Kumaraswamy probability distribution

References

Kumaraswamy, P. (1980). “A generalized probability density function for double-bounded random processes”. Journal of Hydrology. 46 (1-2): 79-88. doi:10.1016/0022-1694(80)90036-0.

Jones, M.C. (2009). “Kumaraswamy’s distribution: A beta-type distribution with some tractability advantages”. Statistical Methodology. 6 (1): 70-81. doi:10.1016/j.stamet.2008.04.001.

“Kumaraswamy distribution”. Wikipedia, https://en.wikipedia.org/wiki/Kumaraswamy_distribution.

mpsci.distributions.kumaraswamy.cdf(x, a, b)

Cumulative distribution function of the Kumaraswamy distribution.

mpsci.distributions.kumaraswamy.entropy(a, b)

Differential entropy of the Kumaraswamy distribution.

mpsci.distributions.kumaraswamy.invcdf(p, a, b)

Inverse of the CDF of the Kumaraswamy distribution.

mpsci.distributions.kumaraswamy.invsf(p, a, b)

Inverse of the survival function of the Kumaraswamy distribution.

mpsci.distributions.kumaraswamy.logpdf(x, a, b)

Natural logarithm of the PDF of the Kumaraswamy distribution.

mpsci.distributions.kumaraswamy.mean(a, b)

Mean of the Kumaraswamy distribution.

mpsci.distributions.kumaraswamy.median(a, b)

Median of the Kumaraswamy distribution.

mpsci.distributions.kumaraswamy.mle(x, *, a=None, b=None)

Maximum likelihood estimate for the Kumaraswamy distribution.

x must be a sequence of numbers with values in the open interval (0, 1).

Returns (a, b), the maximum likelihood estimate for the given data.

When a is not given, the MLE equations are solved numerically, and the solver may fail to converge for some inputs. If this happens, a different initial guess for a may be given by setting the input parameter to mpsci.distributions.Initial(a0), where a0 is the initial guess to use for the estimate of a. The default initial guess for a is 1.

mpsci.distributions.kumaraswamy.nll(x, a, b)

Negative log-likelihood function for the Kumaraswamy distribution.

x must be a sequence of numbers with values in the open interval (0, 1).

mpsci.distributions.kumaraswamy.noncentral_moment(n, a, b)

n-th noncentral moment of the Kumaraswamy distribution.

n must be a nonnegative integer.

mpsci.distributions.kumaraswamy.pdf(x, a, b)

Probability density function (PDF) for the Kumaraswamy distribution.

mpsci.distributions.kumaraswamy.sf(x, a, b)

Survival function of the Kumaraswamy distribution.

mpsci.distributions.kumaraswamy.skewness(a, b)

Skewness of the Kumaraswamy distribution.

mpsci.distributions.kumaraswamy.support(a, b)

Support of the Kumaraswamy distribution.

mpsci.distributions.kumaraswamy.var(a, b)

Variance of the Kumaraswamy distribution.