The truncated distributions has been widely studied, primarily in life-testing and reliability analysis. Most work has assumed an upper bound on the support of the random variable, i.e. the space of the distribution is (0, d). We consider a doubly-truncated Fréchet random variable restricted by both a lower (c) and upper (d) truncation point. We provide forms for the density, cumulative distribution function (CDF), hazard function, characteristic function, rth raw moment, mean, mode, median, variance, skewness, kurtosis, Shannon entropy function, relative entropy and quantile function. We also consider the generating issues. This paper deals also with the determination of R = P[Y < X] when X and Y are two independent doubly truncated Fréchet distributions (DTFD) with different scale parameters, different shape parameters but the same truncations parameters. Different methods to estimate doubly truncated Fréchet distribution parameters are studied, Maximum Likelihood estimator, Moments estimator, Percentile estimator, least square estimator and weighted least square estimator. An empirical study is conducted to compare among these methods.

doubly truncated Fréchet distribution, Percentile estimator, hazard function, characteristic function, Shannon entropy, relative entropy, P[Y < X]