Semi-Parametric Likelihood Functions for Bivariate Survival Data

Because of the numerous applications, characterization of multivariate survival distributions is still a growing area of research. The aim of this thesis is to investigate a joint probability distribution that can be derived for modeling nonnegative related random variables. We restrict the marginals to a specified lifetime distribution, while proposing a linear relationship between them with an unknown (error) random variable that we completely characterize. The distributions are all of positive supports, but one class has a positive probability of simultaneous occurrence. In that sense, we capture the absolutely continuous case, and the Marshall-Olkin type with a positive probability of simultaneous event on a set of measure zero. In particular, the form of the joint distribution when the marginals are of gamma distributions are provided, combining in a simple parametric form the dependence between the two random variables and a nonparametric likelihood function for the unknown random variable. Associated properties are studied and investigated and applications with simulated and real data are given

The Distribution Of The Sum Of Independent Product Of Bernoulu And Exponential

The product of the independent Bernoulli and exponential random variables (rv\u27s), has received great attention in recent literature, in particular because of its applications in network traffic, computer communications, and health sciences. Hoxoever, the behavior of the sum of such independent rvs has not been fully explored. In this article, we present the probability density function (PDF) of tlie product of exponential and Bernoulli sum as a mixture of two types of distribution functions: the Dirac delta and gamma type distributions. The statistical properties of the sum, such as its survival function, moment generating function, and Laplace transform are derived. © Taylor & Francis Group, LLC

Efficient semi-parametric estimation for marginal correlated small sampled data

We propose a bivariate exponential model with exponential marginal densities, correlated via a latent random variables and with finite probability of simultaneous occurrence. We extend this model to a bivariate Erlang type distributions with same shape parameter. We propose an estimation method and illustrate our results with real data