Maxwell distribution¶

The Maxwell distribution is also known as the Maxwell-Boltzmann distribution. See https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution.

The parametrization used here matches that of SciPy.

loc is the location parameter. (The wikipedia article does not include a location parameter for the distribution.)
scale is the scale parameter. scale is the parameter a in the wikipedia article.

mpsci.distributions.maxwell.cdf(x, loc=0, scale=1)¶: Cumulative distribution function for the Maxwell distribution.

mpsci.distributions.maxwell.entropy(loc=0, scale=1)¶: Differential entropy of the Maxwell distribution.

mpsci.distributions.maxwell.invcdf(p, loc=0, scale=1)¶

Inverse of the CDF of the Maxwell distribution.

This function is also known as the quantile function.

The function is implemented by numerically inverting the CDF using the mpmath findroot function. It may fail for extremely small values of p.

mpsci.distributions.maxwell.invsf(p, loc=0, scale=1)¶

Inverse of the survival function of the Maxwell distribution.

The function is implemented by numerically inverting the survival function using the mpmath findroot function. It may fail for values of p very close to 1.

mpsci.distributions.maxwell.logpdf(x, loc=0, scale=1)¶: Natural logarithm of the PDF of the Maxwell distribution.

mpsci.distributions.maxwell.mean(loc=0, scale=1)¶: Mean of the Maxwell distribution.

mpsci.distributions.maxwell.mode(loc=0, scale=1)¶: Mode of the Maxwell distribution.

mpsci.distributions.maxwell.pdf(x, loc=0, scale=1)¶: Probability density function for the Maxwell distribution.

mpsci.distributions.maxwell.sf(x, loc=0, scale=1)¶: Survival function for the Maxwell distribution.

mpsci.distributions.maxwell.support(loc=0, scale=1)¶: Support of the Maxwell distribution.

mpsci.distributions.maxwell.var(loc=0, scale=1)¶: Variance of the Maxwell distribution.