A probability model applicable to the study of inter-live birth intervals and random segments of the same

Abstract This paper deals with an analytical study of two types of birth intervals, viz. 'closed intervals' and 'open intervals' through the application of simple probability theory. The 'closed interval' stands for the time interval between two successive live births of a woman, and the 'open interval' denotes the interval between the date of last live birth and the date of survey for a married woman in the reproductive age group surveyed at a point of time. The study considers the 'closed interval' as the sum of independent random variables, each representing a particular component like post-partum amenorrhea, waiting time in the susceptible state, etc. Approximations to the patterns of distributions of these component random variables are made from the available data collected in fertility surveys at Gandhigram. The 'open interval' for any parity is studied separately for two different (mutually exclusive) categories of women, viz. those who have at least one more live birth at some time or other during their reproductive period and those who cease childbearing. In the first case the 'open interval' is considered as a random segment or partition of the corresponding 'closed interval'; in the second as a random segment of the interval between the date of birth of the last child and date at which the woman attains 45 years of age. The mean and variance of the 'open interval' is obtained separately in each case, and the moments of the 'open interval' distribution for women chosen at random from the population are obtained as an appropriate mixture of the two types.