Statistics for a composite distribution in anthropometric studies: the general case

This study is an extension to an earlier work to find statistics for a composite distribution of two populations with known distributions. The mean, standard deviation, and any percentile may be found for the composite population. Formulae were developed for the mean and standard deviation whereas the percentiles were found by numerical solution and a computer program was prepared to find them. In this study, an analytical solution is developed to find the percentiles in the case of normal distributions for any number of populations. The mean and standard deviation formulae are extended to as many populations as required. A computer program is prepared to find these statistics for composite populations. The cumulative distribution of the composite distribution is defined.