Modeling Mortality Rates Using Heligman-Pollard and  Lee-Carter in Nigeria

Yahaya Haruna Umar; Ugboh Joshua Chukwudi

doi:doi:10.11648/j.ajtas.20190806.14

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Modeling Mortality Rates Using Heligman-Pollard and Lee-Carter in Nigeria

Yahaya Haruna Umar, Ugboh Joshua Chukwudi

Published in American Journal of Theoretical and Applied Statistics (Volume 8, Issue 6)

Received: 25 April 2019 Accepted: 29 September 2019 Published: 13 November 2019

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Abstract

In recent years the need for accurate mortality statistics has been emphasized by researchers in planning, analyzing, monitoring and projection of health situations in the country. It helps the government and other health agencies initiate various programs that can improve life expectancy especially in developing countries like Nigeria. Given the impact of mortality rates on the population size, structure, social security system, life insurance and pension (from actuarial point of view) there is need to understand how mortality patterns change with time. According to past studies the Heligman-Pollard (Henceforth HP) model and Lee-Carter (Henceforth LC) model have been widely accepted and use by researchers in forecasting future mortality. In this study both models were applied to Nigerian data with the objective to investigate the accuracy of their performances by comparing their assumptions. The LC model parameters were estimated based on the singular value decomposition technique (SVD), while HP model parameters were estimated using nonlinear least squares method. Autoregressive Integrated Moving Average (ARIMA) procedure was applied to acquire to forecasted parameters for both models. To investigate the accuracy of the estimation, the forecasted results were compared based on the mean absolute percentage error (MAPE). The results indicate that both models provide better results for female population. However, for the elderly female population, HP model seems to overestimate to the mortality rates while LC model seems to underestimate to the mortality rates. Although the HP model does not seem to follow the pattern of the actual mortality rates, after further analysis was carried out it was discovered that the HP model gave a better forecast than the Lee-Carter model. Based on the HP model the forecasted probabilities of death were used to construct an abridged life table for males and females and the life expectancy at e₀ and e₇₅ were obtained. From our results we see that males experience higher life expectancy than females due to the mortality rates experienced by both sexes. Given the level of mortality rate especially in developing countries like Nigeria, the study therefore recommends the need for a vital registration system that could continuously and reliably collect information because it is well known that incomplete data affect the performance of a model to forecast. To ascertain level and pattern of mortality rate especially in adult, parameterization model especially the HP model should be considered because of it lesser errors, with the view of achieving a robust forecasting model that could improve the understanding of the pattern of general mortality rate and how it affects life expectancy level in the country.

Published in	American Journal of Theoretical and Applied Statistics (Volume 8, Issue 6)
DOI	10.11648/j.ajtas.20190806.14
Page(s)	221-239
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), 2019. Published by Science Publishing Group

Keywords

Mortality Rate, Heligman-Pollard Model, Lee-Carter Model, Levenberg-marquardt Iteration Procedures, Nigeria

References

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[2]	Yahaya. H. U and Tanimu. M Analysis of mortality rate in Nigeria (2016). The International Journal of science and Technoledge (ISSN2321-919x) 80-84.
[3]	Angela U. Chukwu [a], and E. O. Oladipupo March 12, (2012)[a] Modelling Adult Mortality in Nigeria: An Analysis Based on the Lee-Carter Model [a] Department of Statistics, University of Ibadan, Nigeria. 3-5.
[4]	R. I Ibrahim et.al (2017) forecasting the mortality rates using Lee-Carter model and Heligman-Pollard model (journal of physics: conference series 890012128.
[5]	Wouter van Wel (2015), Mortality Modeling and forecasting using Cross-Validation Techniques. I.
[6]	L. Heligman, M. A. and J. H. Pollard (1980) “The age pattern of mortality JIA 107 (1980) 49-80.
[7]	L. Vandenberghe ECE133A (Fall 2018) 13. Nonlinear least squares Algorithm (Minpack).
[8]	R interface of the Levenberg-Marquadt nonlinear Least-squares algorithm. Package “Minpack. lm, Nov 20, (2016) version 1.2-1.
[9]	Renshaw E. A, S. Haberman (2006). A cohort based extension to the lee-Carter model for Mortality reduction factors: Insurance; Mathematics and economics 38: 556-70.
[10]	Lipkovich, Ilya and Smith, Eric P. (June 2002). Biplot and Singular Value Decomposition Macros for Excel.
[11]	Rose Irnawaty Ibrahim Expanding an Abridged Life Table Using the Heligman-Pollard Model. 2008, Volume 24, Number 1, 1{10}.
[12]	Lee, Ronald and Miller, Timothy (November 2000). Evaluating the Performance of Lee-Carter Mortality Forecasts. 50.
[13]	R. McNown and A. Rogers forecasting cause-specific mortality using time series methods (international journal of forecasting 8: 413-432) 1992.
[14]	Ujah I. A. O, Aiseen O. A, Mutihir, J. T Vanderjagt, DJ. Glenwqwand, R, A and Ugwu V., E (2005) factors contributing to maternal mortality in North-central Nigeria: A seventeen-year review (African journal of reproductive health, 9, 27-40.
[15]	Li, Siu-Hang and Chan, Wai-Sum (January 2005). The Lee-Carter Model for Forecasting Mortality Revisited.
[16]	Olsén, Jörgen (July 2005) Modeller och Projektioner för Dödlighetsintensitet – en anpassning till svensk populations data 1970-2004. H. Booth, Rob J. Hyndman, L Tickle and P. de Jong Lee-Carter mortality forecasting: A multi-Country comparison of variants extensions (Demographic research, 15: 289-310, 2006).

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Yahaya Haruna Umar, Ugboh Joshua Chukwudi. (2019). Modeling Mortality Rates Using Heligman-Pollard and Lee-Carter in Nigeria. American Journal of Theoretical and Applied Statistics, 8(6), 221-239. https://doi.org/10.11648/j.ajtas.20190806.14

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ACS Style

Yahaya Haruna Umar; Ugboh Joshua Chukwudi. Modeling Mortality Rates Using Heligman-Pollard and Lee-Carter in Nigeria. Am. J. Theor. Appl. Stat. 2019, 8(6), 221-239. doi: 10.11648/j.ajtas.20190806.14

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AMA Style

Yahaya Haruna Umar, Ugboh Joshua Chukwudi. Modeling Mortality Rates Using Heligman-Pollard and Lee-Carter in Nigeria. Am J Theor Appl Stat. 2019;8(6):221-239. doi: 10.11648/j.ajtas.20190806.14

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@article{10.11648/j.ajtas.20190806.14,
  author = {Yahaya Haruna Umar and Ugboh Joshua Chukwudi},
  title = {Modeling Mortality Rates Using Heligman-Pollard and  Lee-Carter in Nigeria},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {8},
  number = {6},
  pages = {221-239},
  doi = {10.11648/j.ajtas.20190806.14},
  url = {https://doi.org/10.11648/j.ajtas.20190806.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20190806.14},
  abstract = {In recent years the need for accurate mortality statistics has been emphasized by researchers in planning, analyzing, monitoring and projection of health situations in the country. It helps the government and other health agencies initiate various programs that can improve life expectancy especially in developing countries like Nigeria. Given the impact of mortality rates on the population size, structure, social security system, life insurance and pension (from actuarial point of view) there is need to understand how mortality patterns change with time. According to past studies the Heligman-Pollard (Henceforth HP) model and Lee-Carter (Henceforth LC) model have been widely accepted and use by researchers in forecasting future mortality. In this study both models were applied to Nigerian data with the objective to investigate the accuracy of their performances by comparing their assumptions. The LC model parameters were estimated based on the singular value decomposition technique (SVD), while HP model parameters were estimated using nonlinear least squares method. Autoregressive Integrated Moving Average (ARIMA) procedure was applied to acquire to forecasted parameters for both models. To investigate the accuracy of the estimation, the forecasted results were compared based on the mean absolute percentage error (MAPE). The results indicate that both models provide better results for female population. However, for the elderly female population, HP model seems to overestimate to the mortality rates while LC model seems to underestimate to the mortality rates. Although the HP model does not seem to follow the pattern of the actual mortality rates, after further analysis was carried out it was discovered that the HP model gave a better forecast than the Lee-Carter model. Based on the HP model the forecasted probabilities of death were used to construct an abridged life table for males and females and the life expectancy at e0 and e75 were obtained. From our results we see that males experience higher life expectancy than females due to the mortality rates experienced by both sexes. Given the level of mortality rate especially in developing countries like Nigeria, the study therefore recommends the need for a vital registration system that could continuously and reliably collect information because it is well known that incomplete data affect the performance of a model to forecast. To ascertain level and pattern of mortality rate especially in adult, parameterization model especially the HP model should be considered because of it lesser errors, with the view of achieving a robust forecasting model that could improve the understanding of the pattern of general mortality rate and how it affects life expectancy level in the country.},
 year = {2019}
}

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TY  - JOUR
T1  - Modeling Mortality Rates Using Heligman-Pollard and  Lee-Carter in Nigeria
AU  - Yahaya Haruna Umar
AU  - Ugboh Joshua Chukwudi
Y1  - 2019/11/13
PY  - 2019
N1  - https://doi.org/10.11648/j.ajtas.20190806.14
DO  - 10.11648/j.ajtas.20190806.14
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  - 221
EP  - 239
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20190806.14
AB  - In recent years the need for accurate mortality statistics has been emphasized by researchers in planning, analyzing, monitoring and projection of health situations in the country. It helps the government and other health agencies initiate various programs that can improve life expectancy especially in developing countries like Nigeria. Given the impact of mortality rates on the population size, structure, social security system, life insurance and pension (from actuarial point of view) there is need to understand how mortality patterns change with time. According to past studies the Heligman-Pollard (Henceforth HP) model and Lee-Carter (Henceforth LC) model have been widely accepted and use by researchers in forecasting future mortality. In this study both models were applied to Nigerian data with the objective to investigate the accuracy of their performances by comparing their assumptions. The LC model parameters were estimated based on the singular value decomposition technique (SVD), while HP model parameters were estimated using nonlinear least squares method. Autoregressive Integrated Moving Average (ARIMA) procedure was applied to acquire to forecasted parameters for both models. To investigate the accuracy of the estimation, the forecasted results were compared based on the mean absolute percentage error (MAPE). The results indicate that both models provide better results for female population. However, for the elderly female population, HP model seems to overestimate to the mortality rates while LC model seems to underestimate to the mortality rates. Although the HP model does not seem to follow the pattern of the actual mortality rates, after further analysis was carried out it was discovered that the HP model gave a better forecast than the Lee-Carter model. Based on the HP model the forecasted probabilities of death were used to construct an abridged life table for males and females and the life expectancy at e0 and e75 were obtained. From our results we see that males experience higher life expectancy than females due to the mortality rates experienced by both sexes. Given the level of mortality rate especially in developing countries like Nigeria, the study therefore recommends the need for a vital registration system that could continuously and reliably collect information because it is well known that incomplete data affect the performance of a model to forecast. To ascertain level and pattern of mortality rate especially in adult, parameterization model especially the HP model should be considered because of it lesser errors, with the view of achieving a robust forecasting model that could improve the understanding of the pattern of general mortality rate and how it affects life expectancy level in the country.
VL  - 8
IS  - 6
ER  -

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Author Information

Yahaya Haruna Umar

Statistics Department, University of Abuja, Abuja, Nigeria
Ugboh Joshua Chukwudi

Statistics Department, University of Abuja, Abuja, Nigeria

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APA Style

Yahaya Haruna Umar, Ugboh Joshua Chukwudi. (2019). Modeling Mortality Rates Using Heligman-Pollard and Lee-Carter in Nigeria. American Journal of Theoretical and Applied Statistics, 8(6), 221-239. https://doi.org/10.11648/j.ajtas.20190806.14

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ACS Style

Yahaya Haruna Umar; Ugboh Joshua Chukwudi. Modeling Mortality Rates Using Heligman-Pollard and Lee-Carter in Nigeria. Am. J. Theor. Appl. Stat. 2019, 8(6), 221-239. doi: 10.11648/j.ajtas.20190806.14

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AMA Style

Yahaya Haruna Umar, Ugboh Joshua Chukwudi. Modeling Mortality Rates Using Heligman-Pollard and Lee-Carter in Nigeria. Am J Theor Appl Stat. 2019;8(6):221-239. doi: 10.11648/j.ajtas.20190806.14

Copy | Download

@article{10.11648/j.ajtas.20190806.14,
  author = {Yahaya Haruna Umar and Ugboh Joshua Chukwudi},
  title = {Modeling Mortality Rates Using Heligman-Pollard and  Lee-Carter in Nigeria},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {8},
  number = {6},
  pages = {221-239},
  doi = {10.11648/j.ajtas.20190806.14},
  url = {https://doi.org/10.11648/j.ajtas.20190806.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20190806.14},
  abstract = {In recent years the need for accurate mortality statistics has been emphasized by researchers in planning, analyzing, monitoring and projection of health situations in the country. It helps the government and other health agencies initiate various programs that can improve life expectancy especially in developing countries like Nigeria. Given the impact of mortality rates on the population size, structure, social security system, life insurance and pension (from actuarial point of view) there is need to understand how mortality patterns change with time. According to past studies the Heligman-Pollard (Henceforth HP) model and Lee-Carter (Henceforth LC) model have been widely accepted and use by researchers in forecasting future mortality. In this study both models were applied to Nigerian data with the objective to investigate the accuracy of their performances by comparing their assumptions. The LC model parameters were estimated based on the singular value decomposition technique (SVD), while HP model parameters were estimated using nonlinear least squares method. Autoregressive Integrated Moving Average (ARIMA) procedure was applied to acquire to forecasted parameters for both models. To investigate the accuracy of the estimation, the forecasted results were compared based on the mean absolute percentage error (MAPE). The results indicate that both models provide better results for female population. However, for the elderly female population, HP model seems to overestimate to the mortality rates while LC model seems to underestimate to the mortality rates. Although the HP model does not seem to follow the pattern of the actual mortality rates, after further analysis was carried out it was discovered that the HP model gave a better forecast than the Lee-Carter model. Based on the HP model the forecasted probabilities of death were used to construct an abridged life table for males and females and the life expectancy at e0 and e75 were obtained. From our results we see that males experience higher life expectancy than females due to the mortality rates experienced by both sexes. Given the level of mortality rate especially in developing countries like Nigeria, the study therefore recommends the need for a vital registration system that could continuously and reliably collect information because it is well known that incomplete data affect the performance of a model to forecast. To ascertain level and pattern of mortality rate especially in adult, parameterization model especially the HP model should be considered because of it lesser errors, with the view of achieving a robust forecasting model that could improve the understanding of the pattern of general mortality rate and how it affects life expectancy level in the country.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Modeling Mortality Rates Using Heligman-Pollard and  Lee-Carter in Nigeria
AU  - Yahaya Haruna Umar
AU  - Ugboh Joshua Chukwudi
Y1  - 2019/11/13
PY  - 2019
N1  - https://doi.org/10.11648/j.ajtas.20190806.14
DO  - 10.11648/j.ajtas.20190806.14
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  - 221
EP  - 239
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20190806.14
AB  - In recent years the need for accurate mortality statistics has been emphasized by researchers in planning, analyzing, monitoring and projection of health situations in the country. It helps the government and other health agencies initiate various programs that can improve life expectancy especially in developing countries like Nigeria. Given the impact of mortality rates on the population size, structure, social security system, life insurance and pension (from actuarial point of view) there is need to understand how mortality patterns change with time. According to past studies the Heligman-Pollard (Henceforth HP) model and Lee-Carter (Henceforth LC) model have been widely accepted and use by researchers in forecasting future mortality. In this study both models were applied to Nigerian data with the objective to investigate the accuracy of their performances by comparing their assumptions. The LC model parameters were estimated based on the singular value decomposition technique (SVD), while HP model parameters were estimated using nonlinear least squares method. Autoregressive Integrated Moving Average (ARIMA) procedure was applied to acquire to forecasted parameters for both models. To investigate the accuracy of the estimation, the forecasted results were compared based on the mean absolute percentage error (MAPE). The results indicate that both models provide better results for female population. However, for the elderly female population, HP model seems to overestimate to the mortality rates while LC model seems to underestimate to the mortality rates. Although the HP model does not seem to follow the pattern of the actual mortality rates, after further analysis was carried out it was discovered that the HP model gave a better forecast than the Lee-Carter model. Based on the HP model the forecasted probabilities of death were used to construct an abridged life table for males and females and the life expectancy at e0 and e75 were obtained. From our results we see that males experience higher life expectancy than females due to the mortality rates experienced by both sexes. Given the level of mortality rate especially in developing countries like Nigeria, the study therefore recommends the need for a vital registration system that could continuously and reliably collect information because it is well known that incomplete data affect the performance of a model to forecast. To ascertain level and pattern of mortality rate especially in adult, parameterization model especially the HP model should be considered because of it lesser errors, with the view of achieving a robust forecasting model that could improve the understanding of the pattern of general mortality rate and how it affects life expectancy level in the country.
VL  - 8
IS  - 6
ER  -

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