A New Logarithmic Weibull Distribution Statistical Inference

This paper presents a new logarithmic weibull distribution, For this newlogarithmic weibull distribution, we obtain the image of the density function andfailure rate function. Besides, we point out that they have the same shape. At thesame time, we discuss the digital characteristics and perform the statistical analysisfor the new logarithmic weibull distribution. The main works in this paper are asfollows:(1)The moment estimation, maximum likelihood estimation, interval estimationof the parameters is discussed under the full sample size. We discuss the parameter’smoment estimation, maximum likelihood estimates and confidence intervals whilethe other parameter is fixed. After that, we compare the various estimates of theparameters.(2) For incomplete samples, we discuss the maximum likelihood estimation ofone parameter while the other parameter is fixed with TypeⅡcensored samples. Wemay get the following conclusions: If we fix the value of the shape parameter, themean square error of the moment estimation and the maximum likelihoodestimation of the scale parameter is decreasing as the sample size is getting bigger,and the maximum likelihood estimation of is significantly better than the momentestimation.(3) We derive the third-order Taylor expansion for this new logarithmicdistribution of weibull distribution function, it can be seen that the expandedfunction is still a distribution function. Finally, we focus on discussing digital featuresof this distribution after the Taylor expansion.