Abstract
Based on two independent samples from Weinman multivariate exponential distributions with unknown scale parameters, uniformly minimum variance unbiased estimators ofP(X<Y) are obtained for both, unknown and known common location parameter. The samples are permitted to be Type-II censored with possibly different numbers of observations. Since sampling from two-parameter exponential distributions is contained in the model as a particular case, known results for complete and censored samples are generalized. In the case of an unknown common location parameter with a certain restriction of the model, the UMVUE is shown to have a Gauss hypergeometric distribution, which is further examined. Moreover, explicit expressions for the variances of the estimators are derived and used to calculate the relative efficiency.
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Cramer, E., Kamps, U. The UMVUE ofP(X<Y) based on type-II censored samples from Weinman multivariate exponential distributions. Metrika 46, 93–121 (1997). https://doi.org/10.1007/BF02717169
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DOI: https://doi.org/10.1007/BF02717169