ESTIMATION OF THE SCALE PARAMETER FROM THE RAYLEIGH DISTRIBUTION FROM TYPE II SINGLY AND DOUBLY CENSORED DATA

Abstract

As common as the normal distribution is the Rayleigh distribution which occurs in works on radar, properties of sine wave plus-noise, etc. Rayleigh (1880) derived it from the amplitude of sound resulting from many important sources. The Rayleigh distribution is widely used in communication engineering, reliability analysis and applied statistics. Since the Rayleigh distribution has linearly increasing rate, it is appropriate for components which might not have manufacturing defects but age rapidly with time. Several types of electro-vacum devices have this feature. It is connected with one dimension and two dimensions random walk and is some times referred to as a random walk frequency distribution. It is a special case of Weibull distribution (1951) of wide applicability. It can be easily derived from the bivariate normal distribution with and p = 0. For further application of Rayleigh distribution, we refer to Johnson and Kotz (1994). Adatia (1995) has obtained the best linear unbiased estimator of the Rayleigh scale parameter based on fairly large censored samples. Dyer and Whisend (1973) obtained the BLUE of scale parameter based on type II censored samples for small N = 2(1)5. With the advance of computer technology it is now possible to obtain BLUE for large samples. Hirai (1978) obtained the estimate of the scale parameter from the Rayleigh distribution singly type II censored from the left side and right side and variances of the scale parameter. In this paper, we estimate the scale parameter of type II singly and doubly censored data from the Rayleigh distribution using Blom’s (1958) unbiased nearly best estimates and compare the efficiency of this estimate with BLUE and MLE.