Singh S N, Chakrabarty K C, Singh V K
Demography. 1976 Feb;13(1):37-44.
The interval between marriage and the first conception leading to a live birth plays an important role in the determination of fertility components. Several probability models (Potter and Parker, 1964; Singh, 1961, 1964, 1967) based on varying sets of assumptions relating to this interval have been propounded in the recent past. All of them are based on the assumption that the females under study are susceptible to conception at the time of marriage. However, in certain situations, where some of the females already pregnant at the time of marriage report to have conceived within a short interval following marriage, this condition is not satisfied and these models become unsuitable. A probability distribution which is an inflated form of the continuous model proposed by Singh, for the time of the first conception leading to a live birth, is presented in this paper. It describes reasonably well the data on first conception times in the context of premarital conceptions. Simple expressions for the maximum likelihood estimators of the parameters involved in the model are obtained and a method for finding the asymptotic covariance matrix of the estimators is outlined. The model is applied to four sets of data.
从结婚到首次受孕并产下活婴之间的间隔在生育力构成因素的确定中起着重要作用。最近，基于与该间隔相关的各种假设集，提出了几种概率模型（波特和帕克，1964年；辛格，1961年、1964年、1967年）。所有这些模型都基于这样一种假设，即所研究的女性在结婚时易受孕。然而，在某些情况下，一些在结婚时已怀孕的女性报告称在婚后短时间内受孕，这种情况不满足上述假设，这些模型就变得不合适了。本文提出了一种概率分布，它是辛格提出的连续模型的一种扩展形式，用于首次受孕并产下活婴的时间。它能较好地描述婚前受孕情况下首次受孕时间的数据。得到了模型中参数的最大似然估计量的简单表达式，并概述了一种求估计量渐近协方差矩阵的方法。该模型应用于四组数据。
