Based on the generalized log-logistic family (Gleaton and Lynch (2006)) of distributions, we propose a new family of continuous distributions with two extra shape parameters called the exponentiated odd log-logistic family. It extends the class of exponentiated distributions, odd log-logistic family (Gleaton and Lynch (2006)) and any continuous distribution by adding two shape parameters. Some special cases of this family are discussed. We investigate the shapes of the density and hazard rate functions. The proposed family has also tractable properties such as various explicit expressions for the ordinary and incomplete moments, quantile and generating functions, probability weighted moments, Bonferroni and Lorenz curves, Shannon and Rényi entropies, extreme values and order statistics, which hold for any baseline model. The model parameters are estimated by maximum likelihood and the usefulness of the new family is illustrated by means of three real data sets.
Alizadeh, M., Tahmasebi, S., & Haghbin, H. (2020). The exponentiated odd log-logistic family of distributions: properties and applications. Journal of Statistical Modelling: Theory and Applications, 1(1), 29-52. doi: 10.22034/jsmta.2020.1707
MLA
Morad Alizadeh; Saeid Tahmasebi; Hossein Haghbin. "The exponentiated odd log-logistic family of distributions: properties and applications". Journal of Statistical Modelling: Theory and Applications, 1, 1, 2020, 29-52. doi: 10.22034/jsmta.2020.1707
HARVARD
Alizadeh, M., Tahmasebi, S., Haghbin, H. (2020). 'The exponentiated odd log-logistic family of distributions: properties and applications', Journal of Statistical Modelling: Theory and Applications, 1(1), pp. 29-52. doi: 10.22034/jsmta.2020.1707
VANCOUVER
Alizadeh, M., Tahmasebi, S., Haghbin, H. The exponentiated odd log-logistic family of distributions: properties and applications. Journal of Statistical Modelling: Theory and Applications, 2020; 1(1): 29-52. doi: 10.22034/jsmta.2020.1707
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