Services on Demand
Journal
Article
English (pdf)
Article in xml format
Article references
Automatic translation
Send this article by e-mailIndicators
-
Cited by SciELO -
Access statistics
Related links
-
Cited by Google -
Similars in
SciELO -
Similars in Google
Share
Permalink
Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.46 no.2 Bogotá July/Dec. 2023 Epub July 12, 2023
https://doi.org/10.15446/rce.v46n2.105209
ORIGINAL ARTICLES OF RESEARCH
The Topp-Leone-Gompertz-Exponentiated Half Logistic-G Family of Distributions with Applications
La media familia logística exponencial de Topp-Leone-Gompertz de distribución con aplicaciones
1 Department of Mathematics and Statistical Sciences, Faculty of Sciences, Botswana International University of Science and Technology, Palapye, Botswana
This paper introduces and investigates a new family of distributions called the Topp-Leone-Gompertz-exponentiated half logistic-G (TL-Gom-EHL-G) distribution. Some mathematical and statistical properties of this family of distributions are derived. To estimate and evaluate the model parameters, the maximum likelihood estimation technique is used, and the consistency of maximum likelihood estimators is examined using Monte Carlo simulation. Applications to three real data sets from different areas were used to demonstrates the usefulness and versatility of the TL-Gom-EHL-G family of distributions.
Key words: Exponentiated Half Logistic Distribution; Maximum Likelihood Estimation; Gompertz Distribution; Goodness-of-fit Statistics; Simulation Study; Topp-Leone Distribution
Este artículo presenta e investiga una nueva familia de distribuciones denominada distribución Topp-Leone-Gompertz-exponenciada media logística-G (TL-Gom-EHL-G). Se derivan algunas propiedades matemáticas y estadísticas de esta familia de distribuciones. Para estimar y evaluar los parámetros del modelo se utiliza la técnica de estimación de máxima verosimilitud y se examina la consistencia de los estimadores de máxima verosimilitud mediante simulación de Monte Carlo. Se utilizaron aplicaciones a tres conjuntos de datos reales de diferentes áreas para demostrar la utilidad y versatilidad de la familia de distribuciones TL-Gom-EHL-G.
Palabras clave: Distribución de Topp-Leone; Distribución de Gompertz; Distribución logística media exponenciada; Estimación de máxima verosimilitud; Estudio de simulación; Estadísticas de bondad de ajuste
Acknowledgements
The authors are very grateful to the reviewers for their constructive feedback.
References
Aarset, M. V. (1987), 'How to identify a bathtub hazard rate', IEEE Transactions on Reliability 36(1), 106-108. [ Links ]
Aldahlan, M. & Afify, A. Z. (2018), 'The odd exponentiated half-logistic Burr XII distribution', Pakistán Journal of Statistics and Operation Research pp. 305-317. [ Links ]
Algarni, A., M. Almarashi, A., Elbatal, I., S. Hassan, A., Almetwally, E. M., M. Daghistani, A. & Elgarhy, M. (2021), 'Type I half logistic Burr X-G family: Properties, Bayesian, and non-Bayesian estimation under censored samples and applications to COVID-19 data', Mathematical Problems in Engineering 2021, 1-21. [ Links ]
Arnold, B. C., Balakrishnan, N. & Nagaraja, H. N. (2008), A first course in order statistics, SIAM. [ Links ]
Aryal, G. R., Ortega, E. M., Hamedani, G. & Yousof, H. M. (2017), 'The Topp-Leone generated Weibull distribution: regression model, characterizations and applications', International Journal of Statistics and Probability 6(1), 126-141. [ Links ]
Benkhelifa, L. (2017), 'The Marshall-Olkin extended generalized Gompertz distribution', Journal of Data Science 15(2), 239-266. [ Links ]
Boshi, M., Abid, S. & Al-Noor, N. (2020), Generalized gamma-generalized Gompertz distribution, in 'Journal of Physics: Conference Series', Vol. 1591, IOP Publishing, p. 012043. [ Links ]
Castillo, E., Hadi, A. S., Balakrishnan, N. & Sarabia, J.-M. (2005), Extreme value and related models with applications in engineering and science, Wiley Hoboken, NJ. [ Links ]
Chambers, J., William, C., Beat, K. & Paul, T. (1983), Graphical methods for data analysis, Wadsworth. [ Links ]
Chamunorwa, S., Makubate, B., Oluyede, B. & Chipepa, F. (2021), 'The exponentiated half logistic-log-logistic Weibull distribution: Model, properties and applications', Journal of Statistical Modelling: Theory and Applications 2(1), 101-120. [ Links ]
Chipepa, F. & Oluyede, B. (2021), 'The Marshall-Olkin-Gompertz-G family of distributions: Properties and applications', Journal of Nonlinear Sciences and Applications 14(4), 257-260. [ Links ]
Chipepa, F., Oluyede, B. & Makubate, B. (2020), 'The odd generalized half-logistic Weibull-G family of distributions: properties and applications', Journal of Statistical Modelling: Theory and Applications 1(1), 65-89. [ Links ]
Chipepa, F., Oluyede, B. & Wanduku, D. (2021), 'The exponentiated half logistic odd Weibull-Topp-Leone-G: Model, properties and applications', Journal of Statistical Modelling: Theory and Applications 2(1), 15-38. [ Links ]
Cordeiro, G. M., Ortega, E. M. & Nadarajah, S. (2010), 'The Kumaraswamy Weibull distribution with application to failure data', Journal of the Franklin Institute 347(8), 1399-1429. [ Links ]
De Andrade, T. A., Chakraborty, S., Handique, L. & Gomes-Silva, F. (2019), 'The exponentiated generalized extended Gompertz distribution', Journal of Data Science 17(2), 299-330. [ Links ]
Eghwerido, J. T., Nzei, L. C. & Agu, F. I. (2021), 'The alpha power Gompertz distribution: characterization, properties, and applications', Sankhya A 83, 449-475. [ Links ]
El-Bassiouny, A., El-Damcese, M., Mustafa, A. & Eliwa, M. (2017), 'Exponentiated generalized Weibull-Gompertz distribution with application in survival analysis', Journal of Statistics Applications and Probability 6(1), 7-16. [ Links ]
El-Gohary, A., Alshamrani, A. & Al-Otaibi, A. N. (2013), 'The generalized Gompertz distribution', Applied mathematical modelling 37(1-2), 13-24. [ Links ]
El-Morshedy, M., El-Faheem, A. A. & El-Dawoody, M. (2020), 'Kumaraswamy inverse Gompertz distribution: Properties and engineering applications to complete, type-II right censored and upper record data', Plos one 15(12), e0241970. [ Links ]
Elbatal, I., Jamal, F., Chesneau, C., Elgarhy, M. & Alrajhi, S. (2018), 'The modified beta Gompertz distribution: theory and applications', Mathematics 7(1), 3. [ Links ]
Gompertz, B. (1825), 'On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies', Philosophical Transactions of the Royal Society of London 115, 513-583. [ Links ]
Hosking, J. R. M., Wallis, J. R. & Wood, E. F. (1985), 'Estimation of the generalized extreme-value distribution by the method of probability-weighted moments', Technometrics 27(3), 251-261. [ Links ]
Jafari, A. A., Tahmasebi, S. & Alizadeh, M. (2014), 'The beta-Gompertz distribution', Revista Colombiana de Estadistica 37(1), 141-158. [ Links ]
Khaleel, M. A., Al-Noor, N. H. & Abdal-Hameed, M. K. (2020), 'Marshall Olkin exponential Gompertz distribution: Properties and applications', Periodicals of Engineering and Natural Sciences 8(1), 298-312. [ Links ]
Lenart, A. & Missov, T. I. (2016), 'Goodness-of-fit tests for the Gompertz distribution', Communications in Statistics-Theory and Methods 45(10), 2920-2937. [ Links ]
Marinho, P. R. D., Silva, R. B., Bourguignon, M., Cordeiro, G. M. & Nadarajah, S. (2019), 'AdequacyModel: An R package for probability distributions and general purpose optimization', PloS one 14(8), e0221487. [ Links ]
Moakofi, T., Oluyede, B. & Chipepa, F. (2021), 'Type II exponentiated half-logistic Topp-Leone Marshall-Olkin-G family of distributions with applications', Heliyon 7(12), e08590. [ Links ]
Moakofi, T., Oluyede, B. & Gabanakgosi, M. (2022), 'The Topp-Leone odd Burr III-G family of distributions: Model, properties and applications', Statistics, Optimization & Information Computing 10(1), 236-262. [ Links ]
Nzei, L. C., Eghwerido, J. T. & Ekhosuehi, N. (2020), 'Topp-Leone Gompertz distribution: Properties and applications', Journal of Data Science 18(4), 782-794. [ Links ]
Oluyede, B., Chamunorwa, S., Chipepa, F. & Alizadeh, M. (2022), 'The Topp-Leone Gompertz-G family of distributions with applications', Journal of Statistics and Management Systems 25(6), 1399-1423. [ Links ]
Oluyede, B., Chipepa, F. & Wanduku, D. (2021), 'Exponentiated half logistic-power generalized Weibull-G family of distributions: Model, properties and applications', Eurasian Bulletin of Mathematics 3(3), 134-161. [ Links ]
Oluyede, B., Peter, P. O., Ndwapi, N. & Bindele, H. (2022), 'The exponentiated Half-logistic Odd Burr III-G: Model, properties and applications', Pakistan Journal of Statistics and Operation Research (1), 33-57. [ Links ]
Rényi, A. (1961), On measures of entropy and information, in 'Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics', Vol. 4, University of California Press, pp. 547-562. [ Links ]
Roozegar, R., Tahmasebi, S. & Jafari, A. A. (2017), 'The McDonald Gompertz distribution: Properties and applications', Communications in Statistics-Simulation and Computation 46(5), 3341-3355. [ Links ]
Sengweni, W., Oluyede, B. & Makubate, B. (2021), 'The exponentiated half-logistic odd Lindley-G family of distributions with applications', Journal of Nonlinear Sciences & Applications (JNSA) 14(5), 287-309. [ Links ]
Seo, J.-I. & Kang, S.-B. (2015), 'Notes on the exponentiated half logistic distribution', Applied Mathematical Modelling 39(21), 6491-6500. [ Links ]
Shaked, M. & Shanthikumar, J. G. (2007), Stochastic orders, Springer, New York. [ Links ]
Shama, M., Dey, S., Altun, E. & Afify, A. Z. (2022), 'The gamma-Gompertz distribution: Theory and applications', Mathematics and Computers in Simulation 193, 689-712. [ Links ]
Shannon, C. E. (1951), 'Prediction and entropy of printed English', Bell System Technical Journal 30(1), 50-64. [ Links ]
Team (2022), R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/. [ Links ]
Received: October 2022; Accepted: April 2023
This is an open-access article distributed under the terms of the Creative Commons Attribution License
