Author

# W. R. Schucany

Bio: W. R. Schucany is an academic researcher. The author has contributed to research in topics: Stein's unbiased risk estimate & Mean squared error. The author has an hindex of 1, co-authored 1 publications receiving 76 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

##### Cited by

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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 paper, a concise representation of the UMVUE and several representations for the MLE are derived and large-sample results are given and numerical comparison of the two point estimators is made.

Abstract: We consider estimation of P(Y

96 citations

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TL;DR: In this paper, the authors compared three estimators for R = P(Y < X) when Y and X are two independent but not identically distributed random variables, i.e., the minimum variance unbiased, the maximum likelihood and the Bayes estimators.

Abstract: This paper provides a simulation study which compares three estimators for R = P(Y

91 citations

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TL;DR: In this article, three different estimators for Pr(X < Y) when X and Y have a bivariate exponential distribution are provided, and the asymptotic variances of the three estimators are also derived.

Abstract: This paper provides three different estimators for Pr(X < Y) when X and Y have a bivariate exponential distribution. The asymptotic variances of the three estimators are also derived. A test for the equality of the means of X and Y and confidence limits for the difference of the two means are presented. Our results are directly applicable in a reliability context with underlying bivariate exponential distribution.

76 citations