Minimum Variance Unbiased Estimation in the Rayleigh Distribution Under Progressive Type II Censored Data with Binomial Removals

by Ashok Shanubhogue and N.R.Jain.

Abstract: Abstract:This paper concerns with the problem of uniformly minimum variance unbiased estimation of the scale parameter of Rayleigh distribution based on progressive Type II censored data with binomial removals. We obtain the uniformly minimum variance unbiased estimator (UMVUE) for powers of the scale parameter and its functions. The UMVUE of the variance of these estimators are also given. The UMVUE of the (i) mode (ii) rth moment (iii) mean (iv) variance (v) hazard function (vi) median (vii) pth quantile (viii) p.d.f. (ix) positive power of reliability function and (x) c.d.f. of the the Rayleigh distribution are derived. The UMVUE of p.d.f. is utilized to obtain the UMVUE of P(X < Y). An illustrative numerical example is presented.

Key Words: progressive Type II censored sample, Rayleigh distribution, binomial distribution, complete sufficient statistic, UMVUE

Authors:
Ashok Shanubhogue, a_shanubhogue@yahoo.com
N.R.Jain, jain_nirmal@sify.com

Editor: Jain, Kanchan, jaink14@gmail.com

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