Abstract:
Pareto distribution has vast application in different fields of medical and
engineering sciences. In this thesis, we have proposed a new Reflected Pareto
Distribution (RPD) using Cohen (1973) to reflect the parameter of distribution. We
derive different mathematical properties such as mean, variance, rth moment.
Reliability measures are also discussed including Survival Function, Hazard
function and reversed hazard function. The method of Maximum Likelihood
Estimator and Modified maximum likelihood estimator is used to estimate the
model parameters. We used three different data sets to show the performance of
Reflected Pareto distribution over already existing probability distributions. We
also construct the control charts to monitor the shape parameter for reliability
processes using Shewhart control chart and Exponentially weighted moving
averages control chart. We compare the performance of maximum likelihood
estimator and modified maximum likelihood estimator for the shape parameter of
Reflected Pareto distribution.