T-Transmuted X Family of Distributions


  • Girish Babu Moolath Government Arts and Science College, Meenchanda http://orcid.org/0000-0002-3894-3915
  • Jayakumar K University of Calicut




Exponential distribution, Hazard rate, Maximum likelihood estimation, Moments, T-X family of distributions


Using the quadratic transmutation map (QRTM) approach of Shaw and Buckley (2007) and the T -X family method by Alzaatreh et al. (2013b), we have developed a new family of distributions called T -transmuted X family of distributions. Many of the existing family of distributions are sub models of this family. As a special case, exponential transmuted exponential (ETE) distribution is studied in detail. The application and flexibility of this new distribution is illustrated using two real data sets.


A. Z. AFIFY, Z. M.NOFAL, H. M. YOUSOF, Y. M. E.GEBALY,N. S. BUTT (2015). The transmuted Weibull Lomax distribution: properties and application. Pakistan Journal of Statistics and Operation Research, 11, pp. 135–152.

M. ALIZADEH, G. M. CORDEIRO, E. DEBRITO, C. G. B. DEMETRIO (2015). The beta Marshall-Olkin family of distributions. Journal of Statistical Distributions and Applications, 2, pp. 2–18.

M. ALIZADEH, F. MEROVCI, G. HAMEDANI (2017). Generalized transmuted family of distributions: Properties and applications. Hacettepe Journal of Mathematics and Statistics, 46, pp. 645–667.

M. A. ALJARRAH, C. LEE, F. FAMOYE (2014). On generating T-X family of distributions using quantile functions. Journal of Statistical Distributions and Applications, 1, pp. 1–17.

A. ALZAATREH, F. FAMOYE, C. LEE (2013a). Weibull-Pareto distribution and its applications. Communication in Statistics - Theory and Methods, 42, pp. 1673–1691.

A. ALZAATREH, I. GHOSH (2015). On the Weibull-X family of distributions. Journal of Statistical Theory and Applications, 14, pp. 169–183.

A. ALZAATREH, K. KNIGHT (2013). On the gamma-half normal distribution and its applications. Journal of Modern Applied Statistical Methods, 12, pp. 103–119.

A. ALZAATREH, C. LEE, F. FAMOYE (2013b). A new method for generating families of continuous distributions. Metron, 71, pp. 63–79.

D. F. ANDREWS, A. M. HERZBERG (1985). Data: A collection of problems from many fields for the student and research worker. Springer-Verlag, New York.

G. R. ARYAL (2013). Transmuted log-logistic distribution. Journal of Statistics Applications and Probability, 2, pp. 11–20.

G. R. ARYAL, C. P. TSOKOS (2009). On the transmuted extreme value distribution with applications. Nonlinear Analysis: Theory, Methods and Applications, 71, pp. 1401–1407.

G. R. ARYAL, C. P. TSOKOS (2011). Transmuted Weibull distribution: A generalization of the Weibull probability distribution. European Journal of Pure and Applied Mathematics, 4, pp. 89–102.

M. G. BABU (2016). On a generalization of Weibull distribution and its applications. International Journal of Statistics and Applications, 6, pp. 168–176.

I. ELBATAL, G. R. ARYAL (2013). On the transmuted additive Weibull distribution. Australian Journal of Statistics, 42, pp. 117–132.

K. JAYAKUMAR, M. G. BABU (2015). Some generalizations of Weibull distribution and related processes. Journal of Statistical Theory and Applications, 14, pp. 425–434.

M. KHAN, R. KING (2013a). Transmuted modified Weibull distribution: A generalization of the modified Weibull probability distribution. European Journal of Pure and Applied Mathematics, 6, pp. 66–88.

M. KHAN, R. KING (2013b). Transmuted generalized inverse Weibull distribution. Journal of Applied Statistical Sciences, 20, pp. 15–32.

E. T. LEE (1992). Statistical Methods for Survival Data Analysis. JohnWiley, New York.

S.NADARAJAH, K. JAYAKUMAR, M. M. RISTI´C (2013). A newfamily of lifetime models. Journal of Statistical Computation and Simulation, 83, pp. 1389–1404.

A. RÉNYI (1961). On measures of entropy and information. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, 1, pp. 547–561.

C. E. SHANNON (1948). A mathematical theory of communication. The Bell System Technical Journal, 27, pp. 379–423.

W. SHAW, I. BUCKLEY (2007). The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. Research report.




How to Cite

Moolath, G. B., & K, J. (2017). T-Transmuted X Family of Distributions. Statistica, 77(3), 251–276. https://doi.org/10.6092/issn.1973-2201/6800