@article{ajams2016412,
author={Abid, Salah H},
title={Properties of Doubly-Truncated Fr¨Śchet Distribution},
journal={American Journal of Applied Mathematics and Statistics},
volume={4},
number={1},
pages={9--15},
year={2016},
url={http://pubs.sciepub.com/ajams/4/1/2},
issn={2328-7292},
abstract={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>i.e</i>. the space of the distribution is (0, <i>d</i>). We consider a doubly-truncated Fr¨Śchet random variable restricted by both a lower (<i>c</i>) and upper (<i>d</i>) truncation point. We provide forms for the density, cumulative distribution function (CDF), hazard function, characteristic function, <i>r</i>th 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 &lt; X] when X and Y are two independent doubly truncated Fr¨Śchet distributions (<b>DTFD</b>) with different scale parameters, different shape parameters but the same truncations parameters. Different methods to estimate doubly truncated Fr¨Śchet 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.},
doi={10.12691/ajams-4-1-2}
publisher={Science and Education Publishing}
}