Abstract
This paper deals with the problem of parameters estimation of the Exponential-Geometric (EG) distribution based on progressive type-II censored data. It turns out that the maximum likelihood estimators for the distribution parameters have no closed forms, therefore the EM algorithm are alternatively used. The asymptotic variance of the MLEs of the targeted parameters under progressive type-II censoring is computed along with the asymptotic confidence intervals. Finally, a simple numerical example is given to illustrate the obtained results.
Highlights
With no doubt, the analysis of lifetime data has become a very important subject in different scientific disciplines
We mainly study the properties of the EG distribution and estimate the unknown parameters based on progressive type-II censored data
The simulation study was conducted using different censoring schemes and different samples sizes to figure out the maximum likelihood estimators of the EG distribution (MLEs) numerically
Summary
The analysis of lifetime data has become a very important subject in different scientific disciplines. The parameter estimation is a challenging task especially in the case of compounded distributions. For this reason, computational methods are often sought, see for example, [3] and references therein for a comprehensive review of results in this direction. [9], [10] studied parameter estimation under progressive type-II censored data using the Expectation-Maximization (EM) algorithm. We mainly study the properties of the EG distribution and estimate the unknown parameters based on progressive type-II censored data. The rest of the paper is structured as follows: In Section 2, the maximum likelihood estimators of the EG distribution (MLEs) based on progressive type-II censored data will be derived, using the EM algorithm. M-step: Find θt+1 in Θ such that Q( θt+1; θt) ≥ Q(θ; θt) for all θ ∈ Θ
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