Statistical Analysis Of Two Half-Logistic Distributions With Two Parameters

In the present essay, we derive two new distributions with twoparameters, respectively. Based on the scaled-half-logistic distributionwhich put forward by Polovko, we discuss some properties of thedistributions and the estimations of the location parameter, the shapeparameter and the scale parameter.For the location-scale-half-logistic distribution:(1) Based on the full sample, the moment estimation, the maximumlikelihood estimation (MLE) is derived. Meanwhile, we prove theexistence of the MLE of the scale parameters. Furthermore the bestlinear unbiased estimation (BLUE) is derived. And then the precisions ofall the estimations are investigated by Monte-Carlo simulations. For thelocation parameter, BLUE is the best with respect to the MSE. Themoment estimation is the worst. For the scale parameter, BLUE is thebest. The MLE is the worst.(2) Based on the type-II sample, MLE, the approximate maximumlikelihood estimation (AMLE) and the BLUE are discussed. We comparethese three estimations by Monte-Carlo simulations. For the scaleparameter, BLUE is the best with respect to the MSE. The momentestimation is the worst of all. For the scale parameter, BLUE is muchbetter than others.(3) Last, we make a table which contains the coefficient of the BLUE.Meanwhile, the interval estimation is proposed with the pivotal quantity.For the shape-scale-half-logistic distribution:(1) Based on the full sample, t MLE and BLUE are derived.(2) Based on the type-II sample, MLE, AMLE and the BLUE arediscussed. We compare these estimations by Monte-Carlo simulations.For the shape parameter, BLUE is better with respect to the MSE. For thescale parameter, AMLE is better.