We consider the type I generalized half-logistic distribution and derive some new explicit expressions and recurrence relations for marginal and joint moment generating functions of upper record values. Here we show the computations for the first four moments and their variances. Next we show that results for record values of this distribution can be derived from our results as special cases. We obtain the characterization result of this distribution on using the recurrence relation for single moment and conditional expectation of upper record values. We obtain the maximum likelihood estimators of upper record values and their confidence intervals. Also, we compute the maximum likelihood estimates of the parameters of upper record values and their confidence intervals. At last, we present one real case data study to emphasize the results of this paper.
The power generalized Weibull distribution due to Bagdonovacius and Nikulin (2002) is an alternative,and always provides better fits than the exponentiated Weibull family for modeling lifetime data. In this paper, we consider the generalized order statistics (GOS) from this distribution. We obtain exact explicit expressions as well as recurrence relations for the single, product and conditional moments of generalized order statistics from the power generalized Weibull distribution and then we use these results to compute the means and variances of order statistics and record values for samples of different sizes for various values of the shape and scale parameters.
This paper deals with the problem of uniformly minimum variance unbiased estimation for the parameter of the Gompertz distribution based on progressively Type II censored data with binomial removals. We have obtained the uniformly minimum variance unbiased estimator (UMVUE) for powers of the shape parameter and its functions. The UMVUE of the variance of these estimators is also given. The UMVUE of (i) pdf, (ii) cdf, (iii) reliability function, and (iv) hazard function of the Gompertz distribution is derived. Further, an exact % confidence interval for the th quantile is obtained. The UMVUE of pdf is utilized to obtain the UMVUE of . An illustrative numerical example is presented.
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