This paper presents a family of dual to ratio-cum-product estimators for the finite
population mean. Under simple random sampling without replacement
(SRSWOR) scheme, expressions of the bias and mean-squared error (MSE) up to
the first order of approximation are derived. We show that the proposed family is
more efficient than usual unbiased estimator, ratio estimator, product estimator,
Singh estimator (1967), Srivenkataramana (1980) and Bandyopadhyaya estimator
(1980) and Singh et al. (2005) estimator. An empirical study is carried out to
illustrate the performance of the constructed estimator over others.
Authors: Sabiou Inoua
Comments: 2 Pages.
This short paper establishes one more formula for the variance. Consider a random variable X whose possible values are x1, …, xn with probabilities p1, …, pn of occurring, respectively. Pick two of these possible values successively (each xi having the probability pi of being chosen). Compute the difference between the two chosen values. Square the difference. Claim: you are expected to get (twice) the variance of X. This formula makes the variance appear an even more natural measure of dispersion than usually thought.