Estimating Reliability Functions of a Weighted Pareto-Poisson Distribution with the Application
DOI:
https://doi.org/10.62933/mmjkw787Keywords:
Weighted Pareto – Poisson distribution , reliability , Weighted Pareto – Poisson disPercentiles , Downhill simplex algorithm , 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 distribution Pareto-Poisson is distribution with four parameters . In the research, the parameters and distribution reliability function were estimated in this research using two methods, namely Percentiles Estimators Method and Estimation with Downhill simplex algorithm. The mean square error measurement was used to compare the results of the estimates obtained from the two methods, in addition to give 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. As for the applied aspect, the life times of thalassemia patients were studied for a sample size of 60 people in the Specialized Center for Hematology in the Diyala Health Department, where the Downhill simplex method was used to estimate the parameters and the reliability function, as it was the best in simulation
References
[1] A. A. Azzallini’s class of distributions which includes the normal ones. JSTOR.1985; 12(2): 171-178.
[2] A. El-Shahhat The Pareto–Poisson Distribution: Characteristics, Estimations and Engineering Applications. IJS. 2022 December; 85(1): 1-42
[3] A. Moraglio and C. Johnson, ‘Geometric Generalization of the Nelder-Mead Algorithm’ Proc. 10th Eur. Conf. Evol. Comput. in Combin. Optim. (EvoCOP 2010), Istanbul, Turkey, Apr. 7-9, 2010, pp. 131-142.
[4] A. Moraglio and J. Togelius, ‘Geometric Nelder-Mead Algorithm for the permutation representation’, in "Proceedings of the IEEE Congress on Evolutionary Computation" Aug. 2010, pp. 1–8.
[5] B. K. Fahad, ‘Choose the Best Method for Estimation the Parameters of Probability Kappa Distribution With practical application’, Thesis, University of Karbala, Karbala, 2018.
[6] E. Q. Abdel Rahman find better estimate of the parameters and reliability function of the compound distribution (Pareto – Truncated Exponential) With practical application. Al-Basra: Al-Basra University; 2022.
[7] L. A. J. D. A. Helfi, ‘Comparison of the methods of estimating the parameters and reliability function for the lambda distribution with four parameters with practical application’, Thesis, University of Baghdad, Baghdad, 2015.
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Copyright (c) 2025 Inam Abdul Rahman Noaman, Duha Kareem Mahmood (Author)
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