Constructing a New Exponentiated Family Distribution with Reliability Estimation

Shurooq Ahmed Al-Sultany


This paper deals with using one method for transforming two parameters given distribution to another form with three parameters distribution, through using idea of reparameterization with powering the given cumulative distribution function by new parameter, where this work gives a new family through using new parameter which is necessary for generating values of the r.v from given CDF through smoothing the values of the given random variable to obtain new values of r.v using three set of parameters rather than two. The new model Frechet p.d.f is obtained and also its Cumulative distribution function is found then we apply three methods of estimation (which are Maximum likelihood , moments estimator , and the third method is depend on using least square regression approach). Different set of initial values of parameters ( , , ) and different samples size (n=25,50,75,100). The simulation procedure is done using matlab-R2014b, and results are compared using integrated Mean square error.


Cumulative, Maximum likelihood, Moments estimator, Least square regression.

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A. Chaturvedi and A. Pathak. (2014), “Estimating the Reliability Function for a Family of Exponentiated Distributions”. Journal of Probability and Statistics,vol. 2014, pp.1-10.

G. Aryal, I. E. (2015). “On the Exponentiated Generalized Modified Weibull Distribution”, Communications for Statistical Applications and Methods,, Vol. 22, No. 4, 333–348.

V.Nekoukhou, M.H. Alamatsaz, and H.Bidram, , (2012). “A discrete analog of the generalized exponential distribution”. . Communications in Statistics-Theory and Methods, Vol. 41., 2000-2013 .

Gupta, R. D. (2001). Exponentiated Exponential Family: An Alternative to Gamma and Weibull Distributions. Biometrical, Volume 43(Issue 1), pp. 117–130.

S. Nadarajah, A. K. (2007), “A compound beta distribution with applications in finance”. Statistical Methods and Applications,, , Volume 16, Issue 1, pp. 69–83.

S. Nadarajah, S. K. (2006), “The Exponentiated Type Distributions”, ActaApplicandaeMathematica,, , Volume 92, Issue 2, pp 97–111.



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