Beta Fréchet分布的一些结果
Some results for beta Fréchet distribution
摘要：
Nadarajah和Gupta（2004）引入了beta Fréchet（BF）分布，它是指数Fréchet（EF）和Fréchet分布的推广，并获得了概率密度和累积分布函数。然而，他们没有研究它的矩和顺序统计量。本文将BF密度函数和顺序统计量的密度函数表示为Fréchet密度函数的线性组合。这对于根据Fréchet分布的相应性质获得BF分布的一些数学性质是重要的。我们导出了普通矩和L-矩的显式展开式，得到了顺序统计量及其矩。讨论了极大似然估计，并计算了未知信息矩阵。信息矩阵很容易用数字确定。两个实际数据集的应用程序来说明这种分布的潜力。
英文摘要：
Nadarajah and Gupta (2004) introduced the beta Fréchet (BF) distribution, which is a generalization of the exponentiated Fréchet (EF) and Fréchet distributions, and obtained the probability density and cumulative distribution functions. However, they do not investigated its moments and the order statistics. In this paper the BF density function and the density function of the order statistics are expressed as linear combinations of Fréchet density functions. This is important to obtain some mathematical properties of the BF distribution in terms of the corresponding properties of the Fréchet distribution. We derive explicit expansions for the ordinary moments and L-moments and obtain the order statistics and their moments. We also discuss maximum likelihood estimation and calculate the information matrix which was not known. The information matrix is easily numerically determined. Two applications to real data sets are given to illustrate the potentiality of this distribution.
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