A Model for Age-Specific Fertility Rate Pattern of India Using Skew-Logistic Distribution Function
American Journal of Theoretical and Applied Statistics
Volume 6, Issue 1, January 2017, Pages: 32-37
Received: Dec. 26, 2016; Accepted: Jan. 6, 2017; Published: Feb. 3, 2017
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Ruchi Mishra, Department of Statistics, Institute of Science, Banaras Hindu University, Varanasi, India
Kaushalendra Kumar Singh, Department of Statistics, Institute of Science, Banaras Hindu University, Varanasi, India
Anjali Singh, Department of Statistics, Institute of Science, Banaras Hindu University, Varanasi, India
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Fertility governs central and positive role in the study of human population dynamics. The age-specific fertility pattern has a distinct shape for all human population, to describe which, a number of parametric models have been proposed. The purpose of this study is to develop a mathematical model for fitting age-specific fertility rate pattern of various states of India. Skew-logistic probability density function is used for building the model. The real data, to which this model has been fitted, is obtained from National Family Health Survey- III (2005-2006). The used model is very flexible in nature and hence is useful for modeling diverse fertility patterns which are observed across different states of India. The parameters of the model have been estimated through the method of non-linear least square. By fitting the model it is observed that the proposed model fits well on the fertility pattern for almost each state of the country.
Age-Specific Fertility Rate, Parametric Model, Skew-Logistic Probability Density Function, Non-Linear Least Square
To cite this article
Ruchi Mishra, Kaushalendra Kumar Singh, Anjali Singh, A Model for Age-Specific Fertility Rate Pattern of India Using Skew-Logistic Distribution Function, American Journal of Theoretical and Applied Statistics. Vol. 6, No. 1, 2017, pp. 32-37. doi: 10.11648/j.ajtas.20170601.14
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This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
J. M. Hoem, D. Madsen, J. L. Nielsen, E.- M. Ohlsen, H. O. Hansen, and B. Ren-nermalm, “Experiments in modelling recent Danish fertility curves,” Demography, vol. 18, no. 2, pp. 231–244, 1981.
A. J. Coale and T. J. Trussel. “Model fertility schedules: variations in the age structure of childbearing in human populations”, Population Index, vol. 40, no. 2, pp. 185-258, 1974.
A. J. Coale and T. J. Trussel. “Technical note: finding the two parameters that specify a model schedule of marital fertility”, Population Index, vol. 44, no. 2, pp. 203-214, 1978.
H. Hadwiger. “Eine Analytische Reprodutions-Funktion fur Biologische Gesamtheiten”, Skandinavisk Aktuareitidskrift, vol. 23, pp. 101-113, 1940.
E. Gilje. “Fitting Curves to Age-Specific Fertility Rates: Some Examples”, Statistical Review of the Swedish National Central Bureau of Statistics, vol. III, no. 7, pp. 118-134, 1969.
L. Yntema. “On Hadwiger’s fertility function”, Statistical Review of the Swedish National Central Bureau of Statistics, vol.III, no. 7, pp. 113-117, 1969.
S. Mitra. “The Pattern of Age-Specific Fertility Rates”, Demography, vol. 4, pp. 894-906, 1967.
A. Romanuik. “A Three Parameter Model for Birth Projections”, Population Studies, vol. 27, no. 3, pp. 467-478, 1973.
M. N. Islam and S. A. Mallick. “On the Use of a Truncated Personian Type III Curve in Fertility Estimation”, Dhaka Universities Studies Part B Science, vol. 35, no. 1, pp. 23-32, 1987.
W. Brass. “Perspectives in Population Prediction: Illustrated by the Statistics of England and Wales (with discussion)”, Journal of the Royal Statistical Society, vol. 137, pp. 532-583, 1974.
W. Brass. “Population Projections for Planning and Policy”, Papers of the East- West Population Institute, no. 5, 1978.
E. M. Murphy and D. M. Nagnur. “A Gompertz fit that fits: Applications to Canadian Fertility Pattern”, Demography, vol. 9, pp. 35-50, 1972.
W. Brass. “The Graduation of Fertility Distributions by Polynomial Functions”, Population Studies, vol. 14, pp. 148-162, 1960.
R. Islam. “Mathematical modeling of age specific marital fertility rates of Bangladesh”, Research Journal of Mathematics and Statictics, vol. 1, pp.19–22, 2009.
Brijesh P. Singh, Kushagra Gupta and K. K. Singh. “Analysis of fertility pattern through mathematical curves”, American Journal of Theoretical and Applied Statistics, vol. 4, pp. 64-70, 2015.
Kaushalendra K. Singh, Anjali Singh and Anjali Pandey. “Modelling Fertility Curves In India: A Comparison of Four Mathematical Models”, Janasamkhya Volume XXX & XXXII, pp. 13-29, 2012-2014.
P. Peristera and A. Kostaki, “Modeling fertility in modern populations,” Demographic Research, vol. 16, pp. 141–194, 2007.
D. A. Coleman, T. Chandola and R. W. Hiorns. “Recent European fertility patterns: fitting curves to ’distorted’ distributions”, Population Studies, vol. 53, no. 3, pp. 317–329, 1999.
Ortega Osona, J. A. and H.-P. Kohler, “A comment on “Recent European fertility patterns: Fitting curves to ‘distorted’ distributions” by T. Chandola, D. A. Coleman and R. W. Hiorns”, Population Studies, vol. 54, pp. 347–349, 2000.
C. Schertmann. “A System of model fertility schedules with graphical intuitive parameters”, Demographic Research, vol. 9, pp. 81-110, 2003.
A. Azzalini, “A class of distributions which includes the normal ones,” Scandinavian Journal of Statistics, vol. 12, pp. 171–178, 1985.
Y. Ma and M. G. Genton. “Flexible class of skew-symmetric distributions”, Scandinavian Journal of Statistics, vol. 31, pp. 459-468, 2004.
S. Mazzuco and B. Scarpa. “Fitting age-specific fertility rates by a skew-symmetric probability density function”, Working Paper Series Department of Statistical Science, University of Padua, 2011.
A. Azzalini, “Rejoinder,” Scandinavian Journal of Statistics, vol.32, no. 2, pp. 199–200, 2005.
National Family Heath Survey, Government of India, 2005-2006.
S. Asili,S. Rezaei and L. Najjar. “Using skew-logistic probability density function as a model for age-specific fertility rate pattern”, BioMed Research International, vol. 2014, 2014, http://dx.doi.org/10.1155/2014/790294.
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