DISTRIBUTION MODEL OF HUMAN DEVELOPMENT INDEX IN PAPUA PROVINCE BASED ON REGIONAL CLUSTERING

  • Jonathan K. Wororomi Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Cenderawasih, Indonesia https://orcid.org/0000-0003-3879-3731
  • Alvian M. Sroyer Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Cenderawasih, Indonesia https://orcid.org/0000-0003-1194-5774
  • Henderina Morin Department of Government Science, Faculty of Social and Political Sciences, Universitas Cenderawasih, Indonesia https://orcid.org/0009-0001-5766-8111
  • Felix Reba Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Cenderawasih, Indonesia https://orcid.org/0000-0001-8798-2366
  • Ishak S. Beno Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Cenderawasih, Indonesia https://orcid.org/0000-0002-4300-2271
  • Oscar O. O. Wambrauw Department of Management, Faculty of Economics and Business, Universitas Cenderawasih, Indonesia https://orcid.org/0000-0002-1613-7349
DOI: https://doi.org/10.30598/barekengvol19iss4pp2693-2708
Keywords: Clustering, Goodness of Fit (GoF), Human Development Index, Papua, Probability Distribution

Abstract

Modeling the distribution of Human Development Index (HDI) components is essential to uncover underlying disparities and guide targeted policy interventions. This study aims to analyze HDI data, focusing on the average length of schooling across 26 districts in Papua Province from 2010 to 2023, to identify the most suitable probability distribution model. Using the k-means clustering method, two main groups were identified based on the average length of schooling. Cluster 1 includes 11 districts with a Weibull distribution, characterized by a scale parameter of 8.9931 and a shape parameter of 16.1272, indicating significant variation in education duration. Cluster 2 consists of 15 districts with a scale parameter of 3.73006 and a shape parameter of 8.07662, showing a distribution with a long tail and greater variability. This study provides insights into the distribution patterns of education duration in Papua, which could aid policymakers in making more targeted decisions and allocating resources efficiently. The findings also highlight regional disparities and the need for specific educational interventions. These results are valuable for government entities, NGOs, researchers, and international donors interested in improving educational outcomes in underdeveloped areas. However, the analysis is limited by the scope of available data and the assumption of homogeneity within clusters.

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References

R. Karagiannis and G. Karagiannis, “CONSTRUCTING COMPOSITE INDICATORS WITH SHANNON ENTROPY: THE CASE OF HUMAN DEVELOPMENT INDEX,” Socio-Economic Planning Sciences, 2020, doi: https://doi.org/10.1016/j.seps.2019.03.007.

C. Türe and Y. Türe, “A MODEL FOR THE SUSTAINABILITY ASSESSMENT BASED ON THE HUMAN DEVELOPMENT INDEX IN DISTRICTS OF MEGACITY ISTANBUL (TURKEY),” Environment, Development and Sustainability, 2021, doi: https://doi.org/10.1007/s10668-020-00735-9.

Y. Jiang and C. Shi, “ESTIMATING SUSTAINABILITY AND REGIONAL INEQUALITIES USING AN ENHANCED SUSTAINABLE DEVELOPMENT INDEX IN CHINA,” Sustainable Cities and Society, 2023, doi: https://doi.org/10.1016/j.scs.2023.104555.

S. Kwatra, A. Kumar, and P. Sharma, “A CRITICAL REVIEW OF STUDIES RELATED TO CONSTRUCTION AND COMPUTATION OF SUSTAINABLE DEVELOPMENT INDICES,” 2020. doi: https://doi.org/10.1016/j.ecolind.2019.106061.

W. Afalia, I. Hamda, S. A. Adriana, A. F. Alamsyah, and N. L. Wafiroh, “DETERMINANTS OF HUMAN DEVELOPMENT INDEX IN PAPUA PROVINCE 2012-2021,” Wiga : Jurnal Penelitian Ilmu Ekonomi, 2023, doi: https://doi.org/10.30741/wiga.v13i2.1076.

D. P. Rahmawati, I. N. Budiantara, D. D. Prastyo, and M. A. D. Octavanny, “MODELING OF HUMAN DEVELOPMENT INDEX IN PAPUA PROVINCE USING SPLINE SMOOTHING ESTIMATOR IN NONPARAMETRIC REGRESSION,” in Journal of Physics: Conference Series, 2021. doi: https://doi.org/10.1088/1742-6596/1752/1/012018.

A. E. Ezugwu et al., “A COMPREHENSIVE SURVEY OF CLUSTERING ALGORITHMS: STATE-OF-THE-ART MACHINE LEARNING APPLICATIONS, TAXONOMY, CHALLENGES, AND FUTURE RESEARCH PROSPECTS,” 2022. doi: https://doi.org/10.1016/j.engappai.2022.104743.

A. Rajabi, M. Eskandari, M. J. Ghadi, L. Li, J. Zhang, and P. Siano, “A COMPARATIVE STUDY OF CLUSTERING TECHNIQUES FOR ELECTRICAL LOAD PATTERN SEGMENTATION,” Renewable and Sustainable Energy Reviews, 2020, doi: https://doi.org/10.1016/j.rser.2019.109628.

J. Li and J. Liu, “A MODIFIED EXTREME VALUE PERSPECTIVE ON BEST-PERFORMANCE LIFE EXPECTANCY,” Journal of Population Research, 2020, doi: https://doi.org/10.1007/s12546-020-09248-8.

M. S. Dhanoa et al., “A STRATEGY FOR MODELLING HEAVY-TAILED GREENHOUSE GASES (GHG) DATA USING THE GENERALISED EXTREME VALUE DISTRIBUTION: ARE WE OVERESTIMATING GHG FLUX USING THE SAMPLE MEAN?,” Atmospheric Environment, 2020, doi: https://doi.org/10.1016/j.atmosenv.2020.117500.

H. Omrani, A. Alizadeh, and M. Amini, “A NEW APPROACH BASED ON BWM AND MULTIMOORA METHODS FOR CALCULATING SEMI-HUMAN DEVELOPMENT INDEX: AN APPLICATION FOR PROVINCES OF IRAN,” Socio-Economic Planning Sciences, 2020, doi: https://doi.org/10.1016/j.seps.2019.02.004.

B. Giles-Corti, M. Lowe, and J. Arundel, “ACHIEVING THE SDGS: EVALUATING INDICATORS TO BE USED TO BENCHMARK AND MONITOR PROGRESS TOWARDS CREATING HEALTHY AND SUSTAINABLE CITIES,” 2020. doi: https://doi.org/10.1016/j.healthpol.2019.03.001.

S. A. Takyi, O. Amponsah, M. O. Asibey, and R. A. Ayambire, “AN OVERVIEW OF GHANA’S EDUCATIONAL SYSTEM AND ITS IMPLICATION FOR EDUCATIONAL EQUITY,” International Journal of Leadership in Education, 2021, doi: 10.1080/13603124.2019.1613565.

A. Sinha, D. Balsalobre-Lorente, M. W. Zafar, and M. M. Saleem, “ANALYZING GLOBAL INEQUALITY IN ACCESS TO ENERGY: DEVELOPING POLICY FRAMEWORK BY INEQUALITY DECOMPOSITION,” Journal of Environmental Management, 2022, doi: https://doi.org/10.1016/j.jenvman.2021.114299.

T. Ladi, A. Mahmoudpour, and A. Sharifi, “ASSESSING IMPACTS OF THE WATER POVERTY INDEX COMPONENTS ON THE HUMAN DEVELOPMENT INDEX IN IRAN,” Habitat International, 2021, doi: https://doi.org/10.1016/j.habitatint.2021.102375.

R. Zriaa and S. Amali, “A COMPARATIVE STUDY BETWEEN K-NEAREST NEIGHBORS AND K-MEANS CLUSTERING TECHNIQUES OF COLLABORATIVE FILTERING IN E-LEARNING ENVIRONMENT,” in Lecture Notes in Networks and Systems, 2021. doi: https://doi.org/10.1007/978-3-030-66840-2_21.

T. H. T. Nguyen, D. T. Dinh, S. Sriboonchitta, and V. N. Huynh, “A METHOD FOR K-MEANS-LIKE CLUSTERING OF CATEGORICAL DATA,” Journal of Ambient Intelligence and Humanized Computing, 2023, doi: 10.1007/s12652-019-01445-5.

A. Vouros and E. Vasilaki, “A SEMI-SUPERVISED SPARSE K-MEANS ALGORITHM,” Pattern Recognition Letters, 2021, doi: https://doi.org/10.1016/j.patrec.2020.11.015.

M. K. Gupta and P. Chandra, “AN EMPIRICAL EVALUATION OF K-MEANS CLUSTERING ALGORITHM USING DIFFERENT DISTANCE/SIMILARITY METRICS,” in Lecture Notes in Electrical Engineering, 2020. doi: https://doi.org/10.1007/978-3-030-30577-2_79.

D. A. Lusia, I. Salsabila, H. Kusdarwati, and S. Astutik, “CLUSTERING DISTRICTS/CITIES IN EAST JAVA PROVINCE BASED ON HIV CASES USING K-MEANS, AGNES, AND ENSEMBLE,” Barekeng: Jurnal Ilmu Matematika dan Terapan, vol. 19, no. 1, pp. 63–72, March 2025, doi: https://doi.org/10.30598/barekengvol19iss1pp63-72.

Z. A. Zain, N. Saif, M. Mussafi, and E. D. Supandi, “CLUSTER ANALYSIS OF K-MEANS AND WARD METHOD IN FORMING A ROBUST PORTFOLIO : AN EMPIRICAL STUDY OF JAKARTA ISLAMIC INDEX,” Barekeng: Jurnal Ilmu Matematika dan Terapan, vol. 19, no. 1, pp. 537–546, March 2025,doi: https://doi.org/10.30598/barekengvol19iss1pp537-546

M. Daraghmeh, A. Agarwal, and Y. Jararweh, “AN ENSEMBLE CLUSTERING APPROACH FOR MODELING HIDDEN CATEGORIZATION PERSPECTIVES FOR CLOUD WORKLOADS,” Cluster Computing, 2024, doi: https://doi.org/10.21203/rs.3.rs-3246818/v1.

Z. Halim, H. M. Sargana, Aadam, Uzma, and M. Waqas, “CLUSTERING OF GRAPHS USING PSEUDO-GUIDED RANDOM WALK,” Journal of Computational Science, 2021, doi: https://doi.org/10.1016/j.jocs.2020.101281.

Y. M. Kantar and I. Usta, “ANALYSIS OF THE UPPER-TRUNCATED WEIBULL DISTRIBUTION FOR WIND SPEED,” Energy Conversion and Management, vol. 96, pp. 81–88, 2015, doi: https://doi.org/10.1016/j.enconman.2015.02.063.

C. Ozay and M. S. Celiktas, “STATISTICAL ANALYSIS OF WIND SPEED USING TWO-PARAMETER WEIBULL DISTRIBUTION IN ALAÇATI REGION,” Energy Conversion and Management, vol. 121, pp. 49–54, 2016, doi: https://doi.org/10.1016/j.enconman.2016.05.026.

T. Arslan, Y. M. Bulut, and A. Altin Yavuz, “COMPARATIVE STUDY OF NUMERICAL METHODS FOR DETERMINING WEIBULL PARAMETERS FOR WIND ENERGY POTENTIAL,” Renewable and Sustainable Energy Reviews, vol. 40, pp. 820–825, 2014, doi: https://doi.org/10.1016/j.rser.2014.08.009.

P. A. Costa Rocha, R. C. de Sousa, C. F. de Andrade, and M. E. V. da Silva, “COMPARISON OF SEVEN NUMERICAL METHODS FOR DETERMINING WEIBULL PARAMETERS FOR WIND ENERGY GENERATION IN THE NORTHEAST REGION OF BRAZIL,” Applied Energy, vol. 89, no. 1, pp. 395–400, 2012, doi: https://doi.org/10.1016/j.apenergy.2011.08.003.

J. Then, F. J. Permana, and B. Yong, “PARAMETER ESTIMATION OF LOGNORMAL AND PARETO TYPE I DISTRIBUTIONS USING FREQUENTIST AND BAYESIAN INFERENCES,” Barekeng: Jurnal Ilmu Matematika dan Terapan, vol. 19, no. 1, pp. 141–152, March 2025, doi: https://doi.org/10.30598/barekengvol19iss1pp141-152.

E. Salvador, M. B. Gonzalez, F. Campabadal, J. Martin-Martinez, R. Rodriguez, and E. Miranda, “ASSESSMENT OF THE VARIABILITY OF THE I-V CHARACTERISTIC OF HFO2-BASED RESISTIVE SWITCHING DEVICES AND ITS SIMULATION USING THE QUASI-STATIC MEMDIODE MODEL,” Solid-State Electronics, vol. 206, no. May, p. 108667, 2023, doi: https://doi.org/10.1016/j.sse.2023.108667.

M. H. Samuh and A. M. Salhab, “DISTRIBUTION OF SQUARED SUM OF PRODUCTS OF INDEPENDENT NAKAGAMI-M RANDOM VARIABLES,” Communications in Statistics: Simulation and Computation, 2023, doi: https://doi.org/10.1080/03610918.2023.2234668.

H. A. Bayoud, “TESTS OF NORMALITY: NEW TEST AND COMPARATIVE STUDY,” Communications in Statistics: Simulation and Computation, vol. 50, no. 12, pp. 4442–4463, 2021, doi: https://doi.org/10.1080/03610918.2019.1643883.

D. K. Wijekularathna, A. B. W. Manage, and S. M. Scariano, “POWER ANALYSIS OF SEVERAL NORMALITY TESTS: A MONTE CARLO SIMULATION STUDY,” Communications in Statistics: Simulation and Computation, vol. 51, no. 3, pp. 757–773, 2020, doi: https://doi.org/10.1080/03610918.2019.1658780.

W. Zheng, D. Lai, and K. L. Gould, “A SIMULATION STUDY OF A CLASS OF NONPARAMETRIC TEST STATISTICS: A CLOSE LOOK OF EMPIRICAL DISTRIBUTION FUNCTION-BASED TESTS,” Communications in Statistics: Simulation and Computation, vol. 52, no. 3, pp. 1133–1148, 2023, doi: https://doi.org/10.1080/03610918.2021.1874987.

M. Krit, O. Gaudoin, M. Xie, and E. Remy, “SIMPLIFIED LIKELIHOOD BASED GOODNESS-OF-FIT TESTS FOR THE WEIBULL DISTRIBUTION,” Communications in Statistics: Simulation and Computation, vol. 45, no. 3, pp. 920–951, 2016, doi: https://doi.org/10.1080/03610918.2013.879889.

M. H. Ouahabi, H. Elkhachine, F. Benabdelouahab, and A. Khamlichi, “COMPARATIVE STUDY OF FIVE DIFFERENT METHODS OF ADJUSTMENT BY THE WEIBULL MODEL TO DETERMINE THE MOST ACCURATE METHOD OF ANALYZING ANNUAL VARIATIONS OF WIND ENERGY IN TETOUAN - MOROCCO,” Procedia Manufacturing, vol. 46, no. 2019, pp. 698–707, 2020, doi: https://doi.org/10.1016/j.promfg.2020.03.099.

A. K. Azad, M. G. Rasul, M. M. Alam, S. M. Ameer Uddin, and S. K. Mondal, “ANALYSIS OF WIND ENERGY CONVERSION SYSTEM USING WEIBULL DISTRIBUTION,” Procedia Engineering, vol. 90, pp. 725–732, 2014, doi: https://doi.org/10.1016/j.proeng.2014.11.803.

M. Nassar, A. Alzaatreh, M. Mead, and O. Abo-Kasem, “ALPHA POWER WEIBULL DISTRIBUTION: PROPERTIES AND APPLICATIONS,” Communications in Statistics - Theory and Methods, vol. 46, no. 20, pp. 10236–10252, 2017, doi: https://doi.org/10.1080/03610926.2016.1231816.

M. Krit, O. Gaudoin, and E. Remy, “GOODNESS-OF-FIT TESTS FOR THE WEIBULL AND EXTREME VALUE DISTRIBUTIONS: A REVIEW AND COMPARATIVE STUDY,” Communications in Statistics: Simulation and Computation, vol. 50, no. 7, pp. 1888–1911, 2021, doi: https://doi.org/10.1080/03610918.2019.1594292.

P. K. Chaurasiya, S. Ahmed, and V. Warudkar, “STUDY OF DIFFERENT PARAMETERS ESTIMATION METHODS OF WEIBULL DISTRIBUTION TO DETERMINE WIND POWER DENSITY USING GROUND BASED DOPPLER SODAR INSTRUMENT,” Alexandria Engineering Journal, vol. 57, no. 4, pp. 2299–2311, 2018, doi: https://doi.org/10.1016/j.aej.2017.08.008.

A. M. Basheer, “ALPHA POWER INVERSE WEIBULL DISTRIBUTION WITH RELIABILITY APPLICATION,” Journal of Taibah University for Science, vol. 13, no. 1, pp. 423–432, 2019, doi: https://doi.org/10.1080/16583655.2019.1588488.

A. O. Lima, G. B. Lyra, M. C. Abreu, J. F. Oliveira-Júnior, M. Zeri, and G. Cunha-Zeri, “EXTREME RAINFALL EVENTS OVER RIO DE JANEIRO STATE, BRAZIL: CHARACTERIZATION USING PROBABILITY DISTRIBUTION FUNCTIONS AND CLUSTERING ANALYSIS,” Atmospheric Research, vol. 247, no. March 2020, p. 105221, 2021, doi: https://doi.org/10.1016/j.atmosres.2020.105221.

A. Sulis, R. Cozza, and A. Annis, “EXTREME WAVE ANALYSIS METHODS IN THE GULF OF CAGLIARI (SOUTH SARDINIA, ITALY),” Ocean and Coastal Management, vol. 140, pp. 79–87, 2017, doi: https://doi.org/10.1016/j.ocecoaman.2017.02.023.

Q. Han, S. Ma, T. Wang, and F. Chu, “KERNEL DENSITY ESTIMATION MODEL FOR WIND SPEED PROBABILITY DISTRIBUTION WITH APPLICABILITY TO WIND ENERGY ASSESSMENT IN CHINA,” Renewable and Sustainable Energy Reviews, vol. 115, no. September, p. 109387, 2019, doi: https://doi.org/10.1016/j.rser.2019.109387.

K. Mohammadi, O. Alavi, and J. G. McGowan, “USE OF BIRNBAUM-SAUNDERS DISTRIBUTION FOR ESTIMATING WIND SPEED AND WIND POWER PROBABILITY DISTRIBUTIONS: A REVIEW,” Energy Conversion and Management, vol. 143, pp. 109–122, 2017, doi: https://doi.org/10.1016/j.enconman.2017.03.083.

K. S. Guedes, C. F. de Andrade, P. A. C. Rocha, R. dos S. Mangueira, and E. P. de Moura, “PERFORMANCE ANALYSIS OF METAHEURISTIC OPTIMIZATION ALGORITHMS IN ESTIMATING THE PARAMETERS OF SEVERAL WIND SPEED DISTRIBUTIONS,” Applied Energy, vol. 268, no. March, p. 114952, 2020, doi: https://doi.org/10.1016/j.apenergy.2020.114952.

C. Jung and D. Schindler, “GLOBAL COMPARISON OF THE GOODNESS-OF-FIT OF WIND SPEED DISTRIBUTIONS,” Energy Conversion and Management, vol. 133, pp. 216–234, 2017, doi: https://doi.org/10.1016/j.enconman.2016.12.006.

M. A. ul Haq, G. S. Rao, M. Albassam, and M. Aslam, “MARSHALL–OLKIN POWER LOMAX DISTRIBUTION FOR MODELING OF WIND SPEED DATA,” Energy Reports, vol. 6, no. May, pp. 1118–1123, 2020, doi: https://doi.org/10.1016/j.egyr.2020.04.033.

A. M. Basheer, “ALPHA POWER INVERSE WEIBULL DISTRIBUTION WITH RELIABILITY APPLICATION,” Journal of Taibah University for Science, vol. 13, no. 1, pp. 423–432, 2019, doi: https://doi.org/10.1080/16583655.2019.1588488.

M. Mansoor, M. H. Tahir, G. M. Cordeiro, S. B. Provost, and A. Alzaatreh, “THE MARSHALL-OLKIN LOGISTIC-EXPONENTIAL DISTRIBUTION,” Communications in Statistics - Theory and Methods, vol. 48, no. 2, pp. 220–234, 2019, doi: https://doi.org/10.1080/03610926.2017.1414254.

I. Pobočíková, Z. Sedliačková, and M. Michalková, “APPLICATION OF FOUR PROBABILITY DISTRIBUTIONS FOR WIND SPEED MODELING,” Procedia Engineering, vol. 192, pp. 713–718, 2017, doi: https://doi.org/10.1016/j.proeng.2017.06.123.

T. B. M. J. Ouarda, C. Charron, and F. Chebana, “REVIEW OF CRITERIA FOR THE SELECTION OF PROBABILITY DISTRIBUTIONS FOR WIND SPEED DATA AND INTRODUCTION OF THE MOMENT AND L-MOMENT RATIO DIAGRAM METHODS, WITH A CASE STUDY,” Energy Conversion and Management, vol. 124, pp. 247–265, 2016, doi: https://doi.org/10.1016/j.enconman.2016.07.012.

Published
2025-09-01
How to Cite
[1]
J. K. Wororomi, A. M. Sroyer, H. Morin, F. Reba, I. S. Beno, and O. O. O. Wambrauw, “DISTRIBUTION MODEL OF HUMAN DEVELOPMENT INDEX IN PAPUA PROVINCE BASED ON REGIONAL CLUSTERING”, BAREKENG: J. Math. & App., vol. 19, no. 4, pp. 2693-2708, Sep. 2025.
Issue
Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
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Articles

Copyright (c) 2025 Jonathan K. Wororomi, Alvian M. Sroyer, Henderina Morin, Felix Reba, Ishak S. Beno, Oscar O. O. Wambrauw

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