Weibull Distribution

Weibull distribution

Instance methods

Cumulative function

It returns the probability P(x <= X) for an specified X. If X < 0, then the probability is zero.

[85] pry(main)> Distribution::Weibull.new(2, 3)
=> #<Statistics::Distribution::Weibull:0x0000000001213170 @scale=3.0, @shape=2.0>
[86] pry(main)> Distribution::Weibull.new(2, 3).cumulative_function(-1)
=> 0
[87] pry(main)> Distribution::Weibull.new(2, 3).cumulative_function(5)
=> 0.9378234759778837

Probability density function

It returns the probability density value for the specified X. If X < 0, then the returned value is zero. If the scale or the shape defined at initialization time is <= 0, then the function is not defined.

[93] pry(main)> Distribution::Weibull.new(2, 0).density_function(3)
=> nil
[94] pry(main)> Distribution::Weibull.new(0, 2).density_function(3)
=> nil
[95] pry(main)> Distribution::Weibull.new(2, 2).density_function(-3)
=> 0
[96] pry(main)> Distribution::Weibull.new(2, 2).density_function(3)
=> 0.1580988368427965

Mean

It returns the mean based on the specified scale and shape values.

[97] pry(main)> Distribution::Weibull.new(2, 2).mean
=> 1.772453850905516
[98] pry(main)> Distribution::Weibull.new(2, 3).mean
=> 2.658680776358274

Variance

It returns the variance based on the specified scale and shape values.

[99] pry(main)> Distribution::Weibull.new(2, 2).variance
=> 0.8584073464102064
[100] pry(main)> Distribution::Weibull.new(2, 3).variance
=> 1.9314165294229646

Mode

It returns the mode based on the specified scale and shape values.

[101] pry(main)> Distribution::Weibull.new(2, 2).mode
=> 1.4142135623730951
[102] pry(main)> Distribution::Weibull.new(2, 3).mode
=> 2.121320343559643

Random

It returns a random number/sample following a Weibull distribution. You can pass two arguments:

• elements: # where # is the size of the random sample to be generated. If not specified, 1 by default.
• seed: # where # is any number to be used as a seed generator. If not specified, Random.new_seed by default.

> weibull = Distribution::Weibull.new(5.0, 2.0)
=> #<Statistics::Distribution::Weibull:0x0000000124dbb8 @shape=5.0, @scale=2.0>
> weibull.random
=> 0.672463184666854
> weibull.random(elements: 3)
=> [0.9465663642766572, 0.500698386530963, 0.8171442176078962]
> weibull.random(seed: Random.new_seed)
=> 0.6904028173180309