scipy.stats.bernoulli#
- scipy.stats.bernoulli = <scipy.stats._discrete_distns.bernoulli_gen object>[source]#
- A Bernoulli discrete random variable. - As an instance of the - rv_discreteclass,- bernoulliobject 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(p, loc=0, size=1, random_state=None) - Random variates. - pmf(k, p, loc=0) - Probability mass function. - logpmf(k, p, loc=0) - Log of the probability mass function. - cdf(k, p, loc=0) - Cumulative distribution function. - logcdf(k, p, loc=0) - Log of the cumulative distribution function. - sf(k, p, loc=0) - Survival function (also defined as - 1 - cdf, but sf is sometimes more accurate).- logsf(k, p, loc=0) - Log of the survival function. - ppf(q, p, loc=0) - Percent point function (inverse of - cdf— percentiles).- isf(q, p, loc=0) - Inverse survival function (inverse of - sf).- stats(p, loc=0, moments=’mv’) - Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). - entropy(p, loc=0) - (Differential) entropy of the RV. - expect(func, args=(p,), loc=0, lb=None, ub=None, conditional=False) - Expected value of a function (of one argument) with respect to the distribution. - median(p, loc=0) - Median of the distribution. - mean(p, loc=0) - Mean of the distribution. - var(p, loc=0) - Variance of the distribution. - std(p, loc=0) - Standard deviation of the distribution. - interval(confidence, p, loc=0) - Confidence interval with equal areas around the median. - Notes - The probability mass function for - bernoulliis:\[\begin{split}f(k) = \begin{cases}1-p &\text{if } k = 0\\ p &\text{if } k = 1\end{cases}\end{split}\]- for \(k\) in \(\{0, 1\}\), \(0 \leq p \leq 1\) - bernoullitakes \(p\) as shape parameter, 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 - locparameter. Specifically,- bernoulli.pmf(k, p, loc)is identically equivalent to- bernoulli.pmf(k - loc, p).- Examples - >>> import numpy as np >>> from scipy.stats import bernoulli >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) - Get the support: - >>> p = 0.3 >>> lb, ub = bernoulli.support(p) - Calculate the first four moments: - >>> mean, var, skew, kurt = bernoulli.stats(p, moments='mvsk') - Display the probability mass function ( - pmf):- >>> x = np.arange(bernoulli.ppf(0.01, p), ... bernoulli.ppf(0.99, p)) >>> ax.plot(x, bernoulli.pmf(x, p), 'bo', ms=8, label='bernoulli pmf') >>> ax.vlines(x, 0, bernoulli.pmf(x, 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 = bernoulli(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 - cdfand- ppf:- >>> prob = bernoulli.cdf(x, p) >>> np.allclose(x, bernoulli.ppf(prob, p)) True - Generate random numbers: - >>> r = bernoulli.rvs(p, size=1000)