Beta probability distribution¶

This is the “standard” beta distribution, with shape parameters a and b, and support on the interval [0, 1].

mpsci.distributions.beta.cdf(x, a, b)¶: Cumulative distribution function of the beta distribution.

mpsci.distributions.beta.entropy(a, b)¶: Differential entropy of the beta distribution.

mpsci.distributions.beta.interval_prob(x1, x2, a, b)¶

Compute the probability of x in [x1, x2] for the beta distribution.

Mathematically, this is the same as

beta.cdf(x2, a, b) - beta.cdf(x1, a, b)

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.

mpsci.distributions.beta.invcdf(p, a, b)¶: Inverse of the CDF of the beta distribution.

mpsci.distributions.beta.invsf(p, a, b)¶: Inverse of the survival function of the beta distribution.

mpsci.distributions.beta.kurtosis(a, b)¶: Excess kurtosis of the beta distribution.

mpsci.distributions.beta.logpdf(x, a, b)¶: Natural logarithm of the PDF of the beta distribution.

mpsci.distributions.beta.mle(x, *, a=None, b=None)¶: Maximum likelihood estimation for the beta distribution.

mpsci.distributions.beta.mom(x)¶

Method of moments parameter estimation for the beta distribution.

x must be a sequence of numbers from the interval (0, 1).

Returns (a, b).

mpsci.distributions.beta.nll(x, a, b)¶: Negative log-likelihood for the beta distribution.

mpsci.distributions.beta.noncentral_moment(n, a, b)¶

n-th noncentral moment of the beta distribution.

n must be a nonnegative integer.

mpsci.distributions.beta.pdf(x, a, b)¶: Probability density function (PDF) for the beta distribution.

mpsci.distributions.beta.sf(x, a, b)¶: Survival function of the beta distribution.

mpsci.distributions.beta.skewness(a, b)¶: Skewness of the beta distribution.