Some Properties of Gamma Generated Distributions


  • Manisha Pal University of Calcutta
  • Montip Tiensuwan Mahidol University, Bangkok



Gamma generated distributions, failure rate, moment generating function, stress-strength reliability, Rényi entropy, order statistics


Based on standard probability distributions, new families of univariate distributions have been introduced and their properties studied by many authors. The present paper investigates some general properties of a family of Gamma generated distributions proposed by Zografos and Balakrishnan (2009).


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(2), pp. 89–102.

B.M.S.G. BANNEHEKA, G.E.M.U.P.D. c (2009). A new point estimator for the median of gamma distribution. Viyodaya Journal of Science, 14, pp. 95–103.

G. M. CORDEIRA, A. E. GOMES, C. Q. DA-SILVA, E.M.M. ORTEGA (2013). The Beta Exponentiated Weibull Distribution. Journal of Statistical Computation and Simulation, 83, pp. 114–138.

N. EUGENE, C. LEE, F. FAMOYE (2002). Beta-normal distribution and its applications. Communication in Statististics - Theory and Methods, 31, pp. 497–512.

R. C. GUPTA, P. L. GUPTA, R. D. GUPTA (1998). Modeling failure time data by Lehman alternatives. Communication in Statististics - Theory and Methods, 27, pp. 887–904.

R. D. GUPTA, D. KUNDU (2001). Exponentiated exponential family: An alternative to gamma and Weibull distributions. Biomedical Journal, 43, pp. 117–130.

N. L. JOHNSON, S. KOTZ, N. BALAKRISHNAN (1994). Continuous Univariate Distributions. Vol. I, 2nd ed., New York: Wiley.

N. L. JOHNSON, S. KOTZ, N. BALAKRISHNAN (1995). Continuous Univariate Distributions. Vol. 2, 2nd ed., New York: Wiley.

C. LEE, F. FAMOYE, O. OLUMOLADE (2007). Beta-Weibull distribution: some properties and applications to censored data. Journal of Modern Applied Statistical

Methods, 6, pp. 173–186.

G.S. MUDHOLKAR, D.K. SRIVASTAVA (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Transactions on Reliability 42, pp. 299–302.

S. NADARAJAH (2005). Exponentiated Pareto distributions. Statistics, 39(3), pp. 255–260.

MANISHA PAL, M. MASOOM ALI, JUNGSU WOO (2006). Exponentiated Weibull distribution. Statistica, LXVI : 2, 139–147.

MANISHA PAL, MONTIP TIENSUWAN (2014). The Beta transmuted Weibull distribution. Austrian Journal of Statististics, 43(2), pp. 133–149.

A. M. Sarhan, M. Zaindin . Modified Weibull distribution. Applied Sciences, 11, pp. 123–136.

C. E. SHANNON (1948). A mathematical theory of communication. Bell System Technical Journal, 27, pp. 379–432.

K. ZOGRAFOSA, N. BALAKRISHNAN (2009). On families of beta- and generalized gamma-generated distributions and associated inference. Statistical Methodology, 6, pp. 344–362.

K. ZOGRAFOS (2008). On some beta generated distributions and their maximum entropy characterization: The beta-Weibull distribution. In N.S. Barnett, S.S. Dragomir (Eds.), Advances in Inequalities from Probability Theory and Statistics, Nova Science Publishers, New Jersey, pp. 237–260.




How to Cite

Pal, M., & Tiensuwan, M. (2015). Some Properties of Gamma Generated Distributions. Statistica, 75(4), 391–403.