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<p>The descriptive analysis of real data can be used to determine the levels and trends of human fertility. However, some essential and profound properties of the phenomenon, such as fecundability and sterility that are inherent in nature and cannot be observed directly. They can only be estimated using appropriate probability models. This paper attempts to develop some probability models to describe the distribution of waiting time from marriage to first conception based on the data from two different periods i.e. 1969-70 and 2015-16 for Varanasi District. The proposed models effectively address the challenge of variability in fecundability within heterogeneous groups of married women, which is often overlooked by traditional mathematical models. The uniqueness of this approach lies in assuming an appropriate hazard rate instead of the constant hazard rate for fecundability. Further, the proposed model based on appropriate hazard, generalized considering the parameter as a random variable. The generalized distribution provides a better understanding of the data on waiting time to first conception. Utilizing the above two data sets of waiting time to first conception, proposed probability models are used to estimate the parameters.</p>

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Development of Stochastic Models for Waiting Time to First Conception through the Nature of Hazard

  • 期刊论文

  • 发表日期：

    2026年1月28日

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  • Brijesh P. Singh,
  • Sandeep Singh,
  • Utpal Dhar Das

摘要

The descriptive analysis of real data can be used to determine the levels and trends of human fertility. However, some essential and profound properties of the phenomenon, such as fecundability and sterility that are inherent in nature and cannot be observed directly. They can only be estimated using appropriate probability models. This paper attempts to develop some probability models to describe the distribution of waiting time from marriage to first conception based on the data from two different periods i.e. 1969-70 and 2015-16 for Varanasi District. The proposed models effectively address the challenge of variability in fecundability within heterogeneous groups of married women, which is often overlooked by traditional mathematical models. The uniqueness of this approach lies in assuming an appropriate hazard rate instead of the constant hazard rate for fecundability. Further, the proposed model based on appropriate hazard, generalized considering the parameter as a random variable. The generalized distribution provides a better understanding of the data on waiting time to first conception. Utilizing the above two data sets of waiting time to first conception, proposed probability models are used to estimate the parameters.