Maximum Likelihood Estimation of Parameters for Kumaraswamy Distribution Based on Progressive Type Ii Hybrid Censoring Scheme
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Date
2023
Authors
Jaffer, Meymuna Shariff
Journal Title
Journal ISSN
Volume Title
Publisher
Kenyatta University
Abstract
The project considers the MLEs for Kumaraswamy distribution centered on PTHCS using the
expectation maximization algorithm. A two parameter Kumaraswamy distribution can be applied
in natural phenomena that have outcomes with an upper and a lower bound. Kumaraswamy
distribution remains of keen consideration in disciplines such as economics, hydrology and
survival analysis. The field of survival analysis has advanced over the years and extensive
research has been undertaken. Previously, maximum likelihood estimator of various distributions
has been done using methods like Newton-Raphson, Bayesian inference and EM algorithm. The
application of these techniques in survival analysis is mainly intended to save on costs and
duration taken in an experiment. Based on PTHCS, MLEs of Kumaraswamy distribution are
obtained via EM algorithm. EM algorithm has been utilized in manipulation of missing data as it
is a more superior method when handling incomplete data. Comparison of different
combinations of censoring schemes with respect to the MSEs and biases at fixed parameters of
and are obtained through simulation. It is observed that in the three censoring schemes, for
an increasing sample size, the MSEs and biases are generally decreasing. Eventually, an
illustration with real life data set is provided and it illustrates how MLEs works in practice under
different censoring schemes. It is apparent from the observations made that the estimated values
of ^ and ^ increases from scheme one to scheme three.
Description
A Research Project Submitted in Partial Fulfillment of the Requirements for the Award of the Degree of Master of Science
(Statistics) in the School of Pure and Applied Science of Kenyatta University, June 2023
Keywords
Maximum Likelihood Estimation, Parameters for Kumaraswamy Distribution, Progressive Type Ii Hybrid Censoring Scheme