New Class Of Bivariate Distributions Research Articles

On the Bivariate Generalized Gamma-Lindley Distribution

ABSTRACT In this research paper, we propose a new class of bivariate distributions called Bivariate Generalized Gamma-Lindley (BGGL) distribution with four parameters. This model is a mixture of independent Gamma random variables and bivariate generalized Lindley distribution. We investigate various properties of the new bivariate distribution such as graphical representation, joint moments and correlation. Furthermore, we derive a measure of entropy of this bivariate distribution. We also derive the distributions of the random variables X 1 + X 2, X 1/(X 1 + X 2), X 1/X 2 and X 1 X 2 as well as the corresponding moment properties when X 1 and X 2 follow the BGGL distribution. Additionally, we address two approximations of the product of the proposed model and assess their goodness of fit. Next, we elaborate the expectation maximization (E.M) algorithm in order to estimate the BGGL model parameters. Finally, we provide two concrete examples to demonstrate the applicability of the results.

Bivariate Kumaraswamy Distribution Based on Conditional Hazard Functions: Properties and Application

A new class of bivariate distributions is deduced by specifying its conditional hazard functions (hfs) which are Kumaraswamy distribution. The interest of this model is positively, negatively, or zero correlated. Properties and local measures of dependence of the bivariate Kumaraswamy conditional hazard (BKCH) distribution are studied. The estimation of type parameters is considered by used the maximum likelihood and pseudolikelihood of the new class. A simulation study was performed to inspect the bias and mean squared error of the maximum likelihood estimators. Finally, an application is obtained to clarify our results with the maximum likelihood and pseudolikelihood. Also, the results are used to compare BKCH distribution with bivariate exponential conditionals (BEC) and bivariate Lindley conditionals hazard (BLCH) distributions.

From Symmetry to Asymmetry on the Disc Manifold: Modeling of Marion Island Data

The joint modeling of angular and linear observations is crucial as data of this nature are prevalent in multiple disciplines, for example the joint modeling of wind direction and another climatological variable such as wind speed or air temperature, the direction an animal moves and the distance moved, or wave direction and wave height. Hence, there is a need for developing flexible distributions on the hyper-disc, which has support of the interior of the hyper-sphere, as it allows for modeling the combination of angular and linear observations. This paper addresses this need by developing flexible distributions for the disc that have the ability to capture any inherent bimodality present in the data. A new class of bivariate distributions is proposed which has support on the unit disc in two dimensions that includes, as a special case, the existing Möbius distribution on the disc. This class is obtained by expressing the density function in a general form using a measurable function termed as generator. Special cases of this generator are considered to demonstrate the flexibility. By applying a conformal mapping to the generator function a new Möbius distribution class emanates. This class of bivariate distributions on the disc is the first to account for bimodality and skewness present in the data. The flexible behavior of the proposed models in terms of bimodality and skewness is graphically demonstrated. Preliminary evidential analysis of the wind data observed at Marion Island reveals the absence of unimodality in the data. The fit of the proposed models, which account for bimodality, to the Marion Island wind data were evaluated analytically and visually.

Bivariate Gumbel-G Family of Distributions: Statistical Properties, Bayesian and Non-Bayesian Estimation with Application

In this paper, a new class of bivariate distributions called the bivariate Gumbel-G family is proposed, whose marginal distributions are Gumbel-G families. Several of its statistical properties are derived. After introducing the general class, a special model of the new family is discussed in-detail. Bayesian and maximum likelihood techniques are used to estimate the model parameters. Simulation study is carried out to examine the bias and mean square error of Bayesian and maximum likelihood estimators. Finally, a real data set is analyzed for illustrative the flexibility of the proposed bivariate family.

On Bivariate Generalized Exponential-Power Series Class of Distributions

In this paper, we introduce a new class of bivariate distributions by compounding the bivariate generalized exponential and power-series distributions. This new class contains some new sub-models such as the bivariate generalized exponential distribution, the bivariate generalized exponential-poisson, -logarithmic, -binomial and -negative binomial distributions. We derive different properties of the new class of distributions. The EM algorithm is used to determine the maximum likelihood estimates of the parameters. We illustrate the usefulness of the new distributions by means of an application to a real data set.

On Bivariate Generalized Linear Failure Rate-Power Series Class of Distributions

Recently, it has been observed that the bivariate generalized linear failure rate distribution can be used quite effectively to analyze lifetime data in two dimensions. This paper introduces a more general class of bivariate distributions. We refer to this new class of distributions as bivariate generalized linear failure rate-power series model. This new class of bivariate distributions contains several lifetime models such as: generalized linear failure rate-power series, bivariate generalized linear failure rate, and bivariate generalized linear failure rate geometric distributions as special cases among others. The construction and characteristics of the proposed bivariate distribution are presented along with estimation procedures for the model parameters based on maximum likelihood. The marginal and conditional laws are also studied. We present an application to the real data set, where our model provides a better fit than other models.

Archimedean-based Marshall-Olkin Distributions and Related Dependence Structures

A new class of bivariate distributions is introduced that extends the Generalized Marshall-Olkin distributions of Li and Pellerey (2011). Their dependence structure is studied through the analysis of the copula functions that they induce. These copulas, that include as special cases the Generalized Marshall-Olkin copulas and the Scale Mixture of Marshall-Olkin copulas (see Li, 2009),are obtained through suitable distortions of bivariate Archimedean copulas: this induces asymmetry, and the corresponding Kendall's tau as well as the tail dependence parameters are studied.

Baker- Lin-Huang Type Bivariate Distributions Based on Order Statistics

Baker (2008) introduced a new class of bivariate distributions based on distributions of order statistics from two independent samples of size n. Lin and Huang (2010) discovered an important property of Baker’s distribution and showed that the Pearson’s correlation coefficient for this distribution converges to maximum attainable value, i.e., the correlation coefficient of the Fréchet upper bound, as n increases to infinity. Bairamov and Bayramoglu (2013) investigated a new class of bivariate distributions constructed by using Baker’s model and distributions of order statistics from dependent random variables, allowing higher correlation than that of Baker’s distribution. In this article, a new class of Baker’s type bivariate distributions with high correlation are constructed based on distributions of order statistics by using an arbitrary continuous copula instead of the product copula.

On Marshall–Olkin type distribution with effect of shock magnitude

In classical Marshall–Olkin type shock models and their modifications a system of two or more components is subjected to shocks that arrive from different sources at random times and destroy the components of the system. With a distinctive approach to the Marshall–Olkin type shock model, we assume that if the magnitude of the shock exceeds some predefined threshold, then the component, which is subjected to this shock, is destroyed; otherwise it survives. More precisely, we assume that the shock time and the magnitude of the shock are dependent random variables with given bivariate distribution. This approach allows to meet requirements of many real life applications of shock models, where the magnitude of shocks is an important factor that should be taken into account. A new class of bivariate distributions, obtained in this work, involve the joint distributions of shock times and their magnitudes. Dependence properties of new bivariate distributions have been studied. For different examples of underlying bivariate distributions of lifetimes and shock magnitudes, the joint distributions of lifetimes of the components are investigated. The multivariate extension of the proposed model is also discussed.

A multivariate extension of Sarhan and Balakrishnan’s bivariate distribution and its ageing and dependence properties

A new class of bivariate distributions (NBD) was recently introduced by Sarhan and Balakrishnan [A.M. Sarhan, N. Balakrishnan, A new class of bivariate distributions and its mixture, J. Multivariate Anal. 98 (2007) 1508–1527]. In this note, we give the joint survival function of a multivariate extension of the NBD, which is not an absolutely continuous multivariate distribution, and its marginal and extreme order statistics distributions are also derived. The multivariate ageing and dependence properties of the proposed n -dimensional distribution are also discussed, and then we analyze the stochastic ageing of its marginals and its minimum and maximum order statistics.

A new class of positively quadrant dependent bivariate distributions with Pareto

This paper presents a new class of bivariate distributions with Pareto of Marshall-Olkin type. The approach in this paper uses a shock model to derive a class of positively quadrant dependent of bivariate distributions with Pareto. Further this class generalizes the bivariate Pareto distributions which obtained by Muliere and Scarsini (1987). The dependence structure and main other properties of the bivariate distributions with Pareto are investigated. The difference among the dependent and independent cases of bivariate Pareto distributions is discussed.

A new class of bivariate distributions and its mixture

A new class of bivariate distributions is presented in this paper. The procedure used in this paper is based on a latent random variable with exponential distribution. The model introduced here is of Marshall–Olkin type. A mixture of the proposed bivariate distributions is also discussed. The results obtained here generalize those of the bivariate exponential distribution present in the literature.

Bivariate semi α-Laplace distribution and processes

The Laplace distribution is considered as a better choice for modeling whenever data exhibit high kurtosis and heavier tails than Gaussian tails. Even though this is the case, not much work has been done on bivariate Laplace distribution. In this work, we introduce and study a new class of bivariate distributions called bivariate semi α-Laplace distribution, containing bivariate Laplace distributions. Three characterizations of bivariate semi α-Laplace distribution are obtained. Relation with bivariate semi stable distribution is established. An autoregressive model with bivariate semi α-Laplace marginal distributions is developed.

On one class of bivariate distributions

A new class of bivariate distributions is constructed from a given family of distributions. The approach is based on the corresponding exponential representation, which generalizes the well-known exponential representation for the univariate survival function.

Bivariate Distributions with Given Extreme Value Attractor

A new class of bivariate distributions is introduced and studied, which encompasses Archimedean copulas and extreme value distributions as special cases. Its dependence structure is described, its maximum and minimum attractors are determined, and an algorithm is given for generating observations from any member of this class. It is also shown how it is possible to construct distributions in this family with a predetermined extreme value attractor. This construction is used to study via simulation the small-sample behavior of a bivariate threshold method suggested by H. Joe, R. L. Smith, and I. Weissman (1992, J. Roy. Statist. Soc. Ser. B54, 171–183) for estimating the joint distribution of extremes of two random variates.

A class of Large Sample Tests for Bivariate Exponentiality Versus Bifra and Bnbu (to, to) Alternatives

Two related problems are considered here. First, a class of tosts is proposed for testing bivariate exponentiality (BVE) against the class of bivariate increasing failure rate average (IFRA) distributions. Secondly, we propose a test of BVE versus bivariate new better than used of ago (to to)),a new class of bivariate distributions introduced here. The PITMAN asymptotic relative efficiencies of these tests with respect to BASU and EBRAHIMI's (1984) bivariate new better than used (BNBU) test, compared

Frank's Family of Bivariate Distributions

This paper examines the properties of a new class of bivariate distributions whose members are stochastically ordered and likelihood ratio dependent. The proposed class can be used to construct bivariate families of distributions whose marginals are arbitrary and which include the Fréchet bounds as well as the distribution corresponding to independent variables. Three nonparametric estimators of the association parameter are suggested and Monte Carlo experiments are used to compare their small-sample behaviour to that of the maximum likelihood estimate.

Frank's family of bivariate distributions

SUMMARY This paper examines the properties of a new class of bivariate distributions whose members are stochastically ordered and likelihood ratio dependent. The proposed class can be used to construct bivariate families of distributions whose marginals are arbitrary and which include the Frechet bounds as well as the distribution corresponding to independent variables. Three nonparametric estimators of the association parameter are suggested and Monte Carlo experiments are used to compare their small-sample behaviour to that of the maximum likelihood estimate.