Reliablity Statistical Analysis Of Three Parameters Discrete Generalized Inverse Weibull Distribution

Discrete generalized inverse Weibull distribution(DGIWD)is obtained by discretization of generalized inverse Weibull distribution(GIWD),which complements the existence of discrete life data.In practice,the life test usually cannot obtain complete sample data,so this paper studies the reliability statistical inference of the discrete generalized inverse Weibull distribution under type-? truncated data.Firstly,point estimates of parameters,reliability and failure rate and Bootstrap interval estimates are given by using maximum likelihood estimation(MLE)method for DGIWD with single parameter,two parameter and three parameter unknown conditions.Through numerical simulation,the estimation results of different truncation schemes are compared,and the estimation results of type-? truncated sample data and full sample data are further compared.Secondly,the point estimates of parameters,reliability and failure rate and the HPD interval estimates are given by using the Bayesian estimation method for the two cases of the prior distribution,namely,the empirical distribution,and the non-informative prior distribution.The results of Bayesian estimation and MLE under different truncation schemes are compared by numerical simulation.Finally,a real data set is used to solve the example,and the results of the three estimation methods are compared to the original data set.The results show that in MLE,the estimation results of fixed sample size become more accurate with the increase of the truncation number.At the same time,the estimation result of type-? truncated sample data in MLE is slightly worse than that of the full sample data,but the gap is very small.In Bayesian estimation,the performance of Bayesian estimation is much better than MLE in the case of small sample.In practical application,the goodness of fit of Bayesian estimation results is significantly better than that of MLE.