-loss transforms (partial moments). A new bivariate distribution is proposed by extending the characteri...

In this paper, we propose a new bivariate geometric model, derived by linking two univariate geometric distributions through a specific copula function, allowing for positive and negative correlati...

The class of transmuted distributions has received a lot of attention in the recent statistical literature. In this paper, we propose a rich family of bivariate distribution whose condition...

In this paper bivariate vectors of discrete aging and alternative aging intensities are introduced. Using these vector-valued functions we present some results about bivariate discrete dist...

Nadarajah and Mitov [Communications in Statistics—Theory and Methods, 32, 2003, 47-60] derived an expectation formula for continuous multivariate random variables involving the joint survival function. Their result is extended here for discrete multivariate random variables. Examples proposing new discrete bivariate distributions are given.

Several generalizations to the concept of Kullback-Leibler divergence measure and Kerridge inaccuracy measure are available in the literature. In a recent paper Kundu (2015) considered a generalized K-L divergence measure of order (α, β). Nath (1968) has also proposed generalized inaccuracy measure of order α. Here we address the question of extending these measures to higher dimensions with reference to residual lifetimes. In the present work, the generalized divergence and inaccuracy measures are extended for conditional lifetimes of two components having possibly different ages. Several properties, including monotonicity, and bounds of these measures are obtained for conditional random variables. Moreover, we study the effect of (increasing) monotone transformation on these generalized measures.

In this paper we introduced a single parameter, absolutely continuous and radially symmetric bivariate extension of the Farlie-Gumbel-Morgenstern (FGM) family of copulas. Specifically, this extensi...

This paper presents a new model that monitors the basic network formation mechanisms via the attributes through time. It considers the issue of joint modeling of longitudinal inflated (0, 1)-support continuous and inflated count response variables. For joint model of mentioned response variables, a correlated generalized linear mixed model is studied. The fraction response is inflated in two points k and l (k < l) and a k and l inflated beta distribution is introduced to use as its distribution. Also, the count response is inflated in zero and we use some members of zero-inflated power series distributions, hurdle-at-zero, members of zero-inflated double power series distributions and zero-inflated generalized Poisson distribution as our count response distribution. A full likelihood-based approach is used to yield maximum likelihood estimates of the model parameters and the model is applied to a real social network obtained from an observational study where the rate of the ith node’s responsivene...

In a recent research, the quasi-likelihood estimation methodology was developed to estimate the regression effects in the Generalized BINMA(1) (GBINMA(1)) process. The method provides consistent pa...

In this paper, we introduce a new class of bivariate distributions whose marginals are beta-generated distributions. Copulas are employed to construct this bivariate extension of the beta-generated...

The comonotonicity and countermonotonicity provide intuitive upper and lower dependence relationship between random variables. This paper constructs the shuffle of min’s random variable approximations for a given Uniform [0, 1] random vector. We find the two optimal orders under which the shuffle of min’s random variable approximations obtained are shown to be extensions of comonotonicity and countermonotonicity. We also provide the rate of convergence of these random vectors approximations and apply them to compute value-at-risk.

This article investigates the ruin probabilities of a discrete time risk model with dependent claim sizes and dependent relation between insurance risks and financial risks. The risk-free and risky investments of an insurer lead to stochastic discount factors {θn}n ⩾ 1. The claim sizes are assumed to follow a one-sided linear process with independent and identically distributed (i.i.d.) innovations {ϵn}n ⩾ 1. The i.i.d. random pairs {(ϵn, θn)}n ⩾ 1 follow a common bivariate Sarmanov-dependent distribution. When the common distribution of the innovations is heavy tailed, we establish some asymptotic estimates for the ruin probabilities of this discrete time risk model.

The National Research Foundation, South Africa (ref. CPRR13090132066 grant nr 91497 & ref. CPRR160403161466 grant nr. 105840). M. Arashi’s research is supported in part by the National Research Foundation of South Africa (grant nr. 109214).

Competing risks models are of great importance in reliability and survival analysis. They are often assumed to have independent causes of failure in literature, which may be unreasonable. In this a...

In this article, we consider urn models under three types of sampling schemes in terms of the probability-generating functions. The tools are developed for the evaluation of the distributions arising from the urn models along with some examples. Furthermore, the distributions are investigated by making use of the Bell polynomials. The results presented here provide a wide framework for developing the theory of urn models. As examples, we propose new class of probability models, which are called multiple-player problems and examine their properties. Finally, we treat the parameter estimation problem in the waiting time distributions with a numerical example.

This article is concerned with a two-dimensional discrete time risk model based on exchangeable dependent claim occurrences. In particular, we obtain a recursive expression for the finite time non ruin probability under such a dependence among claim occurrences. For an illustration, we define a bivariate compound beta-binomial risk model and present numerical results on this model by comparing the corresponding results of the bivariate compound binomial risk model.

The cumulative past entropy (CPE) of order α, a dual measure of cumulative residual entropy (CRE) of order α, has recently been proposed as a suitable extension of CPE. In this article, we extend the definition of (dynamic) CPE of order α (DCPE(α)) to bivariate setup and obtain some of its properties including bounds. We also look into the problem of extending DCPE(α) for conditionally specified models. Several properties, including monotonicity, and bounds of DCPE(α) are obtained for conditional distributions. Along with some characterization results it is shown that the proposed generalized measure uniquely determines the distribution function. Moreover, we also propose a stochastic order based on this measure and prove interrelation with some existing stochastic orders.

Several attempts were made in the literature to generalize the notions based on univariate quantiles to higher dimensions. As quantile-based reliability concepts are receiving much attention, it is...

This article proposes a bivariate integer-valued autoregressive time-series model of order 1 (BINAR(1) with COM–Poisson marginals to analyze a pair of non stationary time series of counts. The interrelation between the series is induced by the correlated innovations, while the non stationarity is captured through a common set of time-dependent covariates that influence the count responses. The regression and dependence effects are estimated using generalized quasi-likelihood (GQL) approach. Simulation experiments are performed to assess the performance of the estimation algorithms. The proposed BINAR(1) process is applied to analyze a real-life series of day and night accidents in Mauritius.

Recurrent event data often arise in longitudinal studies. In many applications, subjects may experience two different types of events alternatively over time or a pair of subjects may experience recurrent events of the same type. Medical advances have made it possible for some patients to be cured such that the disease of interest does not recur. In this article, we consider non parametric analysis of bivariate recurrent event data with cure fraction. Using the inverse-probability weighted (IPW) approach, we propose non parametric estimators for the proportion of cured patients and for the joint distribution functions of bivariate recurrence times of the uncured ones. The asymptotic properties of the proposed estimators are established. Simulation study indicates that the proposed estimators perform well in finite samples.

This paper deals with bivariate Farlie–Gumbel–Morgenstern distributions. We build the TP2 (RR2) property of the residual lifetime and study the evolution of the dependence of the residual l...

This paper shows that the single risk duration model with two event types is a limiting case of bivariate dependent competing risks model, where the joint distribution of event times are degenerate. Then a new test is proposed for the null hypothesis of single risk against dependent competing risks model under the proportional hazard model assumption.

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 construction approach. Distributional properties for such bivariate distributions are investigated. Parameter estimation strategies for the models are discussed, as are the consequences of fitting two of the models to a particular data set involving the proportion of foggy days at two different airports in Colombia.

Copulas have proved to be very successful tools for the flexible modeling of dependence. Bivariate copulas have been deeply researched in recent years, while building higher-dimensional copulas is still recognized to be a difficult task. In this paper, we study the higher-dimensional dependent reliability systems using a type of decomposition called “vine,” by which a multivariate distribution can be decomposed into a cascade of bivariate copulas. Some equations of system reliability for parallel, series, and k-out-of-n systems are obtained and then decomposed based on C-vine and D-vine copulas. Finally, a shutdown system is considered to illustrate the results obtained in the paper.

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 proposed method are presented. Several structural properties of the bivariate weighted distributions including marginal distributions together with distributions of the minimum and maximum, evaluation of the reliability parameter and verification of total positivity of order two are also presented. In addition, we provide some multivariate extensions of the proposed models. A real life data set is used to show the applicability of these bivariate weighted distributions.

We consider an infinite buffer single server queue wherein batch interarrival and service times are correlated having a bivariate mixture of rational (R) distributions, where R denotes the class of distributions with rational Laplace–Stieltjes transform (LST), i.e., ratio of a polynomial of degree at most n to a polynomial of degree n. The LST of actual waiting time distribution has been obtained using Wiener–Hopf factorization of the characteristic equation. The virtual waiting time, idle period (actual and virtual) distributions, as well as inter-departure time distribution between two successive customers have been presented. We derive an approximate stationary queue-length distribution at different time epochs using the Markovian assumption of the service time distribution. We also derive the exact steady-state queue-length distribution at an arbitrary epoch using distributional form of Little’s law. Finally, some numerical results have been presented in the form of tables and figures.

This paper introduces a new class of bivariate lifetime distributions. Let {Xi}i ≥ 1 and {Yi}i ≥ 1 be two independent sequences of independent and identically distributed positive valued random variables. Define T1 = min (X1, …, XM) and T2 = min (Y1, …, YN), where (M, N) has a discrete bivariate phase-type distribution, independent of {Xi}i ≥ 1 and {Yi}i ≥ 1. The joint survival function of (T1, T2) is studied.

The paper entitled “Bivariate and Multivariate Normal Characterizations: A Brief Survey,” by Hamedani, which was published in 1992, covered the published characterizations of bivariate and multivar...

The popular generalized extreme value (GEV) distribution has not been a flexible model for extreme values in many areas. We propose a generalization – referred to as the Kumaraswamy GEV distribution – and provide a comprehensive treatment of its mathematical properties. We estimate its parameters by the method of maximum likelihood and provide the observed information matrix. An application to some real data illustrates flexibility of the new model. Finally, some bivariate generalizations of the model are proposed.

In this work, we define a new method of ranked set sampling (RSS) which is suitable when the characteristic (variable) Y of primary interest on the units is jointly distributed with an auxiliary characteristic X on which one can take its measurement on any number of units, so that units having record values on X alone are ranked and retained for making measurement on Y. We name this RSS as concomitant record ranked set sampling (CRRSS). We propose estimators of the parameters associated with the variable Y of primary interest based on observations of the proposed CRRSS which are applicable to a very large class of distributions viz. Morgenstern family of distributions. We illustrate the application of CRRSS and our estimation technique of parameters, when the basic distribution is Morgenstern-type bivariate logistic distribution. A primary data collected by CRRSS method is demonstrated and the obtained data used to illustrate the results developed in this work.

Motivated by Lee and Cha [The American Statistician 69 (2015) 221–230], we introduce 18 new families of discrete bivariate distributions. We give explicit expressions for their probability mass functions, cumulative distribution functions, product moments, and moment-generating functions. We reanalyze the football data in Lee and Cha (2015) and show that some of the newly proposed distributions provide better fits than the two families proposed by Lee and Cha.

In this paper, we establish the role of concomitants of order statistics in the unique identification of the parent bivariate distribution. From the results developed, we have illustrated by examples the process of determination of the parent bivariate distribution using a marginal pdf and the pdf of either of the concomitant of largest or smallest order statistic on the other variable. An application of the results derived in modeling of a bivariate distribution for data sets drawn from a population as well is discussed.