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Probability Model of Forward Birth Interval and Its Application

Received: 16 December 2014     Accepted: 24 December 2014     Published: 6 January 2015
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Abstract

In renewal theory approach, it is well known that the limiting forms of the probability density function of backward recurrence time and forward recurrence time which are similar to open birth interval and forward birth interval are identical on the assumption that the renewal densities do not change over time. The forward birth interval defined as the time between the survey date and the date of next birth posterior to the survey date. Forward birth interval is a good index for current change in fertility behavior. The present model has been derived on the assumption that females are not exposed to the risk of conception immediately after the termination of Post-Partum Amenorrhea (PPA). However they may be exposed to the risk of conception at different point of time after the termination of PPA because of some socio-cultural factors or contraceptive practices. In this probability model for forward birth interval regardless of parity assuming that renewal density does not change over time and females are exposed to the risk of conception at different point of time. In this model, fecundability (λ) and the duration of time from the point of termination of PPA to the state of exposure as random variable (µ) which follows exponential distribution. The maximum likelihood estimation technique has been used for the estimation of parameters λ and µ through derived model. The estimated values of λ and µ are 1.1051 and 2.841 respectively. The variance of estimated λ and µ are 0.067 and 0.79 respectively. The co-variance in between estimated λ and µ is -0.026.With these estimates the expected frequencies for the distribution and χ2 = 0.6057 is highly significant. Thus, the derived probability model explains the fertility behavior of observed data satisfactorily well.

Published in American Journal of Theoretical and Applied Statistics (Volume 3, Issue 6)
DOI 10.11648/j.ajtas.20140306.18
Page(s) 223-227
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Fecundability, Birth Interval, Post Partum Amenorrhea, Maximum Likelihood Estimation, Contraceptive Practices

References
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[2] Lenski, G., “The religious factor, Anchor Books”, Doubleday, New York, USA, 1963.
[3] Goldberg, D., “Some observations on recent changes in American fertility based on sample survey data”, Eugenics Quarterly, 14(4), 255, 1967
[4] Gini, C., “Premieres researches sur la fecundabilite de la femme”, Proceedings of the International Mathematics Congress, Toronto, 889-892, 1924.
[5] Sheps, M. C., “Pregnancy wastage as a factor in the analysis of fertility data”, Demography, 1, 111-118, 1964.
[6] Singh, S. N.,“Some probability distributions utilized in human fertility”, Seminar volume in statistics, BHU, Varanasi, India, p.74, 1966.
[7] Bhattacharya, B.N., C. M. Pandey and K. K. Singh, “Model for closed birth interval and some social factors”, Janasankhya, 6 (1); 57, 1988.
[8] Singh, U., “Fertility analysis through birth interval models”, unpublished Ph.D. Thesis, Banaras Hindu University, Varanasi, India, 1988.
[9] Singh, A.S., “Some analytical models for human fertility and their applications”, unpublished Ph.D. Thesis, Institute of Medical Sciences, BHU, Varanasi, India, 1992.
[10] Mturi, A. J., “The determinants of birth intervals among non contracepting Tanzanin women”, African Population Studies, 12(2), 1997.
[11] Rama Rao S., T. John and A. Ian, “Correlates of inter birth intervals: Implications of optional birth spacing strategies in Mozambique”, Population Council, 1-17, 2006.
[12] Singh S.N., S. N. Singh and R. K. Narendra, “Demographic and socio-economic determinants of birth interval dynamics in Manipur: A survival analysis”, Online Journal of Health and Allied Sciences, 9(4), 2011.
[13] Yadav R.C., A. Kumar A. and M. Pratap,“Estimation of parity progression ratios from open and closed birth interval, Journal of Data Science, 11, 607-621, 2013.
[14] Singh, A. S., “Stochastic model for estimation of fecundability in between two successive live births (Closed Birth Interval)”, Presented in 3 International Science Congress, India, Published in Recent Jr. Research Sciences, 3 (ISC-2013), 1-3, 2014.
[15] Cox, D. R., “Renewal Theory”, Methuen and Company Ltd., London, UK, 1962.
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[17] Pathak, K. B. and A. Pandey, A., “Stochastic models of human reproduction”, Himalya Publishing House, Bombay, India, 1993.
[18] Singh, V.K. and O. P. Singh, O.P., “On some probability distributions for forward birth interval”, Mathematical Population Studies, 3(2), 145-153, 1991.
[19] Mishra, R. N.,“Some stochastic models and their utility to describe birth interval data”, unpublished Ph. D. Thesis, Department of Mathematics and Statistics, Faculty of Science, Banaras Hindu University, India, 1983.
[20] James, W.H., “The fecundability of US women”, Population Studies, 27, p. 493, 1973.
[21] Bongarts, J., A method for the estimation of fecundability, Demography, 12, p. 645, 1975.
[22] Bongarts,J. and R. G. Potter, “Fertility, Biology and Behavior ; An analysis of the proximate determinants”, Academic Press, new York, USA, 1983.
[23] Singh, S. N., R. C. Yadav and A. Pandey, “On a generalized distribution of open birth interval regardless of parity, Journal of Scientific Research, BHU, India, (1979)
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    Ajay Shankar Singh. (2015). Probability Model of Forward Birth Interval and Its Application. American Journal of Theoretical and Applied Statistics, 3(6), 223-227. https://doi.org/10.11648/j.ajtas.20140306.18

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    ACS Style

    Ajay Shankar Singh. Probability Model of Forward Birth Interval and Its Application. Am. J. Theor. Appl. Stat. 2015, 3(6), 223-227. doi: 10.11648/j.ajtas.20140306.18

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    AMA Style

    Ajay Shankar Singh. Probability Model of Forward Birth Interval and Its Application. Am J Theor Appl Stat. 2015;3(6):223-227. doi: 10.11648/j.ajtas.20140306.18

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  • @article{10.11648/j.ajtas.20140306.18,
      author = {Ajay Shankar Singh},
      title = {Probability Model of Forward Birth Interval and Its Application},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {3},
      number = {6},
      pages = {223-227},
      doi = {10.11648/j.ajtas.20140306.18},
      url = {https://doi.org/10.11648/j.ajtas.20140306.18},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20140306.18},
      abstract = {In renewal theory approach, it is well known that the limiting forms of the probability density function of backward recurrence time and forward recurrence time which are similar to open birth interval and forward birth interval are identical on the assumption that the renewal densities do not change over time. The forward birth interval defined as the time between the survey date and the date of next birth posterior to the survey date. Forward birth interval is a good index for current change in fertility behavior. The present model has been derived on the assumption that females are not exposed to the risk of conception immediately after the termination of Post-Partum Amenorrhea (PPA). However they may be exposed to the risk of conception at different point of time after the termination of PPA because of some socio-cultural factors or contraceptive practices. In this probability model for forward birth interval regardless of parity assuming that renewal density does not change over time and females are exposed to the risk of conception at different point of time. In this model, fecundability (λ) and the duration of time from the point of termination of PPA to the state of exposure as random variable (µ) which follows exponential distribution. The maximum likelihood estimation technique has been used for the estimation of parameters λ and µ through derived model. The estimated values of λ and µ are 1.1051 and 2.841 respectively. The variance of estimated λ and µ are 0.067 and 0.79 respectively. The co-variance in between estimated λ and µ is -0.026.With these estimates the expected frequencies for the distribution and χ2 = 0.6057 is highly significant. Thus, the derived probability model explains the fertility behavior of observed data satisfactorily well.},
     year = {2015}
    }
    

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    PY  - 2015
    N1  - https://doi.org/10.11648/j.ajtas.20140306.18
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    AB  - In renewal theory approach, it is well known that the limiting forms of the probability density function of backward recurrence time and forward recurrence time which are similar to open birth interval and forward birth interval are identical on the assumption that the renewal densities do not change over time. The forward birth interval defined as the time between the survey date and the date of next birth posterior to the survey date. Forward birth interval is a good index for current change in fertility behavior. The present model has been derived on the assumption that females are not exposed to the risk of conception immediately after the termination of Post-Partum Amenorrhea (PPA). However they may be exposed to the risk of conception at different point of time after the termination of PPA because of some socio-cultural factors or contraceptive practices. In this probability model for forward birth interval regardless of parity assuming that renewal density does not change over time and females are exposed to the risk of conception at different point of time. In this model, fecundability (λ) and the duration of time from the point of termination of PPA to the state of exposure as random variable (µ) which follows exponential distribution. The maximum likelihood estimation technique has been used for the estimation of parameters λ and µ through derived model. The estimated values of λ and µ are 1.1051 and 2.841 respectively. The variance of estimated λ and µ are 0.067 and 0.79 respectively. The co-variance in between estimated λ and µ is -0.026.With these estimates the expected frequencies for the distribution and χ2 = 0.6057 is highly significant. Thus, the derived probability model explains the fertility behavior of observed data satisfactorily well.
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    ER  - 

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Author Information
  • Department of AEM, University of Swaziland, Luyengo campus, Luyengo M205, Swaziland

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