This paper uses nonparametric methods to estimate the confidence intervals for the mean of asymmetric heavy tailed loss distributions. The nonparametric methods employed are the m out of n bootstrap, subsampling bootstrap, refined bootstrap, empirical likelihood ratio method, and bootstrap calibrated empirical likelihood methods. We evaluate the accuracy and compare the performance of the confi...

In diagnostic test studies, one crucial task is to evaluate the diagnostic accuracy of a test. Currently, most studies focus on the Receiver Operating Characteristics Curve and the Area Under the Curve. On the other hand, the Youden index, widely applied in practice, is another comprehensive measurement for the performance of a diagnostic test. For a continuous-scale test classifying diseased a...

This paper considers the simple step-stress model from the Marshall-Olkin generalized exponential distribution when there is time constraint on the duration of the experiment. The maximum likelihood equations for estimating the parameters assuming a cumulative exposure model with lifetimes as the distributed Marshall Olkin generalized exponential are derived. The likelihood equations do not lea...

In this paper we estimate R = P{X ≤ Y } when X and Y are independent random variables from geometric and Poisson distribution respectively. We find maximum likelihood estimator of R and its asymptotic distribution. This asymptotic distribution is used to construct asymptotic confidence intervals. A procedure for deriving bootstrap confidence intervals is presented. UMVUE of R and UMVUE of its v...

Pietra ratio (Pietra index), also known as Robin Hood index, Schutz coefficient (RicciSchutz index) or half the relative mean deviation, is a good measure of statistical heterogeneity in the context of positive-valued data sets. In this thesis, two novel methods namely “adjusted jackknife empirical likelihood” and “extended jackknife empirical likelihood” are developed from the jackknife empiri...

In this paper, the inference on location parameter for skew-normal population is considered when scale and skewness are unknown. Firstly, Bootstrap test statistics confidence intervals of single constructed based methods moment estimation maximum likelihood estimation, respectively. Secondly, Behrens-Fisher type interval problems two populations discussed. Thirdly, by Monte Carlo simulation, pr...

This article proposes the Bayes estimation of parameter and reliability function for xgamma distribution in presence type-I hybrid censored observations. The estimate has been obtained by assuming informative non-informative priors using general entropy loss function. Obviously, censoring adds difficulties procedure; hence estimators computed with observation under mentioned prior often do not ...