Statistical Analysis Of The Three-parameter Generalized Exponential Distribution

Exponential distribution,it is a common life distribution,can be seen everywhere in life product life cycle,the product life to obey exponential distribution,such as computer fault time obey the exponential distribution,the average part of electronic products,such as some lamp life obey exponential distribution,and so on,not only the index distribution in insurance,industrial,military and other different industries have a wide range of applications.In order to fit the data better,model the product life distribution more flexibly,and provide a reference method for the study of product life distribution,this paper proposes the generalized exponential distribution with three parameters based on exponential distribution.Three parameters was deduced theoretically in this paper the generalized exponential distribution of probability density function and failure rate function,through drawing and inspection is deduced under the condition of the three different parameter values of the generalized exponential distribution probability density function image characteristics exist three conditions,respectively,drab,bath and" thirty percent",the failure rate function image characteristics present three scenarios,"monotone decreasing","drab" and "bath" form;The order moment,coefficient of variation,coefficient of skewness and coefficient of kurtosis are given,and the relation between coefficient of variation and coefficient of variation is proved under different conditions.Because both of the two point estimation methods have a priori equation,Python programming is used to solve the problem,and the two parameter estimation methods are compared by numerical simulation.Finally through two simulation examples density calculation parameters of maximum likelihood estimation and approximate interval estimation likelihood ratio,at the same time by KS test to verify the actual data obey the generalized exponential distribution of three parameters,and torque estimator,likelihood ratio estimation and approximate interval estimation,has confirmed that the three parameters of the feasibility of the generalized exponential distribution,and in a certain type of tank maintenance data distribution is better than that of Alam distribution.