التقدير البيزي لتوزيع (Chen-Truncate Poisson) في ظل دوال خسارة مختلفة مع التطبيق

RP-Bayesian Estimation of the (Chen-Truncate Poisson) Distribution Under Different Loss Functions With Application.pdf

Abstract:
The process of fitting probability distributions is one of the important operations because it is an important tool in increasing the flexibility of the basic distributions. The importance of installation has increased in the past few years, This is due to the failure to accurately represent the classical distributions of real data in many applied data, especially those related to machines. In this thesis, the method was adopted (Adamidis،1998) in constructing a proposed probability distribution(Chen-Truncate Poisson),The statistical characteristics of the distribution were obtained Chen Including the moment, The function that generates the moments and other properties that were not reached in previous research and studies, has been found The cumulative probability density function of the proposed distribution (Chen-Truncate Poisson) and some special functions such as the risk and reliability function, As the parameters were estimated for the proposed distribution, among which the reliability function was found using Bayesian methods represented by the Standard Informative Bayesian method and the Expected Bayesian method by using Squared Error Loss function and General Entropy Loss Function, The approximate method suggested by the researcher was relied upon Lindley which is called Lindley Approximation style, In solving nonlinear equations that cannot be solved using numerical analysis methods, By employing a simulation Monte Carlo method by using a program MATLAB For the purpose of evaluating the performance of parameter estimators and reliability function estimators, the proposed distribution of all methods, This is done by conducting several experiments with different sample sizes, small, medium and large, and by adopting the standard of Mean Squares Integral Error IMSE For the comparison between samples sizes and the approved estimation methods, the results showed a preference for the Bayesian expectation method under the entropy loss function over the rest of the estimation methods. has been applied Chen-Poisson Distribution on real data, Obtained from the Ministry of Electricity – Diesel station east of Holy Karbala, which contains 72 engines , represent Engine running times until the failure.