[求助]什么是Weibull分布？

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向各位讨教一下：什么是Weibull分布？

服从这个分布需要什么条件？

服从了这个分布后，对于数据的分析又有什么益处？

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关键词：Weibull分布 Weibull Bull wei 预答辩 Weibull

From mathWorld:

The Weibull distribution is given by

			(1)
			(2)

for , and is implemented in Mathematica as WeibullDistribution[alpha, beta] in the Mathematica add-on package Statistics`ContinuousDistributions` (which can be loaded with the command <<Statistics`) . The raw moments of the distribution are

			(3)
			(4)
			(5)
			(6)

and the mean, variance, skewness, and kurtosis of are

			(7)
			(8)
			(9)
			(10)

where is the gamma function and

(11)

A slightly different form of the distribution is defined by

			(12)
			(13)

(Mendenhall and Sincich 1995). This has raw moments

			(14)
			(15)
			(16)
			(17)

so the mean and variance for this form are

			(18)
			(19)

The Weibull distribution gives the distribution of lifetimes of objects. It was originally proposed to quantify fatigue data, but it is also used in analysis of systems involving a "weakest link."

感谢：zhaosweden

我要慢慢品味

能否告知在经济学的调查分析中

一般在什么情况下，假设满足此分布

无序ｌｏｇｉｔ模型是根据此分布推倒出来的！此分布的好处就是计算上处理方便！

Some stuff from google:

(among others ,,)

Weibull Distribution. As described earlier, the exponential distribution is often used as a model of time-to-failure measurements, when the failure (hazard) rate is constant over time. When the failure probability varies over time, then the Weibull distribution is appropriate. Thus, the Weibull distribution is often used in reliability testing (e.g., of electronic relays, ball bearings, etc.; see Hahn and Shapiro, 1967). The Weibull distribution is defined as:

f(x) = c/b*(x/b)^(c-1) * e^{[-(x/b)^c]}, for 0 £ x < ¥, b > 0, c > 0

where

b	is the scale parameter
c	is the shape parameter
e	is the base of the natural logarithm, sometimes called Euler's e (2.71...)

------------------------------------------------------------------------------

Personal comment:

at least in the above example, the essence is that this distribution is more flexible. Another exmaple I know well is the generalized error distribution (GED, similarly for exponential power distribution, EPD). In Nelson 1991, EGARCH model, the error terms is assumed GED. by varying the parameter v in GED, the distribution can cover fatter, thinner than normal distribution. when v=2, it reduces to normal distribution. For typical finanical time series v_hat is 1.5, for instance.

So whether the error is indeed normal can be seen from the estimated parameter v. It one assumes normality, she actually restricts the innovation to be normal (v=2).

---

All in all, this kind of distribution may avoid possible mistake by not assuming a more restricted distribution. So let the data speak.

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[此贴子已经被作者于2006-3-8 4:36:06编辑过]

非常感谢各位的帮助

我想我已经找到了一些方向

还有一个问题，什么是两参数的Weibull分布，如何对其进行参数估计？

7# 最爱亚美
两参数威布尔分布，一个是形状参数，一个是刻度参数，可以用矩估计实现

7# 最爱亚美
matlab中有专门估计其参数的命令，如果是极大似然估计的话，用wblfit就可以

在可靠性理论，精算学中常用的分布。
而且它是三大极值分布之一。