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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References

Altun, E. (2019). The generalized Gudermannian distribution: inference and volatility modelling. Statistics, 53(2):364–386.
Bantan, R.A., Chesneau, C., Jamal, F., Elgarhy, M., Tahir, M.H., Ali, A., Zubair, M. and Anam, S. (2020). Some new facts about the unit-Rayleigh distribution with applications. Mathematics, 8(11):1954. 
Bhatti, F.A., Ali, A., Hamedani, G., Korkmaz, M.Ç. and Ahmad, M. (2021). The unit generalized log Burr XII distribution: Properties and application. AIMS Mathematics, 6(9):10222–10252.
Chesneau, C. (2021). Study of a unit power-logarithmic distribution. Open Journal of Mathematical Sciences, 5(1):218–235.
Cordeiro, G.M. and Lemonte, A.J. (2014). The McDonald arcsine distribution: A new model to proportional data. Statistics, 48(1):182–199.
El-Monsef, A., Sohsah, N.M. and Hassanein, W.A. (2021). Unit Monsef distribution with regression model. Asian Journal of Probability and Statistics, 15(4):330–340.
Ghosh, I., Dey, S. and Kumar, D. (2019). Bounded MO extended exponential distribution with applications. Stochastics and Quality Control, 34(1):35–51.
Haj Ahmad, H., Almetwally, E.M., Elgarhy, M. and Ramadan, D.A. (2023). On unit exponential Pareto distribution for modeling the recovery rate of COVID-19. Processes, 11(1):232. 
Hassan, A.S., Fayomi, A., Algarni, A. and Almetwally, E.M. (2022). Bayesian and non-Bayesian inference for unit-exponentiated half-logistic distribution with data analysis. Applied Sciences, 12(21):11253. 
Korkmaz, M.Ç. and Chesneau, C. (2021). On the unit Burr-XII distribution with the quantile regression modeling and applications. Computational and Applied Mathematics, 40(1):29. 
Korkmaz, M.Ç., Chesneau, C. and Korkmaz, Z.S. (2021). Transmuted unit Rayleigh quantile regression model: Alternative to beta and Kumaraswamy quantile regression models. University Politehnica of Bucharest Scientific Bulletin Series Applied Mathematics and Physics, 83(3):149–158.
Kumaraswamy, P. (1980). A generalized probability density function for double-bounded random processes. Journal of Hydrology, 46(1-2):79–88.
Mazucheli, J., Menezes, A.F.B. and Chakraborty, S. (2019). On the one parameter unit-Lindley distribution and its associated regression model for proportion data. Journal of Applied Statistics, 46(4):700–714.
Mazucheli, J., Menezes, A.F. and Dey, S. (2018). The unit-Birnbaum-Saunders distribution with applications. Chilean Journal of Statistics, 9(1):47–57.
Mazucheli, J., Menezes, A.F. and Dey, S. (2019). Unit-Gompertz distribution with applications. Statistica, 79(1):25–43.
Nasiru, S., Abubakari, A.G. and Angbing, I.D. (2021). Bounded odd inverse Pareto exponential distribution: Properties, estimation, and regression. International Journal of Mathematics and Mathematical Sciences, 2021:9955657.
Nasiru, S., Abubakari, A.G. and Chesneau, C. (2022). New lifetime distribution for modeling data on the unit interval: Properties, Applications and Quantile regression. Mathematical and Computational Applications, 27(6), 105.
Stock, J.H. and Watson, M.W. (2003). Introduction to Econometrics. New York: Prentice Hall.
Topp, C.W. and Leone, F.C. (1955). A family of J-shaped frequency functions. Journal of the American Statistical Association, 50(269):209–219.
Yousof, H.M., Alizadeh, M., Jahanshahi, S.M.A., Ramires, T.G., Ghosh, I. and Hamedani, G.G. (2017). The transmuted Topp-Leone G family of distributions: theory, characterizations and applications. Journal of Data Science, 15(4):723–740.
Zayed, M.A., Hassan, A.S., Almetwally, E.M., Aboalkhair, A.M., Al-Nefaie, A.H. and Almongy, H.M. (2023). A compound class of unit Burr XII model: Theory, Estimation, Fuzzy, and Application. Scientific Programming, 2023:4509889.
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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