A Polynomial-Based Mathematical Modelling of Age-Specific Fertility and Marital Fertility Rates of Assam

Sourav Jyoti Gogoi; Manab Deka

doi:doi:10.11648/j.ajtas.20231204.15

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A Polynomial-Based Mathematical Modelling of Age-Specific Fertility and Marital Fertility Rates of Assam

Sourav Jyoti Gogoi, Manab Deka

Published in American Journal of Theoretical and Applied Statistics (Volume 12, Issue 4)

Received: 27 July 2023 Accepted: 14 August 2023 Published: 28 August 2023

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Abstract

The emergence of population characteristics has become a significant focus within the field of demographic studies. Among these characteristics, fertility holds a pivotal role. In order to obtain a comprehensive comprehension of the complex dynamics of human fertility behaviour, mathematical models are a commonly used and appropriate tool. However, the scholarly discourse on fertility data modelling in the north-eastern Indian state of Assam has been relatively limited. The objective of this study is to investigate the fertility patterns among women in the reproductive age range by creating a polynomial-based mathematical model for Age-Specific Fertility Rates (ASFRs) and Age-Specific Marital Fertility Rates (ASMFRs) specific to the region of Assam. Moreover, we employed diverse statistical methodologies to ascertain the soundness and reliability of the formulated model. The utilization of a quartic polynomial model facilitates a more precise estimation of both ASFRs and ASMFRs. In addition, the Total Fertility Rate (TFR) and Total Marital Fertility Rate (TMFR) are estimated, as well as the age at which mothers experience elevated fertility rates. Velocity and Elasticity curves are fitted to the ASFRs and ASMFRs, unveiling noteworthy disparities between the velocity curves of 2020 and those of previous years (2015 and 2011). Specifically, the ASFRs in Assam exhibited their highest values among mothers aged approximately 27 years in 2020, while in 2015 and 2011, the peak ASFRs were estimated for mothers around 24 years old. Similarly, the ASMFRs in 2020 reached their zenith among mothers aged approximately 15 years, whereas in 2015 and 2011, the highest ASMFRs were estimated for mothers around 21 and 19 years old, respectively. Furthermore, the study sheds light on the decline in the number of women marrying at an illegal age group in Assam during 2020 compared to 2015 and 2011.

Published in	American Journal of Theoretical and Applied Statistics (Volume 12, Issue 4)
DOI	10.11648/j.ajtas.20231204.15
Page(s)	92-102
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), 2023. Published by Science Publishing Group

Keywords

Age Specific Fertility Rates, Age Specific Marital Fertility Rates, Mathematical Model, Polynomial Regression, Cross-Validity Prediction Power, Shrinkage

References

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APA Style

Sourav Jyoti Gogoi, Manab Deka. (2023). A Polynomial-Based Mathematical Modelling of Age-Specific Fertility and Marital Fertility Rates of Assam. American Journal of Theoretical and Applied Statistics, 12(4), 92-102. https://doi.org/10.11648/j.ajtas.20231204.15

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ACS Style

Sourav Jyoti Gogoi; Manab Deka. A Polynomial-Based Mathematical Modelling of Age-Specific Fertility and Marital Fertility Rates of Assam. Am. J. Theor. Appl. Stat. 2023, 12(4), 92-102. doi: 10.11648/j.ajtas.20231204.15

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AMA Style

Sourav Jyoti Gogoi, Manab Deka. A Polynomial-Based Mathematical Modelling of Age-Specific Fertility and Marital Fertility Rates of Assam. Am J Theor Appl Stat. 2023;12(4):92-102. doi: 10.11648/j.ajtas.20231204.15

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@article{10.11648/j.ajtas.20231204.15,
  author = {Sourav Jyoti Gogoi and Manab Deka},
  title = {A Polynomial-Based Mathematical Modelling of Age-Specific Fertility and Marital Fertility Rates of Assam},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {12},
  number = {4},
  pages = {92-102},
  doi = {10.11648/j.ajtas.20231204.15},
  url = {https://doi.org/10.11648/j.ajtas.20231204.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20231204.15},
  abstract = {The emergence of population characteristics has become a significant focus within the field of demographic studies. Among these characteristics, fertility holds a pivotal role. In order to obtain a comprehensive comprehension of the complex dynamics of human fertility behaviour, mathematical models are a commonly used and appropriate tool. However, the scholarly discourse on fertility data modelling in the north-eastern Indian state of Assam has been relatively limited. The objective of this study is to investigate the fertility patterns among women in the reproductive age range by creating a polynomial-based mathematical model for Age-Specific Fertility Rates (ASFRs) and Age-Specific Marital Fertility Rates (ASMFRs) specific to the region of Assam. Moreover, we employed diverse statistical methodologies to ascertain the soundness and reliability of the formulated model. The utilization of a quartic polynomial model facilitates a more precise estimation of both ASFRs and ASMFRs. In addition, the Total Fertility Rate (TFR) and Total Marital Fertility Rate (TMFR) are estimated, as well as the age at which mothers experience elevated fertility rates. Velocity and Elasticity curves are fitted to the ASFRs and ASMFRs, unveiling noteworthy disparities between the velocity curves of 2020 and those of previous years (2015 and 2011). Specifically, the ASFRs in Assam exhibited their highest values among mothers aged approximately 27 years in 2020, while in 2015 and 2011, the peak ASFRs were estimated for mothers around 24 years old. Similarly, the ASMFRs in 2020 reached their zenith among mothers aged approximately 15 years, whereas in 2015 and 2011, the highest ASMFRs were estimated for mothers around 21 and 19 years old, respectively. Furthermore, the study sheds light on the decline in the number of women marrying at an illegal age group in Assam during 2020 compared to 2015 and 2011.},
 year = {2023}
}

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TY  - JOUR
T1  - A Polynomial-Based Mathematical Modelling of Age-Specific Fertility and Marital Fertility Rates of Assam
AU  - Sourav Jyoti Gogoi
AU  - Manab Deka
Y1  - 2023/08/28
PY  - 2023
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DO  - 10.11648/j.ajtas.20231204.15
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
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PB  - Science Publishing Group
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UR  - https://doi.org/10.11648/j.ajtas.20231204.15
AB  - The emergence of population characteristics has become a significant focus within the field of demographic studies. Among these characteristics, fertility holds a pivotal role. In order to obtain a comprehensive comprehension of the complex dynamics of human fertility behaviour, mathematical models are a commonly used and appropriate tool. However, the scholarly discourse on fertility data modelling in the north-eastern Indian state of Assam has been relatively limited. The objective of this study is to investigate the fertility patterns among women in the reproductive age range by creating a polynomial-based mathematical model for Age-Specific Fertility Rates (ASFRs) and Age-Specific Marital Fertility Rates (ASMFRs) specific to the region of Assam. Moreover, we employed diverse statistical methodologies to ascertain the soundness and reliability of the formulated model. The utilization of a quartic polynomial model facilitates a more precise estimation of both ASFRs and ASMFRs. In addition, the Total Fertility Rate (TFR) and Total Marital Fertility Rate (TMFR) are estimated, as well as the age at which mothers experience elevated fertility rates. Velocity and Elasticity curves are fitted to the ASFRs and ASMFRs, unveiling noteworthy disparities between the velocity curves of 2020 and those of previous years (2015 and 2011). Specifically, the ASFRs in Assam exhibited their highest values among mothers aged approximately 27 years in 2020, while in 2015 and 2011, the peak ASFRs were estimated for mothers around 24 years old. Similarly, the ASMFRs in 2020 reached their zenith among mothers aged approximately 15 years, whereas in 2015 and 2011, the highest ASMFRs were estimated for mothers around 21 and 19 years old, respectively. Furthermore, the study sheds light on the decline in the number of women marrying at an illegal age group in Assam during 2020 compared to 2015 and 2011.
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Author Information

Sourav Jyoti Gogoi

Department of Statistics, Gauhati University, Assam, India
Manab Deka

Department of Statistics, Arya Vidyapeeth College (Autonomous), Assam, India

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APA Style

Sourav Jyoti Gogoi, Manab Deka. (2023). A Polynomial-Based Mathematical Modelling of Age-Specific Fertility and Marital Fertility Rates of Assam. American Journal of Theoretical and Applied Statistics, 12(4), 92-102. https://doi.org/10.11648/j.ajtas.20231204.15

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ACS Style

Sourav Jyoti Gogoi; Manab Deka. A Polynomial-Based Mathematical Modelling of Age-Specific Fertility and Marital Fertility Rates of Assam. Am. J. Theor. Appl. Stat. 2023, 12(4), 92-102. doi: 10.11648/j.ajtas.20231204.15

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AMA Style

Sourav Jyoti Gogoi, Manab Deka. A Polynomial-Based Mathematical Modelling of Age-Specific Fertility and Marital Fertility Rates of Assam. Am J Theor Appl Stat. 2023;12(4):92-102. doi: 10.11648/j.ajtas.20231204.15

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@article{10.11648/j.ajtas.20231204.15,
  author = {Sourav Jyoti Gogoi and Manab Deka},
  title = {A Polynomial-Based Mathematical Modelling of Age-Specific Fertility and Marital Fertility Rates of Assam},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {12},
  number = {4},
  pages = {92-102},
  doi = {10.11648/j.ajtas.20231204.15},
  url = {https://doi.org/10.11648/j.ajtas.20231204.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20231204.15},
  abstract = {The emergence of population characteristics has become a significant focus within the field of demographic studies. Among these characteristics, fertility holds a pivotal role. In order to obtain a comprehensive comprehension of the complex dynamics of human fertility behaviour, mathematical models are a commonly used and appropriate tool. However, the scholarly discourse on fertility data modelling in the north-eastern Indian state of Assam has been relatively limited. The objective of this study is to investigate the fertility patterns among women in the reproductive age range by creating a polynomial-based mathematical model for Age-Specific Fertility Rates (ASFRs) and Age-Specific Marital Fertility Rates (ASMFRs) specific to the region of Assam. Moreover, we employed diverse statistical methodologies to ascertain the soundness and reliability of the formulated model. The utilization of a quartic polynomial model facilitates a more precise estimation of both ASFRs and ASMFRs. In addition, the Total Fertility Rate (TFR) and Total Marital Fertility Rate (TMFR) are estimated, as well as the age at which mothers experience elevated fertility rates. Velocity and Elasticity curves are fitted to the ASFRs and ASMFRs, unveiling noteworthy disparities between the velocity curves of 2020 and those of previous years (2015 and 2011). Specifically, the ASFRs in Assam exhibited their highest values among mothers aged approximately 27 years in 2020, while in 2015 and 2011, the peak ASFRs were estimated for mothers around 24 years old. Similarly, the ASMFRs in 2020 reached their zenith among mothers aged approximately 15 years, whereas in 2015 and 2011, the highest ASMFRs were estimated for mothers around 21 and 19 years old, respectively. Furthermore, the study sheds light on the decline in the number of women marrying at an illegal age group in Assam during 2020 compared to 2015 and 2011.},
 year = {2023}
}

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TY  - JOUR
T1  - A Polynomial-Based Mathematical Modelling of Age-Specific Fertility and Marital Fertility Rates of Assam
AU  - Sourav Jyoti Gogoi
AU  - Manab Deka
Y1  - 2023/08/28
PY  - 2023
N1  - https://doi.org/10.11648/j.ajtas.20231204.15
DO  - 10.11648/j.ajtas.20231204.15
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  - 92
EP  - 102
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20231204.15
AB  - The emergence of population characteristics has become a significant focus within the field of demographic studies. Among these characteristics, fertility holds a pivotal role. In order to obtain a comprehensive comprehension of the complex dynamics of human fertility behaviour, mathematical models are a commonly used and appropriate tool. However, the scholarly discourse on fertility data modelling in the north-eastern Indian state of Assam has been relatively limited. The objective of this study is to investigate the fertility patterns among women in the reproductive age range by creating a polynomial-based mathematical model for Age-Specific Fertility Rates (ASFRs) and Age-Specific Marital Fertility Rates (ASMFRs) specific to the region of Assam. Moreover, we employed diverse statistical methodologies to ascertain the soundness and reliability of the formulated model. The utilization of a quartic polynomial model facilitates a more precise estimation of both ASFRs and ASMFRs. In addition, the Total Fertility Rate (TFR) and Total Marital Fertility Rate (TMFR) are estimated, as well as the age at which mothers experience elevated fertility rates. Velocity and Elasticity curves are fitted to the ASFRs and ASMFRs, unveiling noteworthy disparities between the velocity curves of 2020 and those of previous years (2015 and 2011). Specifically, the ASFRs in Assam exhibited their highest values among mothers aged approximately 27 years in 2020, while in 2015 and 2011, the peak ASFRs were estimated for mothers around 24 years old. Similarly, the ASMFRs in 2020 reached their zenith among mothers aged approximately 15 years, whereas in 2015 and 2011, the highest ASMFRs were estimated for mothers around 21 and 19 years old, respectively. Furthermore, the study sheds light on the decline in the number of women marrying at an illegal age group in Assam during 2020 compared to 2015 and 2011.
VL  - 12
IS  - 4
ER  -

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