Several Methods Of Inference For Geometric Distribution

The geometric distribution is one of the better known discrete probability distributions and has many useful applications. Its applications include in the fields of information engineering, electronics industry, theory of controls and economic, etc. The geometric distribution usually describes the question of fist success. And the lives of many discrete products obey the geometric distribution. Moreover, the geometric distribution also plays an important role in insurance. And the geometric distribution is closely related many other important distributions. In the theory of reliability, geometric distribution is one of the most important discrete probability distributions because of its loss of memory.This article discusses many estimations of the reliability of the geometric distribution. First it discusses two classical estimations of the reliability: MLE and Moments estimation. Assume random variable X is geometric distribution with the density function p ( xθ)= (1-θ)x-1θ, x =1,2,3 , Given sample X 1 , X2,,Xn ,then the MLE ofθis given as Moments estimation ofθSecond it were discussed that the Bayes estimation of the reliability under entropy loss function and square loss function. Some estimations ofθis given as Bayes estimation of the reliability square loss functionBayes estimation of the reliability under entropy loss functionFurther,we give several EB estimation of reliability. by parametric method we have EB estimation ofθisθ? = a +a b++1x,By minimum entropy method we have EB estimation ofθisBy L. E.B method we have EB estimation ofθisBy nonparametric method we have EB estimation ofθisAt last, two applications in the insurance were given.