Abstract:
This thesis deals with statistical analysis of the lifetime mixture models under Bayesian
approach. Type-I right censored sampling scheme is used. Choice of distribution is made
keeping in view the originality and applicability. These contain Inverse Rayleigh, Gun-
mbel Type-II, Frechet, Inverse Weibull and Inverted Exponential distributions. These
mixtures distribution have not been explored so far in Bayesian setup.
Bayes estimators for the parameters of the mixture models are derived in closed
form using type-I right censoring. To conduct Bayesian analysis, informative and non-
informative priors are considered while three di erent loss functions, Squared error loss
function, Precautionary loss function and DeGroot loss function are employed. A thor-
ough simulation study is made to scrutinize the properties of proposed Bayes estimators.
For the Inverse Weibull model, when all the parameters are unknown, Bayes estimators
can not be gained in closed form, thus importance sampling technique is used to get
the Bayes estimate in this case. For the elicitation of hyperparametrs , we used prior
predictive and prior mean method. Limiting expressions of the Bayes estimators and
their corresponding posterior risks are also derived. For the Inverse Weibull distribution,
Bayes estimators and the posterior risks for reliability function are also discussed.
Graphical representation of the simulation analysis results are also presented for each
mixture model. Applications of these mixture models are also o ered by applying a real
data set in each case.
