scipy.stats.betanbinom#
- scipy.stats.betanbinom = <scipy.stats._discrete_distns.betanbinom_gen object>[source]#
A beta-negative-binomial discrete random variable.
As an instance of the
rv_discrete
class,betanbinom
object inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.Methods
rvs(n, a, b, loc=0, size=1, random_state=None)
Random variates.
pmf(k, n, a, b, loc=0)
Probability mass function.
logpmf(k, n, a, b, loc=0)
Log of the probability mass function.
cdf(k, n, a, b, loc=0)
Cumulative distribution function.
logcdf(k, n, a, b, loc=0)
Log of the cumulative distribution function.
sf(k, n, a, b, loc=0)
Survival function (also defined as
1 - cdf
, but sf is sometimes more accurate).logsf(k, n, a, b, loc=0)
Log of the survival function.
ppf(q, n, a, b, loc=0)
Percent point function (inverse of
cdf
— percentiles).isf(q, n, a, b, loc=0)
Inverse survival function (inverse of
sf
).stats(n, a, b, loc=0, moments=’mv’)
Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
entropy(n, a, b, loc=0)
(Differential) entropy of the RV.
expect(func, args=(n, a, b), loc=0, lb=None, ub=None, conditional=False)
Expected value of a function (of one argument) with respect to the distribution.
median(n, a, b, loc=0)
Median of the distribution.
mean(n, a, b, loc=0)
Mean of the distribution.
var(n, a, b, loc=0)
Variance of the distribution.
std(n, a, b, loc=0)
Standard deviation of the distribution.
interval(confidence, n, a, b, loc=0)
Confidence interval with equal areas around the median.
See also
betabinom
Beta binomial distribution
Notes
The beta-negative-binomial distribution is a negative binomial distribution with a probability of success p that follows a beta distribution.
The probability mass function for
betanbinom
is:f(k) = \binom{n + k - 1}{k} \frac{B(a + n, b + k)}{B(a, b)}for k \ge 0, n \geq 0, a > 0, b > 0, where B(a, b) is the beta function.
betanbinom
takes n, a, and b as shape parameters.The probability mass function above is defined in the “standardized” form. To shift distribution use the
loc
parameter. Specifically,betanbinom.pmf(k, n, a, b, loc)
is identically equivalent tobetanbinom.pmf(k - loc, n, a, b)
.References
Added in version 1.12.0.
Examples
>>> import numpy as np >>> from scipy.stats import betanbinom >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)
Get the support:
>>> n, a, b = 5, 9.3, 1 >>> lb, ub = betanbinom.support(n, a, b)
Calculate the first four moments:
>>> mean, var, skew, kurt = betanbinom.stats(n, a, b, moments='mvsk')
Display the probability mass function (
pmf
):>>> x = np.arange(betanbinom.ppf(0.01, n, a, b), ... betanbinom.ppf(0.99, n, a, b)) >>> ax.plot(x, betanbinom.pmf(x, n, a, b), 'bo', ms=8, label='betanbinom pmf') >>> ax.vlines(x, 0, betanbinom.pmf(x, n, a, b), colors='b', lw=5, alpha=0.5)
Alternatively, the distribution object can be called (as a function) to fix the shape and location. This returns a “frozen” RV object holding the given parameters fixed.
Freeze the distribution and display the frozen
pmf
:>>> rv = betanbinom(n, a, b) >>> ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1, ... label='frozen pmf') >>> ax.legend(loc='best', frameon=False) >>> plt.show()
Check accuracy of
cdf
andppf
:>>> prob = betanbinom.cdf(x, n, a, b) >>> np.allclose(x, betanbinom.ppf(prob, n, a, b)) True
Generate random numbers:
>>> r = betanbinom.rvs(n, a, b, size=1000)