The Weibull distribution is a continuous distribution bounded on the
lower side. Because it provides one of the limiting distributions for
extreme values, it is also referred to as the Frechet distribution and
the Weibull-Gnedenko distribution.
Like the Gamma distribution, it has three
distinct regions. For alpha=1, beta=1/lambda
the Weibull distribution is reduced to exponential
(lambda) distribution,
starting at a finite value at minimum x and decreasing monotonically
thereafter. For alpha<1, the Weibull distribution tends to infinity
at
minimum x and decreases monotonically for increasing x. for alpha>1,
the
Weibull distribution is 0 at minimum x, peaks at a value that depends
on both alpha and beta, decreasing monotonically thereafter. Uniquely,
the
Weibull distribution has negative skewness for alpha>3.6.
The Weibull distribution can also be used to approximate the Normal
distribution for alpha=3.6, while maintaining its strictly positive
values
of x [actually (x-min)], although the kurtosis is slightly smaller than
3, the Normal value.
The Weibull distribution derived its popularity from its use to model
the strength of materials, and has since been used to model just about
everything. In particular, the Weibull distribution is used to
represent wearout lifetimes in reliability, wind speed, rainfall
intensity, health related issues, germination, duration of industrial
stoppages, migratory systems, and thunderstorm data.
Generates a sample of the Weibull distribution.
Name |
Type | Description |
alpha |
double | the shape parameter > 0 |
beta |
double | the scale parameter > 0 |
min |
double | the minimum x value |
Type |
Description |
double |
the generated sample |
Generates a sample of the Weibull distribution with min set
to
0. Is equivalent to weibull(alpha, beta, 0).
Name |
Type | Description |
beta |
double | the scale parameter > 0 |
alpha |
double | the shape parameter > 0 |
Type |
Description |
double |
the generated sample |
Generates a sample of the Weibull distribution using the specified random number generator.
Name |
Type | Description |
alpha |
double | the shape parameter > 0 |
beta |
double | the scale parameter > 0 |
min |
double | the minimum x value |
r |
java.util.Random | the random number generator |
Type |
Description |
double |
the generated sample |
This document includes content from the Stat::Fit User's Manual. Copyright © 2016 Geer Mountain Software Corp.