An Extended Inverse Gaussian Distribution: Properties And Application

With the social progress and economic development,people on the product quality requirements have been demanding increasingly.As the emergence of many new methods for reliability analysis,reliability statistics is facing many new tasks and issues.A series of reliability statistical model has been studied and applied to real-life by some scholars such as exponential distribution,Weibull distribution,Maxwell distribution,extreme-value distribution and Gamma distribution.But there seems to be an issue,where each reliability statistical model cannot effectively simulate all kinds of data.Therefore,people need to provide a more suitable distribution for simulating and analyzing given lifetime data.In this paper,methods to solve the above problems are introduced mainly:Firstly,the inverse Gaussian distribution and Weibull distribution are two important lifetime models in the reliability theory area.In recently years,T-X family is a method widely used in extending many classical distributions.For that reason,this paper proposes a new distribution,combining with the inverse Gaussian distribution and Weibull distribution by using the method of T-X family,so-called extended inverse Gaussian(EIG)distribution.We study its fundamental properties such as probability density function curve,hazard rate function,the th raw moment(about the origin),moments generating function,skewness and kurtosis,stochastic ordering and residual life and so on.Secondly,some problems of the parameter estimation have been studied based on the new distribution.We discuss the maximum likelihood estimators of parameters in new distribution and asymptotic confident intervals.The EIG distribution with others are fitted to a actual data and it is shown that the distribution has a superior performance among the compared distributions by making use of various goodness-offit tests.Thirdly,the development and perfection of reliability theory has made it widely used in the processing of the loss and degradation data.Fatigue data is often finitedata,especially in terms of saving time-cost.We can not get the complete sample data even if using a special fatigue test method(accelerated life test),but censored data.Therefore,it is necessary to develop the parameters estimation theories based on censored data.Kundu suggest an adaptive Type-? progressive censoring schemes in 2009,a properly planned adaptive progressively censored life testing experiment can save both the total test time and the cost induced by failure of the units and increase the efficiency of statistical analysis.In this paper,we will discuss the maximum likelihood estimators of new distribution parameters based on the adaptive Type-? censoring samples.