Statistical Analysis Of A Kind Of Generalized Lindley Distribution

Based on the single-parameter Lindley distribution,a new class of generalized Lindley distributions is proposed by adding parameters,which is denoted as X?NGL(?,?).The distribution function,density function and failure rate function of the distribution are given.The image characteristics of the density function and the failure rate function are proved,and the existence of the distribution moment is also proved.When the overall obeys the generalized Lindley distribution NGL(?,?)with parameters,inthe full sample case,when lim g"'(?)>0,(?)(?),the parameters ?,? can be estimated by maximum likelihood.Through 1000 Monte-Carlo simulations,it is found that some of the simulation data does not satisfy this condition,which means that the maximum likelihood estimation does not always exist.In addition,a pivot amount 2(?)was constructed,demonstrating that the pivot amount issubject to ?2(2(n-1)).Based on this conclusion,the inverse moment estimation of the parameters is given by the idea of inverse moment estimation,and the interval estimation of the parameters ?is constructed.However,the interval estimation of the parameters using the pivot quantity(?)needs to be satisfied(?)(?).It is found that the above relationship is not always established by 1000Monte-Carlo simulations,.In other word,the interval estimation of the parameter using the abovepivot quantity(?)is not always It exists.To this end,the Bootstrap method isused to obtain the interval estimate of the parameters.In addition,the paper also illustrates the application of this method through simulation data and actual cases.In the case of type II censoring samples,when lim g"'(?)>0,(?)(?),the parameter ?,? is subjected to a maximum(?)likelihood estimation.The inverse moment estimation and interval estimation of the parametersare obtained by constructing the pivot amount(?).Similar to the full samplecase,it is also found through 1000 Monte-Carlo simulations that interval estimates using this pivot amount of the parameters do not always exist.To this end,the Bootstrap method is also used to obtain the interval estimation of the parameters ?,?.In addition,the paper also illustrates the application of this method through simulation data and actual cases.