Probability Model for Human Fertility Behavior: Straddling Birth Interval Under Realistic Assumptions

Ajay Shankar Singh

doi:doi:10.11648/j.ajtas.20150406.29

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Probability Model for Human Fertility Behavior: Straddling Birth Interval Under Realistic Assumptions

Ajay Shankar Singh

Published in American Journal of Theoretical and Applied Statistics (Volume 4, Issue 6)

Received: 31 October 2015 Accepted: 9 November 2015 Published: 26 November 2015

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Abstract

Fertility analysis is important in understanding past, current and future trends of population size, Composition and growth. Information on fertility levels, patterns and trends experienced by a country is important for socio-economic planning, monitoring and evaluating programs. In recent years the study of birth intervals has acquired importance because of its relationships to fertility. The data on straddling birth interval, defined as a closed birth interval that straddles the survey date, is easy to obtain more accurately, though the collection of data requires retrospective as well as prospective surveys. This type of interval is useful for the study of reproduction of subsequent fecund women of a particular age group. In this paper, a probability distribution for the straddling birth interval regardless of parity has been derived by taking into account that different proportion of females are exposed to the risk of conception at different point of time. In this derived model, fecundability (λ) has been considered to be constant over the study period. The duration of time from the point of termination of PPA to the state of exposure has been taken as random variable (µ) which follows exponential distribution. The maximum likelihood estimation technique has been used for the estimation of parameter (λ) & (µ) through derived model.

Published in	American Journal of Theoretical and Applied Statistics (Volume 4, Issue 6)
DOI	10.11648/j.ajtas.20150406.29
Page(s)	576-580
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), 2024. Published by Science Publishing Group

Keywords

Probability Model, Fecundability, Birth Interval, Post Partum Amenorrhea (PPA), Contraceptive Practices

References

[1]	Freedman, R., “Expected family size and family size value in West Germany”, Population Studies, 13; 136, 159.
[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]	Singh Ajay Shankar, “Probability model for forward birth interval and its application, American Jr. of Theoretical and Applied Statistics, 3(6), 223-227, 2014.
[16]	Henry L.,Fecondite at famille models mathematiques, Population, 16, 261. 1961.
[17]	Sehgal, J.M., “Indices of fertility derived from data on the length of birth intervals, using different ascertainment plans” Thesis from Department of Biostatistics, University of North Carolina, Institute of Statistics Memo Series, 768, 1971.
[18]	Sheps, M.C., Menken, J.A., Ridley, J.C. and Lingner, J.W. (1970): Truncation effect in closed birth interval and open birth interval data, Journal of American Statistical Association, 65:678.
[19]	Sehgal, J.M., “On straddling birth intervals, Demography India, 2; 212, 1973.
[20]	Pandey, A., A study of some probability models for birth intervals, Ph. D. Thesis, Banaras Hindu University, India, 1981.
[21]	Mishra, R. N., “Some stochastic models and their utility to describe birth interval data”, Ph. D. Thesis, Banaras Hindu University, India, 1983.
[22]	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).
[23]	Singh, S. N., A. Pandey and R. N. Mishra, “A generalized probability distribution for open birth interval, The Aligarh Journal of Statistics, 1 (2), p. 183, 1981.
[24]	Bhardwaj, S. D., Ph. D. (Statistics-Preventive and Social Medicine) unpublished thesis, Institute of Medical Sciences, Thesis, Banaras Hindu University, India, 1992.
[25]	Srivastava, P. K., Ph. D. (Statistics-Preventive and Social Medicine) unpublished thesis, Institute of Medical Sciences, Banaras Hindu University, India, 1992.
[26]	Cox, D. R. and H. D. Miller, “The theory of stochastic process’, Methuen Co. Ltd., London, UK, 1965.
[27]	Yadava R.C. and A Pandey, “Probability models for the study of straddling birth intervals”, Biometrical Journal, Wiley Online Library, 1989.

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APA Style

Ajay Shankar Singh. (2015). Probability Model for Human Fertility Behavior: Straddling Birth Interval Under Realistic Assumptions. American Journal of Theoretical and Applied Statistics, 4(6), 576-580. https://doi.org/10.11648/j.ajtas.20150406.29

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ACS Style

Ajay Shankar Singh. Probability Model for Human Fertility Behavior: Straddling Birth Interval Under Realistic Assumptions. Am. J. Theor. Appl. Stat. 2015, 4(6), 576-580. doi: 10.11648/j.ajtas.20150406.29

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AMA Style

Ajay Shankar Singh. Probability Model for Human Fertility Behavior: Straddling Birth Interval Under Realistic Assumptions. Am J Theor Appl Stat. 2015;4(6):576-580. doi: 10.11648/j.ajtas.20150406.29

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@article{10.11648/j.ajtas.20150406.29,
  author = {Ajay Shankar Singh},
  title = {Probability Model for Human Fertility Behavior: Straddling Birth Interval Under Realistic Assumptions},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {6},
  pages = {576-580},
  doi = {10.11648/j.ajtas.20150406.29},
  url = {https://doi.org/10.11648/j.ajtas.20150406.29},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150406.29},
  abstract = {Fertility analysis is important in understanding past, current and future trends of population size, Composition and growth. Information on fertility levels, patterns and trends experienced by a country is important for socio-economic planning, monitoring and evaluating programs. In recent years the study of birth intervals has acquired importance because of its relationships to fertility. The data on straddling birth interval, defined as a closed birth interval that straddles the survey date, is easy to obtain more accurately, though the collection of data requires retrospective as well as prospective surveys. This type of interval is useful for the study of reproduction of subsequent fecund women of a particular age group. In this paper, a probability distribution for the straddling birth interval regardless of parity has been derived by taking into account that different proportion of females are exposed to the risk of conception at different point of time. In this derived model, fecundability (λ) has been considered to be constant over the study period. The duration of time from the point of termination of PPA to the state of exposure has been taken as random variable (µ) which follows exponential distribution. The maximum likelihood estimation technique has been used for the estimation of parameter (λ) & (µ) through derived model.},
 year = {2015}
}

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TY  - JOUR
T1  - Probability Model for Human Fertility Behavior: Straddling Birth Interval Under Realistic Assumptions
AU  - Ajay Shankar Singh
Y1  - 2015/11/26
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150406.29
DO  - 10.11648/j.ajtas.20150406.29
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 576
EP  - 580
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150406.29
AB  - Fertility analysis is important in understanding past, current and future trends of population size, Composition and growth. Information on fertility levels, patterns and trends experienced by a country is important for socio-economic planning, monitoring and evaluating programs. In recent years the study of birth intervals has acquired importance because of its relationships to fertility. The data on straddling birth interval, defined as a closed birth interval that straddles the survey date, is easy to obtain more accurately, though the collection of data requires retrospective as well as prospective surveys. This type of interval is useful for the study of reproduction of subsequent fecund women of a particular age group. In this paper, a probability distribution for the straddling birth interval regardless of parity has been derived by taking into account that different proportion of females are exposed to the risk of conception at different point of time. In this derived model, fecundability (λ) has been considered to be constant over the study period. The duration of time from the point of termination of PPA to the state of exposure has been taken as random variable (µ) which follows exponential distribution. The maximum likelihood estimation technique has been used for the estimation of parameter (λ) & (µ) through derived model.
VL  - 4
IS  - 6
ER  -

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Author Information

Ajay Shankar Singh

Department of Agricultural Economics & Management, University of Swaziland, Luyengo, Swaziland

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APA Style

Ajay Shankar Singh. (2015). Probability Model for Human Fertility Behavior: Straddling Birth Interval Under Realistic Assumptions. American Journal of Theoretical and Applied Statistics, 4(6), 576-580. https://doi.org/10.11648/j.ajtas.20150406.29

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ACS Style

Ajay Shankar Singh. Probability Model for Human Fertility Behavior: Straddling Birth Interval Under Realistic Assumptions. Am. J. Theor. Appl. Stat. 2015, 4(6), 576-580. doi: 10.11648/j.ajtas.20150406.29

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AMA Style

Ajay Shankar Singh. Probability Model for Human Fertility Behavior: Straddling Birth Interval Under Realistic Assumptions. Am J Theor Appl Stat. 2015;4(6):576-580. doi: 10.11648/j.ajtas.20150406.29

Copy | Download

@article{10.11648/j.ajtas.20150406.29,
  author = {Ajay Shankar Singh},
  title = {Probability Model for Human Fertility Behavior: Straddling Birth Interval Under Realistic Assumptions},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {6},
  pages = {576-580},
  doi = {10.11648/j.ajtas.20150406.29},
  url = {https://doi.org/10.11648/j.ajtas.20150406.29},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150406.29},
  abstract = {Fertility analysis is important in understanding past, current and future trends of population size, Composition and growth. Information on fertility levels, patterns and trends experienced by a country is important for socio-economic planning, monitoring and evaluating programs. In recent years the study of birth intervals has acquired importance because of its relationships to fertility. The data on straddling birth interval, defined as a closed birth interval that straddles the survey date, is easy to obtain more accurately, though the collection of data requires retrospective as well as prospective surveys. This type of interval is useful for the study of reproduction of subsequent fecund women of a particular age group. In this paper, a probability distribution for the straddling birth interval regardless of parity has been derived by taking into account that different proportion of females are exposed to the risk of conception at different point of time. In this derived model, fecundability (λ) has been considered to be constant over the study period. The duration of time from the point of termination of PPA to the state of exposure has been taken as random variable (µ) which follows exponential distribution. The maximum likelihood estimation technique has been used for the estimation of parameter (λ) & (µ) through derived model.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Probability Model for Human Fertility Behavior: Straddling Birth Interval Under Realistic Assumptions
AU  - Ajay Shankar Singh
Y1  - 2015/11/26
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150406.29
DO  - 10.11648/j.ajtas.20150406.29
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 576
EP  - 580
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150406.29
AB  - Fertility analysis is important in understanding past, current and future trends of population size, Composition and growth. Information on fertility levels, patterns and trends experienced by a country is important for socio-economic planning, monitoring and evaluating programs. In recent years the study of birth intervals has acquired importance because of its relationships to fertility. The data on straddling birth interval, defined as a closed birth interval that straddles the survey date, is easy to obtain more accurately, though the collection of data requires retrospective as well as prospective surveys. This type of interval is useful for the study of reproduction of subsequent fecund women of a particular age group. In this paper, a probability distribution for the straddling birth interval regardless of parity has been derived by taking into account that different proportion of females are exposed to the risk of conception at different point of time. In this derived model, fecundability (λ) has been considered to be constant over the study period. The duration of time from the point of termination of PPA to the state of exposure has been taken as random variable (µ) which follows exponential distribution. The maximum likelihood estimation technique has been used for the estimation of parameter (λ) & (µ) through derived model.
VL  - 4
IS  - 6
ER  -

Copy | Download