Second, the general case of the distribution of the open interval for any woman not necessarily "fertile" is studied by dividing all married women of parity i in the reproductive age group at the time of the survey into three mutually exclusive types: (1) those women who ever reach next parity (i + 1) (2) those who do not ever reach next parity (i + 1), but who live through the entire reproductive span with husband alive and (3) those who do not ever reach parity (i + 1), but who fail to live through the entire reproductive span in the married state because of mortality or of widowhood. However, the procedure developed can be utilized to obtain the moments of any higher order for the distribution of the open birth interval under the three sets of assumptions. Explicit expressions have been derived only for the first two moments of the open interval under each of the three sets of assumptions. This distribution is derived under three sets of assumptions on the rate of occurrence of births of any specified order in the past and the parity progression ratio (PPR: the probability that a woman who has given birth to her ith child will ever proceed to the \lbrack i + 1 \rbrack the child in her reproductive life). First, the distribution of the open interval in the case of "fertile" women is investigated.
In this article, an attempt is made to develop a set of analytical models which will be helpful in the study of open intervals. Some empirical studies have indicated the potential advantages of this interval as an index of fertility. The open birth interval has been defined as the interval of time since the last live birth to the date of survey for a woman married and in the reproductive age group at the time of the survey.
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