Logit Gudermannian distribution‎: ‎Properties‎, ‎regression and applications

Document Type : Original Scientific Paper

Authors

1 Department of Mathematical Sciences‎, ‎University of Mines and Technology‎, ‎Ghana

2 Statistics Department‎, ‎Tamale Technical University‎, ‎Tamale‎, ‎Ghana

3 Department of Statistics and Actuarial Science‎, ‎School of Mathematical Sciences‎, ‎C‎. ‎K‎. ‎Tedam University of Technology and Applied Sciences‎, ‎Ghana

Abstract

In this paper‎, ‎we propose a unit distribution called the logit Gudermannian distribution and present various statistical properties of the proposed model‎. ‎Six parameter estimation methods are explored in the quest to estimate the parameters of the proposed distribution‎. ‎We determine which estimation methods provide better parameter estimates through simulation studies‎. ‎The study shows that the logit Gudermannian distribution provides a better fit for the datasets used than other unit distributions‎. ‎Consequently‎, ‎the logit Gudermannian distribution is used to develop a parametric regression model for studying the relationship between a unit response variable and other exogenous variables‎. ‎The new regression model's performance is compared to that of other existing regression models and found to be competitive.

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Journal of Statistical Modelling: Theory and Applications
Volume 4, Issue 1
January 2023
Pages 25-44

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History

  • Receive Date: 14 May 2023
  • Revise Date: 08 December 2023
  • Accept Date: 18 December 2023

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