Discreted Lomax And Rayleigh Distributions

In this paper, we mainly study the properties of the discretized Lomax and Rayleigh distributions. Lomax distribution can be viewed as the mixed distribution of Exponential and Gamma distributions. Since the Lomax distributions contain failure rate both monotone increasing and monotone decreasing, and not only take an important role in the disposition of the data of lifetime in medicine, biological and engineering, but also are one of extensively used lifetime distributions. The Rayleigh distributions, which are often used to describe independent multi-path components, are those distributions that statistical characteristics vary from time to time. In practice, the Rayleigh distribution is more often used in the accuracy estimation in the field of engineering measuring.However, in our daily life, there are lots of discrete data which are observed. In this paper, the author first uses a proper approach, which is one of the three methods to discretize the continuous distributions, discretized Lomax and Rayleigh distributions, and then obtain the mean, variance, th original moments, coefficient of kurtosis, coefficient of skewness, and characteristic function. In order to make the discretized Lomax and Rayleigh distributions can be used to real data, the author obtains the maximum likelihood estimation of the parameters, and then presents the numerical simulation.