Prior Selection to Comparison Estimate Parameter Rayleigh Distribution
Abstract: In this study, we present estimation scale parameter of Rayleigh distribution under data the control of type II by using methods Proposed Bayesian as only prior and Double priors with a new suggestion used three Prior by using distributions Exponential and Gamma and Chi-Square. An experimental study was conducted to compare these methods and to demonstrate the efficiency of the methods proposed in practice by relying on the generated observations from Rayleigh distribution. We compare these methods by using Mean square error (MSE). We did this study by using simulation with different values parameter (?) and different sample sizes (N=10, 25, 50, 100). It has been shown through computational results that the best way to estimate is the Bayes method proposed (BAY3).

I. INTRODUCTION Rayleigh distribution is important in various sciences and their applications in life. It has many uses in the medical and industrial field and used widely in wind monitoring and other applications [1]. Usually, when conducting life tests, the experimenter who is studying the tests may not be able to determine and observe the life of all elements tested. This issue is happening because of several different reasons, including time constraints or limitations on the number of failures during a test because the cost of experimenting elements is very expensive. When they are low and directly proportional to the number of failures observed, the experience to be monitored for failures is better and more effective and achieves less time and effort than the time controlled experiment. The researchers also knew the controlled experiment to fail in the name of Type II surveillance. In such a system a type II control system the test is terminated once the number of predefined failures (r) is of observed (n) units tested.