

Title of Thesis
Bayesian Analysis Of Mixture Distributions 
Author(s)
Muhammad Saleem 
Institute/University/Department
Details Department Of Statistics / Quaidiazam
University, Islamabad 
Session 2010 
Subject Statistics 
Number of Pages 142 
Keywords (Extracted from title, table of contents and
abstract of thesis) Classical, Relevant, Mixture, Bayes,
Distributions, Bayesian, Properties, Comparison, Subclass, Real,
Estimators, Analysis 
Abstract In this thesis, we
consider typeI mixtures of the members of a subclass of one
parameter exponential family.This subclass includes Exponential,
Rayleigh, Pareto, a Burr type XII and Power function distributions.
Except the Exponential, mixtures of distributions of this subclass
get either no or least attention in literature so far.
The elegant closed form expressions for the Bayes estimators of the
parameters of each of these mixtures are presented along with their
variances assuming uninformative and informative priors.The proposed
informative Bayes estimators emerge advantageous in terms of their
least standard errors.An extensive simulation study is conducted for
each of these mixtures to highlight the properties and comparison of
the proposed Bayes estimators in terms
of sample sizes, censoring rates, mixing proportions and different
combinations of the parameters of the component densities. A typeIV
sample consisting of ordinary typeI, right censored observations is
considered. Bayesian analysis of the real life mixture data sets is
conducted as an application of each mixture and some interesting
observations and comparisons have been observed.
The systems of nonlinear equations to evaluate the classical
maximum likelihood estimates, the components of the information
matrices, complete sample expressions, the posterior predictive
distributions and the equations for the evaluation of the Bayesian
predictive intervals are derived for each of these mixtures as
relevant algebra. The predictive intervals are evaluated in case of
the Rayleigh mixture only for a number of combinations of the
hyperparameters to look for a trend among the hyperparameters that
may lead towards an efficient estimation. 
