A Note on the Murthy-Sarma Estimators of the Mean of the Normal Distribution for Small Samples

Murthy and Sarma (Assam Statistical Review 12: 1–5, 1998) proposed and studied two biased estimators for the expectation of the normal distribution N(μ, σ 2) when the coefficient of variation is known and is given by . Their estimators for small samples were found to be erroneous on account of a simplification and an analytical error. In this note, these errors are pointed out and corrected. For the corrected estimator the values of the relative efficiency for and sample size n = 2(1)25(5)100 are calculated and displayed in a table.