scipy.stats.poisson_binom#
- scipy.stats.poisson_binom = <scipy.stats._discrete_distns.poisson_binom_gen object>[source]#
- A Poisson Binomial discrete random variable. - As an instance of the - rv_discreteclass,- poisson_binomobject 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. - See also - Notes - The probability mass function for - poisson_binomis:\[f(k; p_1, p_2, ..., p_n) = \sum_{A \in F_k} \prod_{i \in A} p_i \prod_{j \in A^C} 1 - p_j\]- where \(k \in \{0, 1, \dots, n-1, n\}\), \(F_k\) is the set of all subsets of \(k\) integers that can be selected \(\{0, 1, \dots, n-1, n\}\), and \(A^C\) is the complement of a set \(A\). - poisson_binomaccepts a single array argument- pfor shape parameters \(0 ≤ p_i ≤ 1\), where the last axis corresponds with the index \(i\) and any others are for batch dimensions. Broadcasting behaves according to the usual rules except that the last axis of- pis ignored. Instances of this class do not support serialization/unserialization.- The probability mass function above is defined in the “standardized” form. To shift distribution use the - locparameter. Specifically,- poisson_binom.pmf(k, p, loc)is identically equivalent to- poisson_binom.pmf(k - loc, p).- References [1]- “Poisson binomial distribution”, Wikipedia, https://en.wikipedia.org/wiki/Poisson_binomial_distribution [2]- Biscarri, William, Sihai Dave Zhao, and Robert J. Brunner. “A simple and fast method for computing the Poisson binomial distribution function”. Computational Statistics & Data Analysis 122 (2018) 92-100. DOI:10.1016/j.csda.2018.01.007 - Examples - >>> import numpy as np >>> from scipy.stats import poisson_binom >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) - Get the support: - >>> p = [0.1, 0.6, 0.7, 0.8] >>> lb, ub = poisson_binom.support(p) - Calculate the first four moments: - >>> mean, var, skew, kurt = poisson_binom.stats(p, moments='mvsk') - Display the probability mass function ( - pmf):- >>> x = np.arange(poisson_binom.ppf(0.01, p), ... poisson_binom.ppf(0.99, p)) >>> ax.plot(x, poisson_binom.pmf(x, p), 'bo', ms=8, label='poisson_binom pmf') >>> ax.vlines(x, 0, poisson_binom.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 = poisson_binom(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 = poisson_binom.cdf(x, p) >>> np.allclose(x, poisson_binom.ppf(prob, p)) True - Generate random numbers: - >>> r = poisson_binom.rvs(p, size=1000)