MINIMUM VARIANCE UNBIASED ESTIMATION IN THE INVERSE RAYLEIGH DISTRIBUTION
This paper concerns the problem of uniformly minimum variance unbiased estimation of the parameter of inverse Rayleigh distribution. We obtain the uniformly minimum variance unbiased estimator (UMVUE) for positive and negative powers of the scale parameter and its functions. The UMVUE of the variance of these estimators are also given, without finding the expression of the variance itself. The UMVUE of the (i) p.d.f., (ii) reliability function, (iii) c.d.f. and (iv) pth quintile of the inverse Rayleigh distribution are derived. An illustrative numerical example is presented.
inverse Rayleigh distribution, complete sufficient statistic, UMVUE.
