A Comparison of Modality Tests Based on Real Life Data Applications

A Comparison of Modality Tests Based on Real Life Data Applications


  • Rana Muhammad Imran Arshad Department of Statistics Govt., S.E. College, Bahawalpur, Pakistan
  • Shahina Imran Department of Economics Govt., S. E. College, Bahawalpur, Pakistan
  • Farrukh Jamal Department of Statistics Govt., S.A. Postgraduate College, Dera Nawab Sahib, Bahawalpur, Pakistan
  • Gamze Ozel Department of Statistics, Hacettepe University, Ankara, Turkey


Nonparametric tests, Silverman’s bandwidth test, Hartigan’s dip test, Proportional Mass (PM) test, Excess Mass test, unimodality, Real life data application


Nonparametric tests for the modality are known as distribution-free tests to evaluate the evidence about homogeneity in a population. Silverman’s bandwidth test by Silverman [1], the Hartigan’s dip test by Hartigan [6],Hartigan and Hartigan [7], Proportional Mass (PM) test by Cavallo and Ringobon [4] and Excess Mass (EM) test by Muller and Sawitzki [9] are very popular modality tests in literature. The researchers of these tests claimed that their tests perform well to detection of unimodality, bimodality and multimodality. This study focusses on the comparison of these tests based on real data applications. The results show that Silverman’s bandwidth test is the best test for detecting modality whether it is unimodality, bimodality or multimodality.


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How to Cite

Arshad, R. M. I., Imran, S., Jamal, F. ., & Ozel, G. . (2021). A Comparison of Modality Tests Based on Real Life Data Applications: A Comparison of Modality Tests Based on Real Life Data Applications. Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences, 56(1), 69–75. Retrieved from https://ppaspk.org/index.php/PPAS-A/article/view/158




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