Distribution of Sibship Sizes and Correlation between Numbers of Male and Female Children in A Family: Evidence from Sub-Saharan Africa

Abstract

This paper is concerned with the re-investigation of the distribution of sibship sizes as negative binomial distribution, truncated below one and computation of correlation between the numbers of boys and girls in a family. The distribution involves two parameters m and p and these are estimated by the method given in Brass (1958c) which has asymptotic efficiency more than 90 % in comparison to maximum likelihood. It is also found that the scoring method provides the similar estimates as given by Brass. The suitability of the distribution and correlation is tested using 10% sample of new DHS data gathered recently on 26 sub-Saharan African countries dividing in Western-Central, Eastern-Southern, implying a mean sibship size of 4.22 and 3.83 respectively which is significant at 1% level of probability. The observed and expected correlation coefficients are found to be the same in each country. Through the values of c² at 1% and 5% level, we deem the fit to be very good except in few cases. The values of m and p will be useful to generate the underlying sibship sizes for the simulation study.

Keywords: Sibship sizes,Negative binomial distribution,Maximum likelihood,Simulation,Correlation.