Estimation of P (X ≤ Y) for the Uniform Distribution in the Presence of Outliers
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Date
2012-01
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Abstract
The maximum likelihood and the uniformly minimum variance unbiased estimator (UMVUE) of P (X ≤ Y) are derived, where both X and Y have uniform distribution and outliers are generated from Generalized Uniform Distribution (GUD). It is shown that UMVUE is better than MLE when one parameter of GUD is known. When both parameters of the GUD are unknown, P (X ≤ Y) is estimated by using mixture estimate. It is shown that estimator of P (X ≤ Y) is consistent.
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UMVUE, MLE, MSE