In this paper, we study the estimation problems for the two-parameter exponentiated Gumbel distribution based on lower record values. An exact confidence interval and an exact joint confidence region for the parameters are constructed. A simulation study is conducted to study the performance of the proposed confidence interval and region. Finally, a numerical example with real data set is given to illustrate the proposed procedures.

In this article, we consider the problem of estimating the stress-strength reliability $Pr (X > Y)$ based on upper record values when $X$ and $Y$ are two independent but not identically distributed random variables from the power hazard rate distribution with common scale parameter $k$. When the parameter $k$ is known, the maximum likelihood estimator (MLE), the approximate Bayes estimator and the exact confidence intervals of stress-strength reliability are obtained. When the parameter $k$ is unknown, we obtain the MLE and some bootstrap confidence intervals of stress-strength reliability. We also apply the Gibbs sampling technique to study the Bayesian estimation of stress-strength reliability and the corresponding credible interval. An example is presented in order to illustrate the inferences discussed in the previous sections. Finally, to investigate and compare the performance of the different proposed methods in this paper, a Monte Carlo simulation study is conducted.

In this paper, we consider the problem of estimating the scale parameter of exponential distribution after preliminary test when the record values are available. The optimal significance levels based on the minimax regret criterion and the corresponding critical values are obtained. This estimator is illustrated by a numerical example.

In this paper, we consider the problem of estimating stress-strength reliability R = Pr(X > Y ) for Gompertz lifetime models hav-ing the same shape parameters but different location parameters under a set of upper record values. We obtain the maximum likelihood es-timator (MLE), the approximate Bayes estimator and the exact con,-dence intervals of stress-strength reliability when the shape parameter is known. Also, when the shape parameter is unknown, the MLE, the asymptotic con, dence interval and some bootstrap con, dence intervals of stress-strength reliability are studied. Furthermore, a Bayesian ap-proach is proposed for estimating the parameters and then the corre-sponding credible interval are achieved using Gibbs sampling technique via OpenBUGS software. Monte Carlo simulations are performed to compare the performance of different proposed estimation methods. Fi-nally, analysis of a real dataset is performed.