A binomial discrete random variable.
As an instance of the rv_discrete class, binom 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
The probability mass function for binom is:
\[f(k) = \binom{n}{k} p^k (1-p)^{n-k}\]
for \(k \in \{0, 1, \dots, n\}\), \(0 \leq p \leq 1\)
binom takes \(n\) and \(p\) as shape parameters, where \(p\) is the probability of a single success and \(1-p\) is the probability of a single failure.
The probability mass function above is defined in the “standardized” form. To shift distribution use the loc parameter. Specifically, binom.pmf(k, n, p, loc) is identically equivalent to binom.pmf(k - loc, n, p).
Examples
>>> from scipy.stats import binom >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)
Calculate the first four moments:
>>> n, p = 5, 0.4 >>> mean, var, skew, kurt = binom.stats(n, p, moments='mvsk')
Display the probability mass function (pmf):
>>> x = np.arange(binom.ppf(0.01, n, p), ... binom.ppf(0.99, n, p)) >>> ax.plot(x, binom.pmf(x, n, p), 'bo', ms=8, label='binom pmf') >>> ax.vlines(x, 0, binom.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 = binom(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 and ppf:
>>> prob = binom.cdf(x, n, p) >>> np.allclose(x, binom.ppf(prob, n, p)) True
Generate random numbers:
>>> r = binom.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(confidence, n, p, loc=0) | Confidence interval with equal areas around the median. |