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Re: Weibull Distribution

• To: mathgroup at smc.vnet.net
• Subject: [mg5622] Re: Weibull Distribution
• From: browe at netcom.com (Bill Rowe)
• Date: Sun, 29 Dec 1996 00:56:25 -0500
• Organization: none apparent
• Sender: owner-wri-mathgroup at wolfram.com

In article <59vpc7$f82 at dragonfly.wolfram.com>, Brian Rigling
<riglinbd at saber.udayton.edu> wrote:

>I am trying to work with Weibull distribution.  Specifically, I would like
to create random numbers under a Weibull distribution and fit a curve or
data with a Weibull distribution.

To create random Weibull deviates first load the package
Statistics`ContinuousDistributions`. Then a random Weibull deivate can be
generated as

x = Random[WeibullDistribution[a,b]]

Where a,b are the parameters of the desired distribution.

Probably the best way to compute the best fit Weibull distribution to a set
of data points would be to use the Statistics`LinearRegression` package.
The Weibull parameters a,b can be computed from

Log[-Log[1-y] = a (Log[x] - Log[b])

where y is esimated as the number of points less than or equal to x divided
by the total number of points plus one.

There are other possible estimates for y which may give somewhat better
results in some cases.
-- 
"Against stupidity, the Gods themselves contend in vain."