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Transmuted probability distribution corresponding to a distribution function G(x) is defined as F(x) = (1+l )G(x) −lG(x)2; |l | ≤ 1. In this paper we study some general properties of the transmuted probability distribution function in relation to the base distribution G(x). In particular the transmuted exponentiated Frˆechet (TEF) distribution is studied in detail. The different methods of estimation of parameters such as, weighted least squares and the maximum likelihood estimates of this distribution are studied. Finally, a real time data analysis is performed for this distribution and it is found that this class is more flexible class and it shown that the TEF distribution is much better fit for data’s originally fitted and analysed using Frˆechet or Exponentiated Frˆechet distribution.

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