تقدير دالة المعولية للتوزيع المركب "باريتو - الاسي المبتور"

Abstract EN

In this research, the parameters of the distribution of a new compound (Pareto-amputated ace) resulting from the composition of the Pareto distributions of the first type and the truncated exponential were estimated, and the reliability function was estimated because with the development of technology and the frequent use of machines and machines, it became necessary to study the holidays and stops that occur in the machines, but due to the complexity of the real data, there was difficulty in the single distribution workers because they do not give an appropriate description of the behavior of the real data; Therefore, synthesis methods for probability distributions were proposed to produce more appropriate distributions to describe the behavior of the data, study the cause of sudden holidays and stops, and find solutions to solve them.

He used four methods of estimation, namely (the greatest possibility, moments, fractional estimators, and the Bayes estimator (non-informational method)), and the language of statistical programs R was used by issuing (4.0.5) in simulation programs and through the use of a hypothetical sample representing different default values for the parameters and three different sizes of samples, which are (100,50,25) The sample sizes are relatively large to represent the characteristics of the population better than small samples and also increase the chance of rejecting the null hypothesis when it is false (i.e.

reduces the statistical error of the first type) and the experiment was repeated (1000) times, using the MSE criterion) For comparison, it was concluded that the Bayes method It is the best among the estimation methods and that all estimators have the property of consistency because the average squares of error decreases as the sample size increases, and that all estimation methods approach the Bays method at larger sample sizes than the samples used.