Correlation Coefficient between Two types of Children in a Family

Results show that both the modified negative binomial and negative binomial distribution give good fit. Comparing with Chi-square values, the family size fits better with a modified negative binomial distribution than with a negative binomial distribution. The observed correlation co-efficient between the two types of children is 0.2403 and the estimated correlation co-efficient between boys and girls, in case of negative binomial distribution is 0.216, when pq and 0.2164, when p=q=1/2 and in case of modified negative binomial distribution is 0.2244, when pq and 0.2249, when p=q=1/2.