Some Fundamental Curves for the Solution of Sampling Problems

Abstract

In using collateral information in an inverse probability situation to estimate a population fraction from a sample fraction it is necessary to use some particular form for the a priori probability function. This paper points out the advantages of using $Kx^r(1 - x)^s$ for this purpose. The application then involves only the Incomplete Beta Function. Graphs of the 10, 25, 50, 75 and 90 per cent points of the Incomplete Beta Function are given. They cover a range which includes and extends previous tabulations.