Summary: Estimation of population parameters is considered by several statisticians when additional information such as the coefficient of variation, kurtosis or skewness is known. Recently E. Wencheko and P. Wijekoon [ibid. 46, No. 1, 101–115 (2005; Zbl 1057.62020)] have derived minimum mean square error estimators for the population mean in one parameter exponential families when the coefficient of variation is known. In this paper the results presented by L.J. Gleser and J.D. Healy [J. Am. Stat. Assoc. 71, No. 356, 977–981 (1976; Zbl 0336.62003)] and A.T. Arnholt and J.L. Hebert [Optimal combinations of pairs of estimators. http://interstat.statjournals.net/YEAR/2001/articles/0103002.pdf] were generalized by considering \(T(\mathbf X)\) as a minimal sufficient estimator of the parametric function \(g(\theta)\) when the ratio \(\tau^2=[g(\theta )]^{-2}{\mathrm{Var}}[T(\mathbf X)]\) is independent of \(\theta\). Using these results the minimum mean square error estimator in a certain class for both population mean and variance can be obtained. When \(T(\mathbf X)\) is complete and minimal sufficient, the ratio \(\tau^2\) is called ‘WIJLA’ ratio, and a uniformly minimum mean square error estimator can be derived for the population mean and variance. Finally by applying these results, the improved estimators for the population mean and variance of some distributions are obtained.