Maximum Likelihood Estimation of Parameters For Poisson-Exponential Distribution Under Progressive Type I Interval Censoring
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Date
2020
Authors
Situma, Peter Tumwa
Journal Title
Journal ISSN
Volume Title
Publisher
Kenyatta University
Abstract
The problem of estimating the parameters of Poisson-Exponential distribution under
progressive type-I interval censoring is considered. Previously, researchers have considered
maximum likelihood estimation under the progressive type-I interval censoring scheme for
various distribution, but no research has considered Poisson-Exponential. Poisson-Exponential
is a two-parameter lifetime distribution having an increasing hazard function. It has been
applied in complementary risks problems in latent risks, that is in scenarios where maximum
lifetime values are observed but information concerning factors accounting for component
failure is unavailable, which can be experienced in fields such as public health. Under
progressive type I interval censoring, observations are known within two consecutively prearranged times and items would be withdrawn at pre-scheduled time points. Progressive typeI interval censoring scheme is most suitable in those cases where the continuous examination
is impossible. Based on progressive type I interval censored data, the Maximum Likelihood
Estimates of Poisson-Exponential parameters are obtained via the Expectation-Maximization
algorithm. The Expectation-Maximization algorithm is preferred as it has been confirmed to
be a more superior tool when dealing with incomplete data sets having missing values, or
models having truncated distributions. In this study, the estimates derived are compared
through simulation based on bias and the mean squared error under different censoring schemes
and parameter values. It is concluded that for an increasing sample size, the estimated values
of the parameters tend to the true value. Among the four censoring schemes considered, the
third scheme p(3) provides the most precise and accurate results followed by p(4), p(1) and lastly
p(2)
Description
A Research Project Submitted In Partial Fulfilment 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
Keywords
Estimation of Parameters, Poisson-Exponential Distribution, Type I Interval Censoring