Log-gamma probability distribution

• k is the shape parameter of the gamma distribution.

• theta is the scale parameter of the log-gamma distribution.

In SciPy, this distribution is implemented as scipy.stats.loggamma.

In the Wolfram language, this distribution is called ExpGammaDistribution.

Unlike SciPy and Wolfram, a location parameter is not included in this implementation of the log-gamma distribution.

mpsci.distributions.loggamma.cdf(x, k, theta)

Cumulative distribution function of the log-gamma distribution.

k is the shape parameter of the gamma distribution. theta is the scale parameter of the log-gamma distribution.

mpsci.distributions.loggamma.interval_prob(x1, x2, k, theta)

Compute the probability of x in [x1, x2] for the log-gamma distribution.

Mathematically, this is the same as

loggamma.cdf(x2, k, theta) - loggamma.cdf(x1, k, theta)

but when the two CDF values are nearly equal, this function will give a more accurate result.

x1 must be less than or equal to x2.

k is the shape parameter of the gamma distribution. theta is the scale parameter of the log-gamma distribution.

mpsci.distributions.loggamma.invcdf(p, k, theta)

Inverse of the CDF for the log-gamma distribution.

Also known as the quantile function.

k is the shape parameter of the gamma distribution. theta is the scale parameter of the log-gamma distribution.

mpsci.distributions.loggamma.invsf(p, k, theta)

Inverse of the survival functin for the log-gamma distribution.

k is the shape parameter of the gamma distribution. theta is the scale parameter of the log-gamma distribution.

mpsci.distributions.loggamma.kurtosis(k, theta)

Excess kurtosis of the log-gamma distribution.

k is the shape parameter of the gamma distribution. theta is the scale parameter of the log-gamma distribution.

mpsci.distributions.loggamma.logpdf(x, k, theta)

Log of the PDF of the log-gamma distribution.

k is the shape parameter of the gamma distribution. theta is the scale parameter of the log-gamma distribution.

mpsci.distributions.loggamma.mean(k, theta)

Mean of the log-gamma distribution.

k is the shape parameter of the gamma distribution. theta is the scale parameter of the log-gamma distribution.

mpsci.distributions.loggamma.mle(x, *, k=None, theta=None)

Maximum likelihood estimation for the log-gamma distribution.

x must be a sequence of numbers.

mpsci.distributions.loggamma.nll(x, k, theta)

Negative log-likelihood for the log-gamma distribution.

x must be a sequence of numbers.

mpsci.distributions.loggamma.pdf(x, k, theta)

Probability density function for the log-gamma distribution.

k is the shape parameter of the gamma distribution. theta is the scale parameter of the log-gamma distribution.

mpsci.distributions.loggamma.sf(x, k, theta)

Survival function of the log-gamma distribution.

k is the shape parameter of the gamma distribution. theta is the scale parameter of the log-gamma distribution.

mpsci.distributions.loggamma.skewness(k, theta)

Variance of the log-gamma distribution.

k is the shape parameter of the gamma distribution. theta is the scale parameter of the log-gamma distribution.

mpsci.distributions.loggamma.support(k, theta)

Support of the log-gamma distribution.

k is the shape parameter of the gamma distribution. theta is the scale parameter of the log-gamma distribution.

mpsci.distributions.loggamma.var(k, theta)

Variance of the log-gamma distribution.

k is the shape parameter of the gamma distribution. theta is the scale parameter of the log-gamma distribution.