Distributions with a practical application

A thesis

Submitted to the council of the College of Administration and

Economics at the University of Karbala as Partial fulfillment

Of the requirements for the degree Doctor of Philosophy in

Statistics

By

Zainab kadhim Mezher Al-quraishi

Under Supervision Prof. Dr. Shrook Abdulredha Saeed

Abstract           

  Alpha power transformation (APT) is a new and innovative method for any continuous distribution by adding one or more parameters to the basic distribution and its characteristics make the distribution more flexible. The probability density and the cumulative function of the distributions used in the thesis. It should be noted here that finding a function of reliability of a multi-component system S-K stress and  strength  was done by the researcher because it was not available in the sources related to the subject of the research to the extent of the researcher’s knowledge and extracting the unknown parameters using estimation methods, including the method of Maximum Likelihood Method The method of Rank set sampling and the method of shrinkage..

   A set of data has been generated through the simulation method, which is distributed according to the used distributions (exponential distribution and Pareto distribution) using different values for the random strength and stress parameters and with different sample sizes (m) for stress and n for strength) and using the Monte Carlo method) and then comparison Among the methods for estimating the reliability of the k out of s system, two statistical measures were used (bias scale) and the mean square error measure (MSE).

As for the applied side of this thesis, the reliability of the k out of s system was estimated for the stress and strength model in the Ur State Company for the manufacture of electrical wires in Dhi Qar.