Author

# Gary D. Kelley

Bio: Gary D. Kelley is an academic researcher from Southern Methodist University. The author has contributed to research in topics: Stein's unbiased risk estimate & Mean squared error. The author has an hindex of 2, co-authored 2 publications receiving 105 citations.

##### Papers

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TL;DR: In this paper, the minimum variance unbiased estimator of P(Y < X) has been given for the situation in which X and Y are independently exponentially distributed using the rccacnt results of Blight and Rao.

Abstract: The minimum variance unbiased estimator of P(Y < X) has been given for the situation in which X and Y are independently exponentially distributed. Using the rccacnt results of Blight and Rao [2] the variance of the UMVU estimator is derived. The mean-square error of the maximum likelihood estimator is obtained and used for comparison with the variance of the UMVUE.

76 citations

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TL;DR: In this article, a new expression for the minimum variance unbiased estimator of P[Y < X] under the assumption that X and Y are independent normal random variables was obtained, which yields approximations to the UMVUE which are superior to those previously used by Church and Harris [1] and Downton [2].

Abstract: A new expression is obtained for the minimum variance unbiased estimator of P[Y < X] under the assumption that X and Y are independent normal random variables. This new expression yields approximations to the UMVUE which are superior to those previously used by Church and Harris [1] and Downton [2].

31 citations

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TL;DR: In this article, the estimation of P[Y < X] when X and Y are two independent generalized exponential distributions with different shape parameters but having the same scale parameters is dealt with.

Abstract: This paper deals with the estimation of P[Y < X] when X and Y are two independent generalized exponential distributions with different shape parameters but having the same scale parameters. The maximum likelihood estimator and its asymptotic distribution is obtained. The asymptotic distribution is used to construct an asymptotic confidence interval of P[Y < X]. Assuming that the common scale parameter is known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator and Bayes estimator of P[Y < X] are obtained. Different confidence intervals are proposed. Monte Carlo simulations are performed to compare the different proposed methods. Analysis of a simulated data set has also been presented for illustrative purposes.

244 citations

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TL;DR: The asymptotic distribution of the maximum likelihood estimator of R is obtained and the confidence interval of R can be obtained, and two bootstrap confidence intervals are proposed.

Abstract: This paper deals with the estimation of R=P[Y

226 citations

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TL;DR: In this article, the authors considered the estimation of the stress strength parameter R = P (Y X ), when X and Y are independent and both are three-parameter Weibull distributions with the common shape and location parameters but different scale parameters.

Abstract: In this paper we consider the estimation of the stress–strength parameter R = P ( Y X ) , when X and Y are independent and both are three-parameter Weibull distributions with the common shape and location parameters but different scale parameters. It is observed that the maximum likelihood estimators do not exist in this case, and we propose a modified maximum likelihood estimator, and also an approximate modified maximum likelihood estimator of R . We obtain the asymptotic distribution of the modified maximum likelihood estimators of the unknown parameters and it can be used to construct the confidence interval of R . Analyses of two data sets have also been presented for illustrative purposes.

167 citations

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TL;DR: In this article, the estimation of P [Y X ] when X and Y are two independent generalized Pareto distributions with different parameters is dealt with and the maximum likelihood estimator and its asymptotic distribution are obtained.

Abstract: This paper deals with the estimation of P [ Y X ] when X and Y are two independent generalized Pareto distributions with different parameters. The maximum likelihood estimator and its asymptotic distribution are obtained. An asymptotic confidence interval of P [ Y X ] is constructed using the asymptotic distribution. Assuming that the common scale parameter is known, MLE, UMVUE, Bayes estimation of R and confidence interval are obtained. The ML estimator of R , asymptotic distribution and Bayes estimation of R in general case is also studied. Monte Carlo simulations are performed to compare the different proposed methods.

118 citations

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