Negative binomial distribution

There are several different ways to parameterize the negative binomial distribution. Here, the quantiles are the number of “successes” that occur when draws from a binomial distribution are made repeatedly until the number of “failures” drawn is r. p is the probability of drawing a “success”.

mpsci.distributions.negative_binomial.cdf(k, r, p)

Cumulative distribution function of the negative binomial distribution.

Parameters:

• r (int) – Number of failures until the experiment is stopped.

• p (float) – Probability of success.

mpsci.distributions.negative_binomial.logpmf(k, r, p)

Log of the probability mass function of the negative binomial distribution.

Parameters:

• r (int) – Number of failures until the experiment is stopped.

• p (float) – Probability of success.

mpsci.distributions.negative_binomial.mean(r, p)

Mean of the negative binomial distribution.

Parameters:

• r (int) – Number of failures until the experiment is stopped.

• p (float) – Probability of success.

mpsci.distributions.negative_binomial.mle(x, *, counts=None, r=None, p=None, allow_noninteger_r=True)

Maximum likelihood estimation for the negative binomial distribution.

x must be a sequence of nonnegative integers.

mpsci.distributions.negative_binomial.nll(x, r, p, *, counts=None)

Negative log-likelihood of sample for the negative binomial distribution.

Parameters:

• x (sequence of nonnegative integers) – The sample for which the negative log-likelihood is to be calculated.

• r (int) – Number of failures until the experiment is stopped.

• p (float) – Probability of success.

• counts (sequence of integers, optional) – If given, this sequence must be the same length as x. It gives the number of occurrences in the sample of the corresponding value in x.

mpsci.distributions.negative_binomial.pmf(k, r, p)

Probability mass function of the negative binomial distribution.

Parameters:

• r (int) – Number of failures until the experiment is stopped.

• p (float) – Probability of success.

mpsci.distributions.negative_binomial.sf(k, r, p)

Survival function of the negative binomial distribution.

Parameters:

• r (int) – Number of failures until the experiment is stopped.

• p (float) – Probability of success.

mpsci.distributions.negative_binomial.support(r, p)

Support of the negative binomial distribution.

The support is the integers 0, 1, 2, 3, …, so the support is returned as an instance of itertools.count(start=0).

Examples

>>> from mpsci.distributions import negative_binomial
>>> sup = negative_binomial.support()
>>> next(sup)
0
>>> next(sup)
1

mpsci.distributions.negative_binomial.var(r, p)

Variance of the negative binomial distribution.

Parameters:

• r (int) – Number of failures until the experiment is stopped.

• p (float) – Probability of success.