scipy.stats.binom=<scipy.stats._discrete_distns.binom_gen object>[source]# 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.
| |