A two stage shrinkage testimator for the mean of an exponential distribution

Abstract

Let X be a random variable having an exponential distribution with unknown mean 8. Further, it is assumed that prior knowledge about 8 is available in the form of an initial estimate 80 of 8.It is proposed to estimate 8 by a testimator 9 that is based upon the result of a test of the hypothesis Ho: 8 = 80. If Ho is accepted based on the first sample of size nl we take 6 = Sl t (1 -R)80 where the weighting factor R is a function of the test statistic for testing Ho. However, if Ho is rejected we obtain a second sample of size n2, and take 6 = (nlX1 + n2X2)/(nl + n2). Choosing the weighing factor L appropriately, an expression for the mean squared error of 6 is derived and comparisons are made with the variance of a single sample mean. Also an expression for the bias of 6 is derived.

Estimation of Common Variance in Normal Distribution Using Linex Loss Function

“…In section 3, the author also proposes preliminary test estimator for σ1 2 in case of two normal populations and properties of the preliminary test estimators for σ1 2 is also discussed. It is found that results are same as Adke et al (1987).…”

Shrinkage Estimation in the Inverse Rayleigh Distribution

“…The expressions of the relative bias and the risk under the LLF are given as A double-stage procedure using prior information in the form of an initial estimate or a guessed value has been considered by many authors (Katti, 1962;Shah, 1964;Waikar & Katti, 1971;Al-Bayyati & Arnold, 1972;Waikar, et al, 1984;Adke, et al, 1987). Arnold & Al-Bayyati (1970) considered the doublestage shrinkage estimator for the mean of a normal population when a prior guessed value of the mean is available.…”

Shrinkage estimation in exponential type-II censored data under LINEX loss

“…Adke, Waikar, and Schuurmann (1987) and Pandey, Malik, and Srivastava (1988) have considered this type of shrinkage factor. The risk of the shrinkage testimatorθ 3 is given by …”