Properties And Application Of Alpha Power Gamma Distribution

With the rapid progress of science and technology,products with high reliability and long life have been widely applied in various fields,which leads to great challenges in reliability statistical analysis.And,many methods have emerged in the literature to generate new distributions by adding one or more parameters,this technique can be used to generate a new distribution with more flexibility in modeling actual data sets,resulting in a wider range of data fit.Therefore,it can not be ignored that the proposed new distribution with good simulation data effect and flexible shape of hazard rate function plays an important role in the field of life analysis.Recently,Mahdavi et al.(2017)[1]proposed a new method of extending the distribution by adding a shape parameter,we refer to the new method as called the alpha power transformation(APT).In this paper,we extend the gamma distribution by the APT method and obtain a new distribution called alpha power gamma(APG)distribution.First of all,we discussed the shape of hazard rate function and density function of APG distribution.It is found that the distribution has a flexible hazard rate function,which presents monotonically increasing,monotonically decreasing,constant and uni-modal shapes.The properties of the new distribution are studied,including explicit expressions for the sth raw moments,moment generating function and distribution of order statistics.Also,the integral expressions for the entropy,mean residual life and mean waiting time are obtained.Secondly,we studied the problems for point and interval estimation of parameters based on APG distribution.The maximum likelihood estimation and fisher informa-tion matrix of parameters for APG distribution are obtained theoretically.Since the likelihood equations is nonlinear,it is hard to get its analytical solution,so we get its numerical solution by using a real data set with R software,by comparing with some classical distributions,it is found that the fitting effect of APG distribution is the best,and the goodness of the proposed model is evaluated by Kolmogorov-Smirnov(K-S)test.Finally,it is difficult to obtain complete observation data in the life test.There?fore,in order to save costs and improve efficiency,the censored life test schemes is often selected to obtain the censored observation data for more applications.In this paper,we discuss the parameters estimation problem of APG distribution under the general progressive type-II censoring samples.A practical data set is used to illustrate the practicality of the proposed distribution.