Correlation between the numbers of two types of children when the family size distribution is zero-truncated negative binomial.
Let family size N be a random variable formed from two types of children B and C (B + C = N). The correlation coefficient between B and C has been recently studied by Rao et al. [1973]. We consider this problem when the frequency of fertile childless families (N = 0) is not available or cannot be estimated. Assuming the distribution of N is zero-truncated negative binomial, a formula for the correlation coefficient is derived. Applying this formula to the data of Reed and Reed [1965] gives a correlation coefficient of 0.27. The corresponding empirical coefficient for non-zero size families calculated directly from the data is 0.24.
D002648:Child; D005191:Family Characteristics; D005260:Female; D006801:Humans; D008297:Male; D013223:Statistics as Topic