Estimating the parameters and reliability functions of a weighted probability distribution
DOI:
https://doi.org/10.24237/Keywords:
Weighted (Pareto – Poisson) distribution, Parameter estimation, Maximum Likelihood Method, Moment Method, SimulationAbstract
This research is concerned with studying the estimation of the parameters and reliability function of a weighted probability distribution consisting of a combination of the Pareto distribution and the Poisson distribution. It is called the weighted Pareto-Poisson distribution, which is a new probability distribution for life time.
The weighted (Pareto-Poisson) distribution is a four-parameter distribution . In the research, the parameters and distribution reliability function were estimated in this research using two methods, namely the maximum likelihood method and the moments method. The mean square error measurement was used to compare the results of the estimates obtained from the two methods, in addition to giving three sets of initial default values for the distribution parameters and three sizes for the samples used in the estimation (30, 60, 90). The sizes are considered small, medium, and large. The process was repeated. 1000 times. In addition, five failure times were taken to estimate the reliability function. The Python programming language was used to simulate this data distribution.
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