A Comparison of Unimodality Based on Size of the Test Criterion

Rana Muhammad Imran Arshad; Sadaf Khan; Farrukh Jamal; Shahina Imran

doi:10.64060/JASRv2i33

Authors

Rana Muhammad Imran Arshad Department of Statistics, Govt. Sadiq Egerton College, Bahawalpur, Pakistan Author
Sadaf Khan Department of Statistics, The Islamia University of Bahawalpur, Pakistan Author https://orcid.org/0000-0002-0258-5124
Farrukh Jamal Department of Statistics, Faculty of Science, University of Tabuk, Saudi Arabia Author https://orcid.org/0000-0001-6192-9890
Shahina Imran Department of Economics, Govt. College for Women, Dubai Mahal Road, Bahawalpur, Pakistan Author

DOI:

https://doi.org/10.64060/JASRv2i33

Keywords:

Modality Tests, Hartigan’s Dip Test, Silverman Bandwidth Test, Proportional Mass (PM) Test and Excess Mass (EM) Test, Size of the test, Monte Carlo Simulation Technique

Abstract

Non-parametric modality tests are widely and frequently used in every field of life especially in Economics, Social Sciences, Sports Sciences, Medical Sciences, and Biological Sciences etc. Some tests for modality are used for parametric (depend upon any distribution) and some are used for non-parametric (distribution free tests). But this study discusses the four famous non-parametric tests for modality or multimodality (a) Hartigan Dip Test; (b) Silverman Bandwidth test; (c) Proportional Mass test (d); Excess Mass test. These tests are frequently used in the literature of statistics. Most of the studies used these tests for testing modality. But nobody in the available literature compared these tests on the basis of size. This study compares these tests on the basis of the size and finds that which of them is the best test and which of them is the worst test. In addition to size, this study also evaluates the power of these tests under four alternative bimodal scenarios using Monte Carlo simulations with 10,000 replications. The simulation procedure is described in detail with a step-by-step algorithm and a flowchart to ensure full reproducibility.

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