The age-specific fertility curves normalized by total fertility can be considered as the density of the age at childbearing distribution. Generally the shape of age specific fertility rate changes from convex to concave after it reaches its maximum value. Proportion bearing children before age 35 may be interpreted as tempo of fertility and rest may be interpreted as excess fertility, which is risky for mother as well as child both. Thus, the purpose of this study is to observe the pattern of fertility over time and space keeping the above idea into consideration. To experience the modest change in fertility, the estimated total fertility rate, are computed for the data through simple mathematical model. For this purpose the secondary data on age-specific fertility rate and its forward and backward cumulative distributions have been considered. Also the validity of proposed models has been checked through appropriate technique.
| Published in | American Journal of Theoretical and Applied Statistics (Volume 4, Issue 2) |
| DOI | 10.11648/j.ajtas.20150402.14 |
| Page(s) | 64-70 |
| 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 |
Age specific fertility rate, Mathematical Model, Polynomial Curve, Cross Validity Prediction Power, Shrinkage
| [1] | Asari, V.G. and John, C. (1998). “Determinants of desired family size in Kerala.” Demography India, 27, 369-381. |
| [2] | Azzalini, A. (1985). “A class of distributions which includes the normal ones.” Scand. J. Statist., 12, 171–178. |
| [3] | Azzalini, A. (2005) “The skew-normal distribution and related multivariate families (with discussion).” Scand. J.Statist., 32, 159–200. |
| [4] | Bhasin, M. K. and Nag, S. (2002). “A Demographic profile of the people of Jammu and Kashmir: Estimates, trends and differentials in fertility.” Journal of Human Ecology, 13, 57-112. |
| [5] | Bhasin, V. (1990). “Habitat, Habitation and Health in the Himalayas.” Kamla Raj Enterprises, Delhi. |
| [6] | Bhatia, J.C. (1970). “Prevalent knowledge and attitude of males towards family planning in a Punjab village.” Journal of Family Welfare, 16, 3-14. |
| [7] | Brass, W. (1960). “The graduation of fertility distributions by polynomial functions.”Population Studies, 14: 148-162. |
| [8] | Brass, W. (1974). “Perspectives in Population Prediction: Illustrated by the Statistics ofEngland and Wales (with discussion).” Journal of the Royal Statistical SocietyA, 137: 532-583. |
| [9] | Brass, W. (1978). “Population Projections for Planning and Policy.” Papers of the East- West Population Institute, No 55. Honolulu, Hawaii. |
| [10] | Chachra, S. P. and Bhasin, M. K. (1998). “Anthropo-demographic study among the caste and tribal groups of central Himalayas: fertility differentials and determinants.” Journal of Human Ecology, 9, 417-429. |
| [11] | Chandola,T., Coleman,D. and Hiorns, R.W. (1999). “Recent European fertility patterns: fitting curves to ‘distorted’distributions.” Popln Stud., 53, 317–329. |
| [12] | Coale, A.J. and Trussell, T. J. (1974). “Model fertility schedules: variations in the age structure of childbearing in human populations.” Population Index, 40, 2: 185-258. |
| [13] | Coale, A.J. and Trussell, T. J. (1978). “Technical note: finding the two parameters that specify a model schedule of marital fertility.” Population Index, 44, 2: 203-214. |
| [14] | Das, N. (1984). “Sex preference pattern and its stability in India: 1970-80.” Demography India, 13, 108-119. |
| [15] | Farid, S. M. (1973). “On the pattern of cohort fertility.” Population Studies, 27: 159-168. |
| [16] | Gilje, E. (1969). “Fitting curves to age-specific fertility rates: some examples.” Statistical Review of the Swedish National Central Bureau of Statistics III, 7:118-134. |
| [17] | Gilks, W. R. (1986). “The relationship between birth history and current fertility indeveloping countries”, Population Studies, 40. |
| [18] | Goody, J. R., Duly, C. J., Beeson, I. and Harrison, G. (1981). “Implicit sex preferences: A comparative study.” Journal of Biosocial Sciences, 13, 455-466. |
| [19] | Hadwiger, H. (1940). “Eineanalytischereprodutions-funktion fur biologischeGesamtheiten.”,SkandinaviskAktuarietidskrift, 23, 101-113. |
| [20] | Herzberg, P. A. (1969). “The parameter of cross validation.” Psyshometrika (Monograph Supplement, No. 16). |
| [21] | Hoem, J. M. and Rennermalm, B. (1978). “On the statistical theory of graduation by Splines”, University of Copenhagen, Laboratory of Actuarial Mathematics. Working Paper No. 14. |
| [22] | Hoem, J. M., Madsen, D., Nielsen, J. L., Ohlsen, E., Hansen, H. O., Rennermalm, B. (1981). “Experiments in modelling recent Danish fertility curves.”,Demography, 18: 231-244. |
| [23] | Islam, R. (2009). “Mathematical Modeling of Age Specific Marital Fertility Rates of Bangladesh”, Research Journal of Mathematics and Statictics 1(1): 19-22, 2009. |
| [24] | Mahadevan, K. (1979). “Sociology of Fertility: Determinants of Fertility Differentials in South India.” Sterling Publishers, New Delhi, India. |
| [25] | Mitra, S. (1967). “The pattern of age-specific fertility rates.”.Demography, 4: 894-906. |
| [26] | Murphy, E. M. and Nagnur, D.N. (1972). “A Gompertz fit that fits: Applications toCanadian Fertility Patterns.” Demography, 9: 35-50. |
| [27] | Mysore Population Study. (1961). “Sponsored by United Nations and Government of India.” Mysore Population Study. |
| [28] | Nurul Islam, M. and Mallick S. A. (1987). “On the use of a truncated Pearsonian TypeIII curve in fertility estimation.”,Djaka University Studies, Part B Science, 35,1: 23-32. |
| [29] | Ortega Osona, J. A. and Kohler, H.-P. (2000). “A comment on “Recent European fertility patterns: fitting curvesto ‘distorted’ distributions”, by T. Chandola, D. A. Coleman and R. W. Hiorns”. Popln Stud., 54, 347–349. |
| [30] | Peristera, P. and Kostaki, A. (2007) “Modelling fertility in modern populations.” Demogr. Res., 16, 141–194. |
| [31] | Preston, H. S. (1978). “The Effects of Infant and Child Mortality on Fertility”. Academic Press, New York. |
| [32] | Romaniuk, A. (1973). “A three parameter model for birth projections.” Population Studies, 27, 3: 467-478. |
| [33] | Verma, R.B.P. and S. Loh. 1992. “Evaluation of Pearsonian Type I Curve of Fertility by Age of Mother for Canada, Provinces and Territories, 1980–1989”. Paper presented at the Canadian Population Society meeting, Charlottetown, P.E.I., June 2–5. |
| [34] | Verma, R.B.P., S. Loh, S.Y. Dai, and D. Ford. 1996. “Fertility Projections for Canada, Provinces and Territories, 1993-2016”. Statistics Canada, Catalogue no. 91F001MIE, Ottawa. |
| [35] | Vlassof, C. (1990). “Fertility intentions and subsequent behavior: A longitudinal study in rural India.” Studies in Family Planning, 21, 216-225. |
| [36] | Vlassof, M. and Vlassof, C. (1980). “Old age security and the utility of children in rural India.” Population Studies, 34, 487-499. |
| [37] | Wunsch, G. (1966). “Courbes de Gompertz et prespectives de fecondirte.”,RecherchesEconomiques de Louvain, 6: 457-468. |
| [38] | Yntema, L. (1969). “On Hadwiger‘s fertility function.”, Statistical Review of the Swedish National Central Bureau of Statistics III, 7, 113-117. |
APA Style
Brijesh P. Singh, Kushagra Gupta, K. K. Singh. (2015). Analysis of Fertility Pattern Through Mathematical Curves. American Journal of Theoretical and Applied Statistics, 4(2), 64-70. https://doi.org/10.11648/j.ajtas.20150402.14
ACS Style
Brijesh P. Singh; Kushagra Gupta; K. K. Singh. Analysis of Fertility Pattern Through Mathematical Curves. Am. J. Theor. Appl. Stat. 2015, 4(2), 64-70. doi: 10.11648/j.ajtas.20150402.14
AMA Style
Brijesh P. Singh, Kushagra Gupta, K. K. Singh. Analysis of Fertility Pattern Through Mathematical Curves. Am J Theor Appl Stat. 2015;4(2):64-70. doi: 10.11648/j.ajtas.20150402.14
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.ajtas.20150402.14,
author = {Brijesh P. Singh and Kushagra Gupta and K. K. Singh},
title = {Analysis of Fertility Pattern Through Mathematical Curves},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {4},
number = {2},
pages = {64-70},
doi = {10.11648/j.ajtas.20150402.14},
url = {https://doi.org/10.11648/j.ajtas.20150402.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150402.14},
abstract = {The age-specific fertility curves normalized by total fertility can be considered as the density of the age at childbearing distribution. Generally the shape of age specific fertility rate changes from convex to concave after it reaches its maximum value. Proportion bearing children before age 35 may be interpreted as tempo of fertility and rest may be interpreted as excess fertility, which is risky for mother as well as child both. Thus, the purpose of this study is to observe the pattern of fertility over time and space keeping the above idea into consideration. To experience the modest change in fertility, the estimated total fertility rate, are computed for the data through simple mathematical model. For this purpose the secondary data on age-specific fertility rate and its forward and backward cumulative distributions have been considered. Also the validity of proposed models has been checked through appropriate technique.},
year = {2015}
}
TY - JOUR T1 - Analysis of Fertility Pattern Through Mathematical Curves AU - Brijesh P. Singh AU - Kushagra Gupta AU - K. K. Singh Y1 - 2015/03/21 PY - 2015 N1 - https://doi.org/10.11648/j.ajtas.20150402.14 DO - 10.11648/j.ajtas.20150402.14 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 - 64 EP - 70 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.20150402.14 AB - The age-specific fertility curves normalized by total fertility can be considered as the density of the age at childbearing distribution. Generally the shape of age specific fertility rate changes from convex to concave after it reaches its maximum value. Proportion bearing children before age 35 may be interpreted as tempo of fertility and rest may be interpreted as excess fertility, which is risky for mother as well as child both. Thus, the purpose of this study is to observe the pattern of fertility over time and space keeping the above idea into consideration. To experience the modest change in fertility, the estimated total fertility rate, are computed for the data through simple mathematical model. For this purpose the secondary data on age-specific fertility rate and its forward and backward cumulative distributions have been considered. Also the validity of proposed models has been checked through appropriate technique. VL - 4 IS - 2 ER -
Information
Email: