Estimation of Distribution Function Parameters for Cases of Risk of Mortality Rate due to Malnutrition and Unhealthy Sanitation in Indonesia

Moch Panji Agung Saputra; Tubagus Robbi Megantara; Sulidar Fitri

doi:10.47194/ijgor.v3i1.117

Authors

Moch Panji Agung Saputra
moch16006@mail.unpad.ac.id
Master of Mathematics Study Program, Faculty of Mathematics and Natural Science Universitas Padjadjaran, Indonesia
Tubagus Robbi Megantara Master of Mathematics Study Program, Faculty of Mathematics and Natural Science Universitas Padjadjaran, Indonesia
Sulidar Fitri Department of Computer Science Education, Universitas Muhammadiyah Tasikmalaya, Indonesia

Abstract

Child undernutrition is a significant problem in Indonesia; persistently high rates of stunting, underweight and wasting. Data about malnutrition and sanitation that taken for this research is data of age-standardized death rate, measured per 100,000 individuals from unsafe sanitation and malnutrition in Indonesia. The purpose of this research is to determine the distribution function and estimate the parameter distribution, so the values can provide identification of risk events. The method used for this research is Maximum Likelihood Estimation (MLE) and Newton Raphson iterations. The distribution function formed is gamma and Generalized Pareto Distribution (GPD), respectively for sanitation and malnutrition problems in Indonesia. The projected probability of occurrence of the risk of death due to malnutrition tends to be low in the future. So that the risk classification of the mortality rate due to malnutrition is considered low based on the results of the probability distribution approach on the GPD function. While, the projected probability of occurrence of the risk of death due to sanitation tends to decrease in the future. Based on the graph, the risk value with a high probability is around 20. So, the risk classification of the mortality rate due to malnutrition is considered moderate based on the results of the probability distribution approach on this gamma function.

References

Maehara, M., Rah, JH., Roshita, A., Suryantan J, Rachmadewi A, Izwardy D. (2019). Patterns and risk factors of double burden of malnutrition among adolescent girls and boys in Indonesia. PLoS ONE, 14(8).

Mahmudiono, T., Sumarmi, S., & Rosenkrantz, R. (2017). Household dietary diversity and child stunting in East Java, Indonesia. Asia Pacific Journal of Clinical Nutrition, 26(2), 317-325.

Mboi, N., Surbakti, I. M., Trihandini, E., Elyazar, I., Smith, K. H. (2018). On the road to universal health care in Indonesia, 1990â€“2016: a systematic analysis for the Global Burden of Disease Study 2016. The Lancet, 392(10147), 581 â€“ 591.

Sandjaja, S., Budiman, B., Harahap, H. (2013). Food consumption and nutritional and biochemical status of 0Â·5â€“12-year-old Indonesian children: the SEANUTS study. British Jourcal of Nutrition, 110.

Oddo, V. M., Maehara, M., Izwardy, D,. Sugihantono, A., Ali, P. B., and Rah, J. H. (2019). Risk factors for nutrition-related chronic disease among adults in Indonesia. PLoS ONE, 14(8).

Beal, T., Tumilowicz, A., Sutrisna, A., Izwardy, D., and Neufeld, L. (2018). A review of child stunting determinants in Indonesia. Maternal and Child Nutrition, 1-10.

Watson, F. (2019) Nutrition in Indonesia, Background Paper for The 2018 Health Sector Review, UNICEF Indonesia 6.

World Health Organization (WHO). (2019). National systems to support drinking-water, sanitation and hygiene: global status report 2019. UN-Water global analysis and assessment of sanitation and drinking- water (GLAAS) 2019 report. Geneva: World Health Organization.

Cronin, A. A., Odagiri, M., Arsyad, B., Nuryetty, M. T., Amannullah, G., Santoso H., Darundiyah, K., and Nasution, N. A. (2017). Piloting water quality testing coupled with a national socioeconomic survey in Yogyakarta province, Indonesia, towards tracking of Sustainable Development Goal 6, International Journal of Hygiene and Environmental Health, Vol. 220(7).

Luby, S., Rahman, M., and Arnold, B. Effects of water quality, sanitation, handwashing, and nutritional interventions on diarrhoea and child growth in rural Bangladesh: a cluster randomised controlled trial. Lancet Global Health, 6 (2018).

United Nations Childrenâ€™s Fund. The State of Children in Indonesia â€“ Trends, Opportunities and Challenges for Realizing Childrenâ€™s Rights. Jakarta: UNICEF Indonesia.

Smith, R. Maximum likelihood estimation in a class of nonregularcasesâ€. Journal of Biometrika,72(1), 1985, 67â€“90.

Mathews, J. H, and Fink K. D. Numerical Methods for Computer Science, Engineering, and Mathematics. Prentice-Hall, Englewood Cliffs 2nd, 1992.

Frank, J. and Massey, Jr. The Kolmogorov-Smirnov Test for Goodness of Fit. Journal of the American Statistical Association. Vol. 46(253) (1951) 68-78.

S. Kang and J. Song, Parameter and Quantile Estimation for the Generalized Pareto Distribution In Peaks Over Threshold Framework. Journal of the Korean Statistical Society, Vol. 46(4), 2017, 487-501.

Jockovic, J. Quantile Estimation for The Generalized Pareto Distribution with Application to Finance. Yugoslav Journal of Operations Research. 22 (2012) 297-311.

D. Matthias, E. Paul, and D. D. Lambrigger, The Quantitative Modeling of Operational Risk : Between G and H and EVT, Astin Bulletin, Vol 37(2), 2007, 265-291.

Thom, H. C. A note on the gamma distribution. Monthly Weather Review. 86(4) (1958) 117-122.

Smith, R. (1985). Maximum Likelihood Estimation in A Class of Non-regular Cases. Journal of Biometrika, 72(1), 67â€“90.

Esterhuysen, J., Styger, P., and Vuuren, G. V. (2008). Calculating Operational Value-at-Risk in a Retail Bank, South African Journal of Economic and Management Sciences, 11(1), 1-16.