Weibull probability distribution (for maxima)

This is the same distribution as:

• scipy.stats.weibull_max;

• the Type III extreme value distribution used in the text “An Introduction to Statistical Modeling of Extreme Values” by Stuart Coles (Springer, 2001);

• the Weibull distribution given in the text “Modelling Extremal Events” by Embrechts, Klüppelberg and Mikosch (Springer, 1997).

This is the same distributions as weibull_min, but with x replaced by -x. The weibull_min distribution is the same distribution as:

• scipy.stats.weibull_min;

• numpy.random.Generator.weibull (restricted to loc=0 and scale=1);

• Wolfram Alpha’s WeibullDistribution;

• the distribution discussed in the wikipedia article “Weibull distribution” (https://en.wikipedia.org/wiki/Weibull_distribution);

• the Weibull distribution in the text “Statistical Distribution” (fourth ed.) by Forbes, Evans, Hastings and Peacock (Wiley, 2011).

mpsci.distributions.weibull_max.cdf(x, k, loc, scale)

Cumulative distribution function for the Weibull distribution (for maxima).

This is a three-parameter version of the distribution. The more typical two-parameter version has just the parameters k and scale.

mpsci.distributions.weibull_max.entropy(k, loc, scale)

Differential entropy of the Weibull distribution (for maxima).

This is a three-parameter version of the distribution. The more typical two-parameter version has just the parameters k and scale.

mpsci.distributions.weibull_max.invcdf(p, k, loc, scale)

Inverse of the CDF for the Weibull distribution (for maxima).

This is a three-parameter version of the distribution. The more typical two-parameter version has just the parameters k and scale.

mpsci.distributions.weibull_max.invsf(p, k, loc, scale)

Inverse of the survival function for the Weibull distribution (for maxima).

This is a three-parameter version of the distribution. The more typical two-parameter version has just the parameters k and scale.

mpsci.distributions.weibull_max.kurtosis(k, loc, scale)

Excess kurtosis of the Weibull distribution (for minima).

This is a three-parameter version of the distribution. The more typical two-parameter version has just the parameters k and scale.

mpsci.distributions.weibull_max.logpdf(x, k, loc, scale)

Log of the PDF of the Weibull distribution (for maxima).

This is a three-parameter version of the distribution. The more typical two-parameter version has just the parameters k and scale.

mpsci.distributions.weibull_max.mean(k, loc, scale)

Mean of the Weibull distribution (for maxima).

This is a three-parameter version of the distribution. The more typical two-parameter version has just the parameters k and scale.

mpsci.distributions.weibull_max.mle(x, *, k=None, loc=None, scale=None)

Maximum likelihood estimate of the Weibull(max) distribution parameters.

loc must be given.

Return value is (k, loc, scale).

mpsci.distributions.weibull_max.mode(k, loc, scale)

Mode of the Weibull distribution (for maxima).

This is a three-parameter version of the distribution. The more typical two-parameter version has just the parameters k and scale.

mpsci.distributions.weibull_max.nll(x, k, loc, scale)

Negative log-likelihood function for the Weibull(min) distribution.

mpsci.distributions.weibull_max.noncentral_moment(n, k, loc=0, scale=1)

Noncentral moment of the Weibull distribution (for maxima).

The value is also known as the raw moment.

mpsci.distributions.weibull_max.pdf(x, k, loc, scale)

Probability density function for the Weibull distribution (for maxima).

This is a three-parameter version of the distribution. The more typical two-parameter version has just the parameters k and scale.

mpsci.distributions.weibull_max.sf(x, k, loc, scale)

Survival function for the Weibull distribution (for maxima).

This is a three-parameter version of the distribution. The more typical two-parameter version has just the parameters k and scale.

mpsci.distributions.weibull_max.skewness(k, loc, scale)

Skewness of the Weibull distribution (for maxima).

This is a three-parameter version of the distribution. The more typical two-parameter version has just the parameters k and scale.

mpsci.distributions.weibull_max.support(k, loc, scale)

Support of the Weibull distribution (for maxima).

This is a three-parameter version of the distribution. The more typical two-parameter version has just the parameters k and scale.

mpsci.distributions.weibull_max.var(k, loc, scale)

Variance of the Weibull distribution (for maxima).

This is a three-parameter version of the distribution. The more typical two-parameter version has just the parameters k and scale.