Re: WeibullDistribution
- To: mathgroup at smc.vnet.net
- Subject: [mg42486] Re: WeibullDistribution
- From: Bill Rowe <listuser at earthlink.net>
- Date: Thu, 10 Jul 2003 03:37:13 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
On 7/9/03 at 8:24 AM, gohtk at rocketmail.com (goh tat kean) wrote: > The formula for the probability density function of the general > Weibull distribution is given in: > http://www.itl.nist.gov/div898/handbook/eda/section3/eda3668.htm <snip> > Fit the dummy data by using NonlinearRegress to obtain a and b, > NonlinearRegress[data, PDF[WeibullDistribution[a, b], x], x, {a, b}, > MaxIterations -> 1000000] Under ideal conditions this will work fine. But real world data is seldom ideal and this method will generally not be either efficient or robust. For the Weibull distribution it is much better to do a linear regression on Log[H] vs Log[x] where H is the cumulative hazard function since Log[H] == a Log[x] - a Log[b]. Note for all distributions H = -Log[R] and R = 1-F where R is the reliability function and F is the cumulative distribution function