weibull
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 WeibullGnedenko 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 (xmin)], 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.
Samples

weibull(double
alpha,
double beta, double min)

Description
Generates a sample of the Weibull distribution.
Parameters
Name 
Type 
Description 
alpha 
double 
the shape
parameter > 0 
beta 
double 
the
scale parameter > 0 
min 
double 
the
minimum
x value 
Result
Type 
Description 
double 
the
generated sample 

weibull(double
beta, double alpha)

Description
Generates a sample of the Weibull distribution with min set
to
0. Is equivalent to weibull(alpha, beta, 0).
Parameters
Name 
Type 
Description 
beta 
double 
the scale
parameter > 0 
alpha 
double 
the
shape parameter > 0 
Result
Type 
Description 
double 
the
generated sample 

weibull(double
alpha,
double beta, double min, java.util.Random r)

Description
Generates a sample of the Weibull distribution using the
specified random number generator.
Parameters
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 
Result
Type 
Description 
double 
the
generated sample 