A New Extended Lomax Distribution: Properties And Applications

With the progress of science and technology and the rapid development of the times,people are paying more and more attention to the life quality and reliability of products,which makes the research of reliability face huge challenges,the analysis and processing of reliability data has become an increasingly important subject.In the statistical analysis of reliability,there are some more classic lifetime distributions,such as exponential distribution,Weibull distribution,gamma distribution,etc,these classic lifetime distributions have been applied to real life by many experts and scholars,However,these traditional lifetime distributions often have limitations such as poor fitting effect and narrow application range when performing data analysis,Therefore,the generation of new lifetime distributions from these traditional lifetime distributions has gradually become a new direction in the study of lifetime distributions,and this paper is an extension of the Lomax distribution.First of all,this paper introduces some progress of distribution extension and some extension distribution of APT extension method,based on APT method and scholars’ extension of this method,as well as the important role of Lomax distribution in life distribution.A New Alpha Power Transformed Lomax distribution（NAPTL distribution）is proposed.We derive its related probability density function,hazard function and distribution function.From the hazard function images under different parameters,it can be seen that the NAPTL distribution has flexible hazard functions,such as monotonically decreasing,concave,and inverted tub To a certain extent,it can explain that the proposed NAPTL distribution is meaningful.Based on the proposed NAPTL distribution,we study its related statistical properties,The series representation of probability density function of NAPTL distribution,quantile,skewness and kurtosis,asymptotic case of probability density function and distribution function of NAPTL distribution,moment and moment generating function,Renyi entropy,order statistics,stress-strength model,mean residual life,mean waiting time and stochastic ordering,etc.Secondly,in this paper,point and interval estimates of the distribution parameters are performed for the NAPTL distribution,and the maximum likelihood estimates of the parameters of the NAPTL distribution and the Fisher information matrix are obtained theoretically,and Monte-Carlo simulation studies are performed to evaluate the performance of the maximum likelihood estimates of the parameters of the NAPTL distribution.The maximum likelihood estimation of the parameters under general type II truncated-tailed samples is also considered.Finally,the practicality of the proposed distribution model is illustrated by applying the NAPTL distribution on two data sets.The fitting effect of NAPTL distribution and other extended Lomax on the bladder cancer data set was compared,and the fitting effect of other extended distributions was compared on the head and neck cancer data set,and the log-likelihood value,AIC value,BIC value of each distribution model was calculated,through the fitting effect of these two data sets,it shows that the NAPTL distribution has relatively important application and potential research value in the reliability lifetime distribution.