In this paper moment estimators and maximum likelihood estimators of unknown parameters in the exponentiated half-logistic distribution are derived, and an entropy estimator is obtained for the distribution. An exact expression of Fisher information is derived to obtain approximate confidence intervals for unknown parameters in the distribution, and for illustration purposes, the validity of the proposed estimation method is assessed using real data.

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In this paper, we derive maximum likelihood estimators (MLEs) and approximate MLEs (AMLEs) of the unknown parameters in a generalized half logistic distribution when the data are upper record values. As an illustration, we examine the validity of our estimation using real data and simulated data. Finally, we compare the proposed estimators in the sense of the mean squared error (MSE) through a Monte Carlo simulation for various record values of size.

The maximum likelihood method is the most widely used estimation method. On the other hand, it can produce substantial bias, and an approximate confidence interval based on the maximum likelihood estimator cannot be valid when the sample size is small. Because the sizes of the record values are considerably smaller than the original sequence observed in the majority of cases, a method appropriate for this situation is required for precise inference. This paper provides the exact confidence intervals for unknown parameters and exact predictive intervals for the future upper record values by providing some pivotal quantities in the two-parameter Rayleigh distribution based on the upper record values. Finally, the validity of the proposed inference methods was examined from Monte Carlo simulations and real data.

The inverse Weibull distribution(IWD) is a complementary Weibull distribution and plays an important role in many application areas. In this paper, we develop a Bayesian estimator in the context of record statistics values from the exponentiated inverse Weibull distribution(EIWD). We obtained Bayesian estimators through the squared error loss function (quadratic loss) and LINEX loss function. This is done with respect to the conjugate priors for shape and scale parameters. The results may be of interest especially when only record values are stored.