Abstract: : Normally, one may think that the distribution of closed birth interval of any specific order may be the same as the distribution of most recent closed birth interval of the same order. But it is not true. Here the distinction between the distribution of a specific order of usual closed birth interval and most recent closed birth interval of the same order is examined. In this context, firstly we demonstrate the distinction between the most recent closed birth interval and usual closed birth interval empirically by considering a real data set. Further, the distinction between these distributions is demonstrated theoretically, by taking certain hypothetical values of fertility parameters involved in the stochastic model proposed for the purpose.