Prevalence of Child Undernutrition in India: Estimating Extent of Deficits Using Distributions of Nutritional Outcomes

  • Tapan Kumar ChakrabartyEmail author
Part of the India Studies in Business and Economics book series (ISBE)


Anthropometric indicators height for age, weight for age, and weight for height, calculated from the data of the children’s height, weight, and age are transformed to Z-scores in order to assess nutritional status of under-five children. Following World Health Organization (WHO) classification scheme, the degree of prevalence in a population is defined as the percentage of subjects whose Z-scores are lying more than two standard deviations below the reference median. Although this formulation facilitates a gross comparison among sub-populations under question, two of its shortcomings are noteworthy. First, it fails to capture the salient distributional aspects of sample Z-scores different from those of the reference population and thereby the nutritional status estimates may be significantly biased. Second, empirical evidences suggest that the distribution under question can be skewed and substantially away from normal for the developing countries. The present article shows that for the selected states of India, distribution of Z-scores follows a general class of skew normal distribution, in which the reference population is a member and compares two and more members in this family. The degree of nutritional deficit is then quantified in terms of the population parameters. Empirical illustrations are given using data on Z-scores for selected Indian states (IIPS and Macro International 2007). The findings are indicative of the existence of comprehensive gaps in the perceived level of undernutrition prevalence for the selected Indian states.


Anthropometric z-scores Box–Cox transformation Location and scale family Reference population Skew normal distribution 


  1. Arnold, B. C., & Beaver, R. J. (2002). Skewed multivariate models related to hidden truncation and/or selective reporting. Test, 11, 7–54.CrossRefGoogle Scholar
  2. Arnold, B. C., Beaver, R. J., Groeneveld, R. A., & Meeker, W. Q. (1993). The nontruncated marginal of a truncated bivariate normal distribution. Psychometrika, 58, 471–488.CrossRefGoogle Scholar
  3. Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12, 171–178.Google Scholar
  4. Azzalini, A., & Capitanio, A. (1999). Statistical applications of the multivariate skew-normal distribution. Journal of the Royal Statistical Society: Series B, 61, 579–602.CrossRefGoogle Scholar
  5. Azzalini, A. (2011). The skew normal and skew t distributions, package ‘sn’ for R. URL
  6. Chakrabarty, T. K. (2011). Under-nutrition among children in India: Evidences of gender inequality from North-East India. In De, U. K., & Ghosh, B. N. (Eds.), Gender deprivation and empowerment of women. Germany: Lambert Academic Publishing GmbH & Co.Google Scholar
  7. Chakrabarty, T. K. (2013). Efficient estimation of tail probability for anthropometric Z-scores using parametric bootstrap: Measuring undernutrition prevalence among children under age five from North East India. Assam Statistical Review, 27(2), 96–115.Google Scholar
  8. Cole, T. J. (1988). Fitting smoothed centile curves to reference data. Journal of the Royal Statistical Society Series A., 151, 385–418.CrossRefGoogle Scholar
  9. Cole, T. J., & Green, P. J. (1992). Smoothing reference centile curves: The LMS method and penalized likelihood. Statistics in Medicine, 11, 1305–1319.CrossRefGoogle Scholar
  10. Cullen, A. C., & Frey, H. C. (1999) Probabilistic techniques in exposure assessment (pp. 81–159). USA: Plenum Press. Evans, M., Hastings, N., & Peacock, B. (2000). Statistical distributions. New Jersey: Wiley.Google Scholar
  11. D’Agostino, R., & Stephens, M. (1986). Goodness-of-fit Techniques. NewYork: Marcel Dekker.Google Scholar
  12. Dibley, M. J., Goldsby, J. B., Staehling, N. W., & Trowbridge, F. L. (1987). Development of normalized curves for the international growth reference: Historical and technical considerations. American Journal of Clinical Nutrition, 46, 736–748.Google Scholar
  13. Gel, Yulia R., Weiwen, Miao, & Gastwirth, Joseph L. (2006). Robust directed tests of normality against heavy-tailed alternatives. Computational Statistics & Data Analysis, 51(2007), 2734–2746.Google Scholar
  14. Genton, M. G. (2004). Skew-elliptical distributions and their applications: A journey beyond normality. New York: Chapman and Hall.CrossRefGoogle Scholar
  15. Glewwe, P., & Miguel, E. A. (2007). The impact of child health and nutrition on education in less developed countries. In Schultz, T. P., Strauss, J. A. (Eds.), Handbook of development economics (pp. 3561–3606 Vol. 4). Amsterdam: Elsevier, (chapter 56).Google Scholar
  16. International Institute for Population Sciences (IIPS) and ORC Macro. (2002). National Family Health Survey (NFHS-2), India, 1998–99: (Vol. I). Mumbai: IIPS.Google Scholar
  17. International Institute for Population Sciences (IIPS) and Macro International. (2007). National Family Health Survey (NFHS-3), 2005–06: India: (Vol. I). Mumbai: IIPS.Google Scholar
  18. Jarque, C., & Bera, A. (1980). Efficient tests for normality, homoscedasticity and serial independence of regression residuals. Economics Letters, 6, 255–259.CrossRefGoogle Scholar
  19. Lilliefors, H. (1967). On the Kolmogorov-Smirnov test for normality with mean and variance unknown. Journal of the American Statistical Association, 62, 399–402.CrossRefGoogle Scholar
  20. Mora, J. O. (1989). A new method for estimating a standardized prevalence of child malnutrition from anthropometric indicators. Bulletin of the World Health Organization, 67(2), 133–142.Google Scholar
  21. O’Donnell, et al. (2008). Analyzing health equity using household survey data: A guide to techniques and their implementation. Washington DC: World Bank Institute.Google Scholar
  22. Pourahmadi, M. (2007). Construction of skew-normal random variables: Are they linear combinations of normal and half-normal? Journal of Statistical Theory and Application, 3, 314–328.Google Scholar
  23. Schroeder, D. G., & Brown, K. H. (1994). Nutritional status as a predictor of child survival: Summarizing the association and quantifying its global impact. Bulletin of the World Health Organization, 72(4), 569–579.Google Scholar
  24. Shapiro, S., & Wilk, M. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52, 591–611.CrossRefGoogle Scholar
  25. Tarozzi, A. (2008). Growth reference charts and the nutritional status of Indian children. Economics and Human Biology, 6, 455–468.CrossRefGoogle Scholar
  26. United Nations. (2011). The millennium development goals report 2011, New York.Google Scholar
  27. Waterlow, J. C., Buzina, R., Keller, W., Lane, J. M., Nichaman, M. Z., & Tanner, J. M. (1977). The presentation and use of height and weight data for comparing the nutritional status of groups of children under the age of 10 years. Bulletin of the World Health Organization, 55, 489–498.Google Scholar
  28. Wang, Y., & Chen, H. (2012). Use of percentiles and Z-scores in anthropometry, In Preedy, V. R.(Ed.), Handbook of anthropometry: Physical measures of human form in health and disease Springer Science+Buisness Media, LLC.Google Scholar
  29. WHO Working Group. (1986). Use and interpretation of anthropometric indicators of nutritional status. Bulletin of the World Health Organization, 64, 929–941.Google Scholar
  30. World Health Organization. (1978). A growth chart for international use in maternal and child health care. Geneva.Google Scholar
  31. World Health Organization. (1994). Working group on infant growth. Geneva: An Evaluation of Infant Growth.Google Scholar
  32. World Health Organization. (1995). Physical status: The use and interpretation of anthropometry. Report of a WHO expert committee. World Health Organization Technical Report Series, 854, 1–452.Google Scholar
  33. World Health Organization. (2006). WHO child growth standards: Length/height-for-age, weight-for-age, weight-for-length, weight-for-height, and body mass index-for-age: Methods and development. Geneva, Switzerland: World Health Organization.Google Scholar

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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of StatisticsNorth-Eastern Hill UniversityShillong, MeghalayaIndia

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