Determining Optimum Strata Boundaries and Sample Sizes for Skewed Population with Log-Normal Distribution

The method of choosing the best boundaries that make strata internally homogenous as far as possible is known as optimum stratification. To achieve this, the strata should be constructed in such a way that the strata variances for the characteristic under study be as small as possible. If the frequency distribution of the study variable x is known, the optimum strata boundaries (OSB) could be obtained by cutting the range of the distribution at suitable points. If the frequency distribution of x is unknown, it may be approximated from the past experience or some prior knowledge obtained at a recent study. Many skewed populations have log-normal frequency distribution or may be assumed to follow approximately log-normal frequency distribution. In this article, the problem of finding the OSB and the optimum sample sizes within the stratum for a skewed population with log-normal distribution is studied. The problem of determining the OSB is redefined as the problem of determining optimum strata widths (OSW) ...