Statistic Inference Of Logit Slash Logistic Distribution And Inverse Gaussian Distribution

With the progress of the times,people have entered the age of informationization.Everything that people deal with and record is essentially data.The constantly generated data calls for more updated distribution and inference methods.Heavy-tailed distribution plays an important role in both reliability and financial fields.Considering that the data types,in reality,are mostly bounded,people have an urgent need for more bounded heavy-tailed data.It seems that the distribution that can maintain both the bounded and heavy tail properties at the same time is still scarce in quantity.For the existing distribution,some of its difficult inference problems still exist.As for the inverse Gaussian distribution,it's still difficult to obatin the exact pivotal quantities of its underlying parameters?,and some statistical variables based on the underlying parameters,which has led to many research difficulties.New statistical inference methods are required to meet this need.Based on the existing logistic distribution,logistic transformation,and slash-type transformation,this paper first proposes a new bounded heavy-tailed distribution,named the logit slash-type logistic distribution,and then its probability density function,cumulative distribution function,and reliability The derivation research is carried out in the aspects of,failure rate,moment,skewness,and kurtosis,and the specific images and estimation methods are given.Finally,through the Monte Carlo method and the empirical data analysis of the failure time data of mechanical components,the logic slash type is explained.The logistic distribution is flexible and adaptable to data with outliers.Secondly,this paper uses the generalized method proposed by Weerahandi(1995)to obtain the generalized confidence interval of parameters,quantiles,reliability,failure rate,average remaining life,and the future failure time of the inverse Gaussian distribution.The simulation research illustrates the proposed method Compared with Bootstrap and Wald confidence intervals,the generalized confidence interval coverage is always closer to the nominal coverage,and empirical data research on the effective repair time of airborne communication transceivers is given.So that the inverse Gaussian distribution has an accurate solution of?since then,and some statistics like the stress-strength model based on the underlying parameters can be derived from this.Finally,the generalized confidence interval under the stress-strength model that obeys the inverse Gaussian distribution is given,and the lower confidence limit of this method is revised.The Monte Carlo method is used to illustrate that the generalized confidence interval of this method and the revised lower confidence limit are better than Bootstrap in coverage.The confidence interval is closer to the nominal coverage rate,the empirical data study of the carbon monoxide level of the refinery compared with the Gulf standard is given,and the generalized pivot quantity of the reliability under the inverse Gaussian stress model is given.