Abstract
The study of semiparametric families is useful because it provides methods of extending families for adding flexibility in fitting data. The main aim of this paper is to introduce a class of bivariate semiparametric families of distributions. One especial bivariate family of the introduced semiparametric families is discussed in details with its sub-models and different properties. In most of the cases the joint probability distribution, joint distribution and joint hazard functions can be expressed in compact forms. The maximum likelihood and Bayesian estimation are considered for the vector of the unknown parameters. For illustrative purposes a data set has been re-analyzed and the performances are quite satisfactory. A simulation study is performed to see the performances of the estimators.
Highlights
To mathematically describe any family of distributions, various alternative functions are in common use
Bivariate Marshal-Olkin family of great importance for understanding and analyzing the failure time of two variables interacting together, because it takes into consideration all different scenarios of the random variables.The main aim of this paper is to introduce a bivariate extension of the semiparametric families of distributions implies in such a way that their marginals follow univariate semiparametric distributions
Let FB be a baseline distribution function with cumulative reversed hazard function RB = log FB Suppose that SURP(·; α) is defined in terms of FB by FURP (x; α) = [FB(x)]α = exp {αRB (x)}, α > 0
Summary
To mathematically describe any family of distributions, various alternative functions are in common use These functions include distribution functions, survival functions, densities; hazard functions, reversed hazard functions, cumulative hazard and cumulative reversed hazard functions. Semiparametric families of distributions which are distinguished by having a parameter that itself a distribution function These families have a real valued parameter; a possible procedure making use of a semiparametric model is to first select the parameter that is a distribution function. This distribution function is called the underlying distribution.
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