The unit log-normal distribution : An alternative for beta and Kumaraswamy distributions

Ribeiro-Reis, Lucas David

doi:10.47974/JSMS-1018

Open Access Research Article

The unit log-normal distribution : An alternative for beta and Kumaraswamy distributions

^*Lucas David Ribeiro-ReisCorresponding authorecon.lucasdavid@gmail.comDepartment of Economics Federal University of Alagoas Santana do Ipanema-ALBrazilView full profile →

* Corresponding author · click or hover a name for details

pp. 785–796Vol. 27Issue 4May 2024DOI: 10.47974/JSMS-1018XML

Received:: 15 Jun 2022
Published Online:: 27 May 2024
Article type:: Research Article
Language:: EN
Article no.:: JSMS-1018
Pages:: 785–796

Abstract

In this paper, through a transformation in the random variable with log-normal distribution, a new distribution was introduced called unit log-normal. Some properties of this new distribution are investigated. It is shown that the unit log-normal distribution belongs to the exponential family and that the maximum likelihood estimators for the two parameters that index the distribution have closed-forms. The accuracy of the maximum likelihood estimators for the two parameters is performed through a simulation study. Two applications to real data are considered, showing the potentiality of the new distribution.

Keywords

Unit log-normal distribution Exponential family Maximum likelihood method Monte Carlo simulation

Subject Classifications

(2010) 65C1046N30

References

[1] Altun, E., The log-weighted exponential regression model: alternative to the beta regression model. Communications in Statistics-Theory and Methods, 50(10) : 2306–2321 (2021).
[2] Firjan (2020). Federação das Indústrias do Estado do Rio de Janeiro. Índice FIRJAN de Desenvolvimento Municipal.
[3] Ghitany, M. E., Mazucheli, J., Menezes, A. F. B., and Alqallaf, F., The unit-inverse Gaussian distribution: A new alternative to two-parameter distributions on the unit interval. Communications in Statistics-Theory and Methods, 48(14) : 3423–3438 (2019).
[4] Gómez-Déniz, E., Sordo, M. A., and Calderín-Ojeda, E. (2014). The log–Lindley distribution as an alternative to the beta regression model with applications in insurance. Insurance: Mathematics and Economics, 54:49–57.
[5] Ipeadata. Instituto de Pesquisa Econômica Aplicada. Base de Dados (2020).
[6] Kumaraswamy, P., A generalized probability density function for doublebounded random processes. Journal of Hydrology, 46(1-2) : 79–88 (1980).
[7] Mazucheli, J., Menezes, A. F. B., and Dey, S., Unit-Gompertz distribution with applications. Statistica, 79(1) : 25–43 (2019).
[8] Mazucheli, J., Menezes, A. F. B., Fernandes, L. B., de Oliveira, R. P., and Ghitany, M. E., The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates. Journal of Applied Statistics, 47(6) : 954–974 (2020).
[9] Nwezza, E. E. and Ugwuowo, F. I., An extended normal distribution for reliability data analysis. Journal of Statistics and Management Systems, 25(2) : 369–392 (2022).
[10] R Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria(2020).
[11] Ribeiro-Reis, L. D., Unit log-logistic distribution and unit log-logistic regression model. Journal of the Indian Society for Probability and Statistics, 22(2) : 375–388 (2021).
[12] Ribeiro-Reis, L. D., Truncated exponentiated-exponential distribution: A distribution for unit interval. Journal of Statistics and Management Systems, pages 1–12 (2022).

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