A new bivariate generalized Poisson distribution

In this paper, a new bivariate generalized Poisson distribution (GPD) that allows any type of correlation is defined and studied. The marginal distributions of the bivariate model are the univariate GPDs. The parameters of the bivariate distribution are estimated by using the moment and maximum likelihood methods. Some test statistics are discussed and one numerical data set is used to illustrate the applications of the bivariate model.     

Characterizations of bivariate distributions using concomitants of record values

In this paper, we consider a family of bivariate distributions which is a generalization of the Morgenstern family of bivariate distributions. We have derived some properties of concomitants of record values which characterize this generalized class of distributions. The role of concomitants of record values in the unique determination of the parent bivariate distribution has been established. We have also derived properties of concomitants of record values which characterize each of the following families viz Morgenstern family, bivariate Pareto family and a generalized Gumbel’s family of bivariate distributions. Some applications of the characterization results are discussed and important conclusions based on the characterization results are drawn.     

A new bivariate distribution in natural exponential family

We propose a new bivariate distribution following a GLM form i.e., natural exponential family given the constantly correlated covariance matrix. The proposed distribution can represent an independent bivariate gamma distribution as a special case. In order to derive the distribution we utilize an integrating factor method to satisfy the integrability condition of the quasi-score function. The derived distribution becomes a mixture of discrete and absolute continuous distributions. The proposal of our new bivariate distribution will make it possible to develop some bivariate generalized linear models. Further the discrete correlated bivariate distribution will also arise from an independent bivariate Poisson mass function by compounding our proposed distribution (Iwasaki and Tsubaki, 2002).Received March 2003     

On three and five parameter bivariate beta distributions

Summary In this paper two bivariate beta distributions have been studied. The five parameter bivariate beta distribution is derived from the Morgenstern-system of curves while the three parameter distribution is the bivariate Dirichlet distribution. In both cases the distributions of the product and the quotient of random variables are derived and other properties are also studied.     

Bivariate and multivariate scaled association models. An application to homogamy of social origin and education in Hungary between 1930 and 1979

In this article we compare bivariate and multivariate models for homogamy of social origin and education to test whether bivariate models of homogamy lead to biased results. We use data on Hungarian couples married between 1930 and 1979 and loglinear models of scaled association. The results indicate some differences between bivariate and multivariate analyses. At each point of time bivariate models overestimate homogamy, both with respect to education and social origin. However, results on trends in time do not differ much between the two analyses. The exception is the period 1940–1959, in which bivariate analysis showed decreasing educational homogamy, and multivariate analysis showed an increasing trend. The latter finding can be explained by declining homogamy of social origin, as well as the weaker reproduction and cross-effects in this period.     

Bivariate exponentiated‐exponential geometric regression model

A bivariate exponentiated‐exponential geometric regression model that allows negative, zero, or positive correlation is defined and studied. The model can accommodate under‐ or over‐dispersed count data. The regression model is based on the univariate exponentiated‐exponential geometric distribution, and the marginal means of the bivariate model are functions of the explanatory variables. The parameters of the bivariate regression model are estimated by using the maximum likelihood method. Some test statistics including goodness of fit are discussed. A simulation study is conducted to compare the model with the bivariate generalized Poisson regression model. One numerical data set is used to illustrate the application of the regression model.     

A bivariate Poisson count data model using conditional probabilities

The applied econometrics of bivariate count data predominantly focus on a bivariate Poisson density with a correlation structure that is very restrictive. The main limitation is that this bivariate distribution excludes zero and negative correlation. This paper introduces a new model which allows for a more flexible correlation structure. To this end the joint density is decomposed by means of the multiplication rule in marginal and conditional densities. Simulation experiments and an application of the model to recreational data are presented.     

A new family of bivariate max-infinitely divisible distributions

In this article we discuss the asymptotic behaviour of the componentwise maxima for a specific bivariate triangular array. Its components are given in terms of linear transformations of bivariate generalised symmetrised Dirichlet random vectors introduced in Fang and Fang (Statistical inference in elliptically contoured and related distributions. Allerton Press, New York, 1990). We show that the componentwise maxima of such triangular arrays is attracted by a bivariate max-infinitely divisible distribution function, provided that the associated random radius is in the Weibull max-domain of attraction.     

Large sample properties for a class of copulas in bivariate survival analysis

This work is concerned with asymptotic properties of the bivariate survival function estimator using the functional relationship between marginal survival functions and a class of copulas for the dependence structure. Specifically, we study consistency and weak convergence of the bivariate survival function estimator obtained considering a two-step procedure of estimation. The obtained results are found from a key decomposition of the bivariate survival function in quantities that can be studied separately. In particular, we use relating results to almost sure and weak convergence of estimators, almost sure convergence of uniformly equicontinuous functions, and the delta method for functionals.     

Characterizations and Modelling of Multivariate Lack of Memory Property

In this article we establish characterizations of multivariate lack of memory property in terms of the hazard gradient (whenever exists), the survival function and the cumulative hazard function. Based on one of these characterizations we establish a method of generating bivariate lifetime distributions possessing bivariate lack of memory property (BLMP) with specified marginals. It is observed that the marginal distributions have to satisfy certain conditions to be stated. The method generates absolutely continuous bivariate distributions as well as those containing a singular component. Bivariate exponential distributions due to Proschan and Sullo (Reliability and biometry, pp 423–440, 1974), Freund (in J Am Stat Assoc 56:971–977, 1961), Block and Basu (J Am Stat Assoc 89:1091–1097, 1974) and Marshall and Olkin (J Am Math Assoc 62:30–44, 1967) are generated as particular cases among others using the proposed method. Some other distributions generated using the method may be of practical importance. Shock models leading to bivariate distributions possessing BLMP are given. Some closure properties of a class of univariate failure rate functions that can generate distributions possessing BLMP and of the class of bivariate survival functions having BLMP are studied.     

Non-normal bivariate densities with normal marginals and linear regression functions *

Summary It is well known that for a bivariate density in order to be bivariate normal, the possession of univariate normal marginal densities alone is not sufficient. In this paper it will be shown by means of some counterexamples that the additional requirement of linearity of the regression functions does not supply a sufficient condition either.     

A unified approach to bivariate discrete distributions

Here we introduce a bivariate generalized hypergeometric factorial moment distribution (BGHFMD) through its probability generating function (p.g.f.) whose marginal distributions are the generalized hypergeometric factorial moment distributions introduced by Kemp and Kemp (Bull Int Stat Inst 43:336–338,1969). Well-known bivariate versions of distributions such as binomial, negative binomial and Poisson are special cases of this distribution. A genesis of the distribution and explicit closed form expressions for the probability mass function of the BGHFMD, its factorial moments and the p.g.f.’s of its conditional distributions are derived here. Certain recurrence relations for probabilities, moments and factorial moments of the bivariate distribution are also established.     

Probabilistic forecasting in day-ahead electricity markets: Simulating peak and off-peak prices

In this article we include dependency structures for electricity price forecasting and forecasting evaluation. We work with off-peak and peak time series from the German-Austrian day-ahead price; hence, we analyze bivariate data. We first estimate the mean of the two time series, and then in a second step we estimate the residuals. The mean equation is estimated by ordinary least squares and the elastic net, and the residuals are estimated by maximum likelihood. Our contribution is to include a bivariate jump component in a mean reverting jump diffusion model in the residuals. The models’ forecasts are evaluated with use of four different criteria, including the energy score to measure whether the correlation structure between the time series is properly included. It is observed that the models with bivariate jumps provide better results with the energy score, which means that it is important to consider this structure to properly forecast correlated time series.     

Fisher information in order statistics and their concomitants in bivariate censored samples

We evaluate the Fisher information (FI) contained in a collection of order statistics and their concomitants from a bivariate random sample. Special attention is given to Type II censored samples. We present a general decomposition result and recurrence relations that are useful in finding the FI in all types of censored samples. We also obtain some asymptotic results for the FI. For the bivariate normal parent, we obtain explicit and asymptotic expressions for the elements of the FI matrix for Type II censored samples. We discuss implications of our findings on inference on the bivariate normal parameters, especially on the correlation. The first author’s research was supported in part by National Institutes of Health, USA, Grant # M01 RR00034 and the second author’s research was supported by a training grant from the Egyptian government     

Modelling and Estimation for Bivariate Financial Returns

Maximum likelihood estimates are obtained for long data sets of bivariate financial returns using mixing representation of the bivariate (skew) Variance Gamma (VG) and two (skew) t distributions. By analysing simulated and real data, issues such as asymptotic lower tail dependence and competitiveness of the three models are illustrated. A brief review of the properties of the models is included. The present paper is a companion to papers in this journal by Demarta & McNeil and Finlay & Seneta.     

Estimating a generalized correlation coefficient for a generalized bivariate probit model

In this paper we consider semiparametric estimation of a generalized correlation coefficient in a generalized bivariate probit model. The generalized correlation coefficient provides a simple summary statistic measuring the relationship between the two binary decision processes in a general framework. Our semiparametric estimation procedure consists of two steps, combining semiparametric estimators for univariate binary choice models with the method of maximum likelihood for the bivariate probit model with nonparametrically generated regressors. The estimator is shown to be consistent and asymptotically normal. The estimator performs well in our simulation study.     

Bivariate semi-Pareto minification processes

Marshall-Olkin bivariate semi-Pareto distribution (MO-BSP) and Marshall-Olkin bivariate Pareto distribution (MO-BP) are introduced and studied. AR(1) and AR(k) time series models are developed with minification structure having MO-BSP stationary marginal distribution. Various characterizations are investigated.Acknowledgements. The authors thank the Editor and the referee for their valuable suggestions which led to an improved version of the original paper. The first author is grateful to the University Grants Commission of India for the support under Teacher Fellowship Scheme.     

Non-causality in bivariate binary time series

In this paper we develop a dynamic discrete-time bivariate probit model, in which the conditions for Granger non-causality can be represented and tested. The conditions for simultaneous independence are also worked out. The model is extended in order to allow for covariates, representing individual as well as time heterogeneity. The proposed model can be estimated by Maximum Likelihood. Granger non-causality and simultaneous independence can be tested by Likelihood Ratio or Wald tests. A specialized version of the model, aimed at testing Granger non-causality with bivariate discrete-time survival data is also discussed. The proposed tests are illustrated in two empirical applications.     

On bivariate generalized binomial and negative binomial distributions

The present paper deals with two types of generalized general binomial (binomial or negative binomial) distributions: (i) a univariate general binomial generalized by a bivariate distribution and (ii) a bivariate general binomial generalized by two independent univariate distributions. The probabilities, moments, conditional distributions and regression functions for these distributions are obtained in terms of bipartitional polynomials. Moreover recurrence relations for the probabilities and moments, independent of the bipartitional polynomials, are given. Finally these general results are applied to the (i) Binomial-Bivariate Poisson and (ii) Bivariate Binomial-Poissons distributions.     

On the construction of multivariate permutation tests in the two–sample case

This paper is concerned with multivariate generalizations of two–sample rank tests, the bivariate Wilcoxon test in particular.