The logistic-X family of distributions and its applications

By Muhammad Hussain Tahir, Gauss Moutinho Cordeiro, Ayman Alzaatreh, Muhammad Mansoor, Muhammad Zubair. 2016

184 citations recorded by the source corpus.

ABSTRACT The logistic distribution has a prominent role in the theory and practice of statistics. We introduce a new family of continuous distributions generated from a logistic random variable called the logistic-X family. Its density function can be symmetrical, left-skewed, right-skewed, and reversed-J shaped, and can have increasing, decreasing, bathtub, and upside-down bathtub hazard rates shaped. Further, it can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. We derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves, Shannon entropy, and order statistics. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. We also investigate the properties of one special model, the logistic-Fréchet distribution, and illustrate its importance by means of two applications to real data sets.

Subfields: Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/40581860e8cb34991f0bf3ec023c55aef415b7d8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Global and Planetary Change

1. G. Hamedani
2. Morad Alizadeh
3. Gauss Moutinho Cordeiro
4. Faton Merovci
5. Muhammad Hussain Tahir
6. Edwin M. M. Ortega
7. Muhammad Zubair
8. Muhammad Mansoor

In Statistics and Probability

1. G. Hamedani
2. Morad Alizadeh
3. Haitham M. Yousof
4. Gauss Moutinho Cordeiro
5. Faton Merovci
6. Edwin M. M. Ortega
7. Emrah Altun
8. R. Gokarna

Citations in the corpus

• Generalized Transmuted Family of Distributions: Properties and Applications (2017, background): “[52], Kumaraswamy MarshalOlkin family by Alizadeh et al.”
• Odd-Burr generalized family of distributions with some applications (2017, unknown): “,[7] Lomax generator by Cordeiro et al.”
• The Kumaraswamy Marshal-Olkin family of distributions (2015, background): “[19] and new Weibull-G by Tahir et al.”
• The generalized odd log-logistic family of distributions: properties, regression models and applications (2017, methodology): “[8] and Lomax generator by Cordeiro et al.”
• The Exponentiated Generalized-G Poisson Family of Distributions (2017, background): “…Zografos-Balakrishnan odd log-logistic family of distributions by Cordeiro et al. (2016b), logistic-X by Tahir et al. (2016a), a new Weibull-G by Tahir et al. (2016b), the generalized odd log-logistic family by Cordeiro et al. (2016c), the beta odd log-logistic generalized family of…”
• A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension (2020, background): “[14] (logistic-X) and Topp-Leone-G (2017) have received increased attention in recent statistical literature.”