The Kumaraswamy Marshal-Olkin family of distributions

By Morad Alizadeh, Muhammad Hussain Tahir, Gauss Moutinho Cordeiro, Muhammad Mansoor, Muhammad Zubair, G. Hamedani. 2015

124 citations recorded by the source corpus.

Abstract We introduce a new family of continuous distributions called the Kumaraswamy Marshal-Olkin generalized family of distributions. We study some mathematical properties of this family. Its density function is symmetrical, left-skewed, right-skewed and reversed-J shaped, and has constant, increasing, decreasing, upside-down bathtub, bathtub and S-shaped hazard rate. We present some special models and investigate the asymptotics and shapes of the family. We derive a power series for the quantile function and obtain explicit expressions for the moments, generating function, mean deviations, two types of entropies and order statistics. Some useful characterizations of the family are also proposed. The method of maximum likelihood is used to estimate the model parameters. We illustrate the importance of the family by means of two applications to real data sets.

Subfields: Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/97b577c90a0a728dd1c8bbc54f40d40b433c81b4

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. Haitham M. Yousof
3. Morad Alizadeh
4. Nadeem Shafique Butt
5. Gauss Moutinho Cordeiro
6. Faton Merovci
7. Edwin M. M. Ortega
8. Thiago G. Ramires

In Statistics and Probability

1. Haitham M. Yousof
2. G. Hamedani
3. Morad Alizadeh
4. Nadeem Shafique Butt
5. Gauss Moutinho Cordeiro
6. Faton Merovci
7. Edwin M. M. Ortega
8. Thiago G. Ramires

Citations in the corpus

• The Burr XII System of densities: properties, regression model and applications (2018, background): “[10], transmuted exponentiated generalized-G by Yousof et al.”
• Recent Developments in Distribution Theory: A Brief Survey and Some New Generalized Classes of distributions (2019, background): “Using (15), we can generate the extended version of the existing distributions.”
• Generalized Transmuted Family of Distributions: Properties and Applications (2017, unknown): “[4], Beta Marshal-OLkin family by Alizadeh et al.”
• Odd-Burr generalized family of distributions with some applications (2017, background): “[10] and type-1 half-logistic family of distributions by Cordeiro et al.”
• The exponentiated transmuted-G family of distributions: Theory and applications (2017, background): “© Taylor & Francis Group, LLC by Cordeiro et al. (2014), Kumaraswamy Odd log-logistic-G by Alizadeh et al. (2015), Kumaraswamy Marshall–Olkin by Alizadeh et al. (2015), beta Marshall–Olkin by Alizadeh et al. (2015), Kummer-beta generalized distributions by Pescim et al. (2012), a new family of…”
• The Topp–Leone odd log-logistic family of distributions (2017, unknown): “[8], generalized transmuted-G by Nofal et al.”