The Zubair-dagum Distribution

Main Article Content

O. R. Uwaeme
N. P. Akpan


This article examines the flexibility of the Zubair-G family of distribution using the Dagum distribution. The proposed distribution is called the Zubair-Dagum distribution. The various mathematical properties of this distribution such as the Quantile function, Moments, Moment generating function, Reliability analysis, Entropy and Order statistics were obtained. The parameter estimates of the proposed distribution were also derived and estimated using the maximum likelihood estimation method. The new distribution is right skewed and has various bathtub and monotonically decreasing shapes. Our numerical illustrations using two real-life datasets substantiate the applicability, flexibility and superiority of the proposed distribution over competing distributions.

Dagum distribution, Zubair-G family, hazard rate function, entropy, order statistics.

Article Details

How to Cite
Uwaeme, O. R., & Akpan, N. P. (2021). The Zubair-dagum Distribution. Asian Journal of Probability and Statistics, 10(3), 25-35.
Original Research Article


Dagum C. A new model of personal income distribution: specification and estimation. In Modeling Income Distributions and Lorenz Curves. Springer, New York, NY. 2008;3-25.

Kleiber C. A guide to the Dagum distributions. In Modeling income distributions and Lorenz curves. Springer, New York, NY. 2008;97-117.

Domma F, Giordano S, Zenga M. Maximum likelihood estimation in Dagum distribution with censored samples. Journal of Applied Statistics. 2011;38(12):2971-2985.

Domma F. Landamento della hazard function nel modello di dagum a tre parametri. Quaderni di Statistica. 2002;4:1-12.

Shahzad MN, Asghar Z. Transmuted Dagum distribution: A more flexible and broad shaped hazard function model. Hacettepe Journal of Mathematics and Statistics. 2016;45(1):1-18.

Domma F, Condino F. The beta-dagum distribution: definition and properties. Communications in Statistics-Theory and Methods. 2013;42(22):4070-4090.

Oluyede BO, Rajasooriya S. The Mc-Dagum distribution and its statistical properties with applications. Asian Journal of Mathematics and Applications. 2013;1.

Oluyede BO, Huang S, Pararai M. A new class of generalized dagum distribution with applications to income and lifetime data. Journal of Statistical and Econometric Methods. 2014;3(2):125.

Oluyede BO, Ye Y. Weighted Dagum and related distributions. Afrika Matematika. 2014;25(4):1125-1141.

Huang S, Oluyede BO. Exponentiated Kumaraswamy-Dagum distribution with applications to income and lifetime data. Journal of Statistical Distributions and Applications. 2014;1(1):8.

Oluyede BO, Motsewabagale G, Huang S, Warahena-Liyanage G, Pararai M. Dagum-poisson distribution: model, properties and application. Electronic Journal of Applied Statistical Sciences. 2016;9(1):169.

Nasiru S, Mwita PN, Ngesa O. Exponentiated generalized exponential Dagum distribution. Journal of King Saud University-Science. 2019;31(3):362-371.

Bakouch HS, Khan MN, Hussain T, Chesneau C. A power log-Dagum distribution: estimation and applications. Journal of Applied Statistics. 2019;46(5):874-892.

Ekum MI, Adamu MO, Akarawak EE. T-Dagum: A way of generalizing dagum distribution using lomax quantile function. Journal of Probability and Statistics; 2020.

Gomes-Silva F, da Silva RV, Percontini A, Ramos MWA, Cordeiro GM. An extended dagum distribution: Properties and Applications. International Journal of Applied Mathematics & Statistics. 2017;56(1):35-53.

Ahmad Z. The Zubair-G family of distributions: Properties and applications. Annals of Data Science. 2020;7(2):195-208.

Tahir MH, Cordeiro GM. Compounding of distributions: A survey and new generalized classes. Journal of Statistical Distributions and Applications. 2016;3(1):13.

Shannon CE. Prediction and entropy of printed English. Bell System Technical Journal. 1951;30(1):50-64.

Rényi A. On measures of entropy and information. In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Contributions to the theory of statistics. The Regents of the University of California. 1961;1.

Marinho PRD, Silva RB, Bourguignon M, Cordeiro GM, Nadarajah S. Adequacy Model: An R package for probability distributions and general purpose optimization. PloS one. 2019;14(8):e0221487. R package version 2.0.0. Available:

Team RC. R foundation for statistical computing; Vienna, Austria: 2016. R: A language and environment for statistical computing; 2017. Available:URL http://www. R-project. org/.

Lawless JF. Statistical models and methods for lifetime data Wiley. New York; 1982.

Quesenberry CP, Kent J. Selecting among probability distributions used in reliability. Technometrics. 1982;24(1):59-65.

Pal M, Tiensuwan M. The beta transmuted Weibull distribution. Austrian Journal of Statistics. 2014;43(2):133-149.