On the skew Laplace distribution
On the skew Laplace distribution
复制标题
DOI：
10.1080/02522667.2005.10699644
复制
发表时间：
2005-01-01
影响因子：
1.4
通讯作者：
Aryal, Gokarna
中科院分区：
文献类型：
--
作者：
Aryal, Gokarna
如果随机变量X的pdf为f（x）= 2g（x）G（lambda x），则称X具有偏拉普拉斯分布，其中g（中心点）和G（中心点）分别表示拉普拉斯分布的pdf和cdf。这种分布尽管简单，但似乎没有被详细研究过。唯一的工作，似乎给一些细节，这个分布是古普塔等。[Random Operators and Stochastic Equations，Vol. 10（2002），pp. 133-140]，其中给出了X的期望、方差、偏度和峰度的表达式。但这些表达似乎包含一些错误。在本文中，我们提供了一个全面的描述的数学性质的X。导出了阶矩、方差、偏度、峰度、矩母函数、特征函数、累积量母函数、阶累积量、风险率函数、均值离差、中值离差、Renyi熵、Shannon熵、累积剩余熵和极值顺序统计量的渐近分布等性质。我们还考虑估计和模拟问题。
A random variable X is said to have the skew-Laplace distribution if its pdf is f (x) = 2g (x) G (lambda x), where g (center dot) and G (center dot), respectively, denote the pdf and the cdf of the Laplace distribution. This distribution -in spite of its simplicity -appears not to have been studied in detail. The only work that appears to give some details of this distribution is Gupta et. al [Random Operators and Stochastic Equations, Vol. 10 (2002), pp. 133-140], where expressions for the expectation, variance, skewness and the kurtosis of X are given. But these expressions appear to contain some errors. In this paper, we provide a comprehensive description of the mathematical properties of X. The properties derived include the k th moment, variance, skewness, kurtosis, moment generating function, characteristic function, cumulant generating function, the k th cumulant, hazard rate function, mean deviation about the mean, mean deviation about the median, Renyi entropy, Shannon's entropy, cumulative residual entropy and the asymptotic distribution of the extreme order statistics. We also consider estimation and simulation issues.