بنــاء توزيع احتمـالي باستعمــال قاعــدة(Topp Leone G-Family)لتقديـر دالـة المعوِليَة مع تطبيق عمـلي

Rp-Building a probability distribution using (Topp Leone G-Family) the rule To estimate.pdf.

The (Topp Leone dist.), which was discovered by (C.W. Topp and F.C. Leone), as well as the (Rayleigh dist.), by the English scientist (The Lord Rayleigh), are an among the continuous statistical distributions, that are widely used in the analysis of survival functions on Life and failure functions, and reliability function. The reliability function is one of the important statistical indicators that has increased significantly in recent times due to its suitability for most practical applications related to maintenance and repairable equipment and devices.
Because of the inefficiency of probability distributions in representing most of the real data. The Researcher using the (Topp Leone distribution) as a base called the (Topp Leone generator family (TLG-F)) it used to build probability distributions. To propose new probability distribution called the (Topp Leon G-Rayleigh Rayleigh (TLG-RR)). It has three parameters. To be a generalized extension of the (Rayleigh) distribution. By adding a new parameter (ϑ>0) to the original distribution (Rayleigh Rayleigh distribution), the new probability distribution (TLG-RR) is characterized by high flexibility and accuracy in representing the real data of the investigated sample.
The researcher extracted some of the basic characteristics of the distribution, and he estimate that parameters and reliability function estimated by four different estimation methods, which are (the MLE method, the least squares method, OLS, the weighted least squares method, WLS. And by using the experimental simulation method on hypothetical data, with several experiments and with different sample sizes (25,50,100,200), And based on the value of the two statistical indicators, the mean squared error (MSE) and the mean square error of the integral (IMSE). A comparison made between the estimation methods used in the estimation process. The results of the study showed the advantage of the Shrinkage method in estimating the parameters and calculating the reliability function estimator for the proposed distribution at all sample sizes, followed by the greatest possibility method, the weighted least squares method, and the ordinary least squares method in the last rank .
This study was applied to a sample of real data represented in the working times until holidays for (100) printers from the National Card Department in the Holy Karbala. On the practical side, the study was able to prove that the proposed probability distribution (TLG-RR) is better and more flexible in representing this data compared to the (Rayleigh Rayleigh) distribution, using the approved good-matching tests using Approved good-matching tests. The reliability function of the real data was also estimated using the best method (the Shrinkage method), for the best sample size that was reached on the experimental side. Reliability and average uptime for printers.