Three-parameter Weibull Distribution

There is also a three-parameter version of the Weibull distribution, which adds a location parameter γ. The probability density function (pdf) of this distribution is

pdf 3-parameter Weibull

for xγ. Here β > 0 is the shape parameter and α > 0 is the scale parameter.

The cumulative distribution function (cdf) is

cdf 3-parameter Weibull

The inverse cumulative distribution function is

inverse-3-parameter Weibull

Thus, we can calculate the pdf and cdf in Excel by the following formula:

         WEIBULL.DIST(xγ, β, α, cum)

where if cum = TRUE, then the cdf is calculated, and if cum = FALSE then the pdf is calculated. We can also use the following Real Statistics formula to calculate the inverse function.

         WEIBULL_INV(p, β, α) + γ

Key statistical properties of the 3-parameter Weibull distribution are:

3-parameter Weibull properties

Figure 1 – Statistical properties

Reference

Wikipedia (2021) The Weibull distribution
http://reliawiki.org/index.php/The_Weibull_Distribution

9 thoughts on “Three-parameter Weibull Distribution”

  1. In Figure 1, are you assuming that the mu in the variance equation is the mean that is presented in that same figure? If so, I believe that is incorrect. The variance equation should not depend on the gamma parameter.

    Reply
  2. Hi
    My name is Ki Jong. Can i get an advice from you?
    I conducted experiment on sloshing.
    From the experimental data, I wanna to fit the data using 3-parameters Webull distribution by means of excel. X axis is peak pressure and Y axis is probability.
    But, it is not working. can I get your email in order to explain my problems?

    Reply

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