scipy.stats.nbinom¶
-
scipy.stats.
nbinom
= <scipy.stats._discrete_distns.nbinom_gen object>[source]¶ A negative binomial discrete random variable.
As an instance of the
rv_discrete
class,nbinom
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.Notes
Negative binomial distribution describes a sequence of i.i.d. Bernoulli trials, repeated until a predefined, non-random number of successes occurs.
The probability mass function of the number of failures for
nbinom
is:nbinom.pmf(k) = choose(k+n-1, n-1) * p**n * (1-p)**k
for
k >= 0
.nbinom
takesn
andp
as shape parameters where n is the number of successes, whereas p is the probability of a single success.The probability mass function above is defined in the “standardized” form. To shift distribution use the
loc
parameter. Specifically,nbinom.pmf(k, n, p, loc)
is identically equivalent tonbinom.pmf(k - loc, n, p)
.Examples
>>> from scipy.stats import nbinom >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)
Calculate a few first moments:
>>> n, p = 0.4, 0.4 >>> mean, var, skew, kurt = nbinom.stats(n, p, moments='mvsk')
Display the probability mass function (
pmf
):>>> x = np.arange(nbinom.ppf(0.01, n, p), ... nbinom.ppf(0.99, n, p)) >>> ax.plot(x, nbinom.pmf(x, n, p), 'bo', ms=8, label='nbinom pmf') >>> ax.vlines(x, 0, nbinom.pmf(x, n, p), 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 = nbinom(n, p) >>> 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 = nbinom.cdf(x, n, p) >>> np.allclose(x, nbinom.ppf(prob, n, p)) True
Generate random numbers:
>>> r = nbinom.rvs(n, p, size=1000)
Methods
rvs(n, p, loc=0, size=1, random_state=None)
Random variates. pmf(k, n, p, loc=0)
Probability mass function. logpmf(k, n, p, loc=0)
Log of the probability mass function. cdf(k, n, p, loc=0)
Cumulative distribution function. logcdf(k, n, p, loc=0)
Log of the cumulative distribution function. sf(k, n, p, loc=0)
Survival function (also defined as 1 - cdf
, but sf is sometimes more accurate).logsf(k, n, p, loc=0)
Log of the survival function. ppf(q, n, p, loc=0)
Percent point function (inverse of cdf
— percentiles).isf(q, n, p, loc=0)
Inverse survival function (inverse of sf
).stats(n, p, loc=0, moments='mv')
Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). entropy(n, p, loc=0)
(Differential) entropy of the RV. expect(func, args=(n, p), loc=0, lb=None, ub=None, conditional=False)
Expected value of a function (of one argument) with respect to the distribution. median(n, p, loc=0)
Median of the distribution. mean(n, p, loc=0)
Mean of the distribution. var(n, p, loc=0)
Variance of the distribution. std(n, p, loc=0)
Standard deviation of the distribution. interval(alpha, n, p, loc=0)
Endpoints of the range that contains alpha percent of the distribution