Parameters estimation of new mixed Weibull Rayleigh and Exponential distribution

Abstract

Abstract A new idea of mixing was introduced in this paper. Mixing parameters; pi where 0 ≤ pi ≤ 1 and ∑ i = 1 n p i = 1 are used to find a new distribution from mixing some distributions. Therefore, we can get many mixed distributions with several parameters. Three distributions Weibull, Rayleigh, and Exponential are mixed to get a new distribution which is more flexible than these distributions. The mixed distribution with a new parameter is representing the ratio of contribution of each of these distributions which are mixed. Several values of the mixing parameter were taken, and the properties of the mixed distribution were found. Two methods (MLE and OLS) of estimation are used to estimate the parameters of the new distribution. Simulation studies are used to prove the properties of new distribution and to apply the estimation method to estimate the parameters of new distribution.