An Addendum to the Estimators of Murthy–Sarma and Anis–Pandey of the Mean of the Normal Distribution

Abstract Anis and Pandey [Economic Quality Control 18: 83–90, 2003] have pointed out that the bias and mean squared error expressions of the estimators of the mean μ of a normally distributed random variable envisaged by Murthy and Sarma [Assam Statistical Review 12: 1–5, 1998] for small samples were found to be erroneous. Keeping this in view, Anis and Pandey [Economic Quality Control 18: 83–90, 2003] have derived an alternative expression for the mean squared error (MSE) of one of the estimators proposed in Murthy and Sarma [Assam Statistical Review 12: 1–5, 1998] claiming that the MSE expression obtained by them is correct. Unfortunately the MSE expression of the estimator given by both Murthy and Sarma [Assam Statistical Review 12: 1–5, 1998] and Anis and Pandey [Economic Quality Control 18: 83–90, 2003] are found incorrect for small samples. In this paper we have derived the correct expressions for biases and MSEs of the estimators suggested in Murthy and Sarma [Assam Statistical Review 12: 1–5, 1998] for small samples of a normally distributed random variable. We also propose two new estimators of the mean μ when the coefficient of variation is known and their properties are studied for small samples. Numerical illustration is given in support of the present study. It is shown both theoretically and empirically that the proposed optimum estimators are more efficient than those considered by Murthy and Sarma [Assam Statistical Review 12: 1–5, 1998].