scipy.stats.poisson#
- scipy.stats.poisson = <scipy.stats._discrete_distns.poisson_gen object>[source]#
- A Poisson discrete random variable. - As an instance of the - rv_discreteclass,- poissonobject 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 - poissonis:\[f(k) = \exp(-\mu) \frac{\mu^k}{k!}\]- for \(k \ge 0\). - poissontakes \(\mu \geq 0\) as shape parameter. When \(\mu = 0\), the- pmfmethod returns- 1.0at quantile \(k = 0\).- The probability mass function above is defined in the “standardized” form. To shift distribution use the - locparameter. Specifically,- poisson.pmf(k, mu, loc)is identically equivalent to- poisson.pmf(k - loc, mu).- Examples - >>> import numpy as np >>> from scipy.stats import poisson >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) - Calculate the first four moments: - >>> mu = 0.6 >>> mean, var, skew, kurt = poisson.stats(mu, moments='mvsk') - Display the probability mass function ( - pmf):- >>> x = np.arange(poisson.ppf(0.01, mu), ... poisson.ppf(0.99, mu)) >>> ax.plot(x, poisson.pmf(x, mu), 'bo', ms=8, label='poisson pmf') >>> ax.vlines(x, 0, poisson.pmf(x, mu), 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(mu) >>> 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.cdf(x, mu) >>> np.allclose(x, poisson.ppf(prob, mu)) True - Generate random numbers: - >>> r = poisson.rvs(mu, size=1000) - Methods - rvs(mu, loc=0, size=1, random_state=None) - Random variates. - pmf(k, mu, loc=0) - Probability mass function. - logpmf(k, mu, loc=0) - Log of the probability mass function. - cdf(k, mu, loc=0) - Cumulative distribution function. - logcdf(k, mu, loc=0) - Log of the cumulative distribution function. - sf(k, mu, loc=0) - Survival function (also defined as - 1 - cdf, but sf is sometimes more accurate).- logsf(k, mu, loc=0) - Log of the survival function. - ppf(q, mu, loc=0) - Percent point function (inverse of - cdf— percentiles).- isf(q, mu, loc=0) - Inverse survival function (inverse of - sf).- stats(mu, loc=0, moments=’mv’) - Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). - entropy(mu, loc=0) - (Differential) entropy of the RV. - expect(func, args=(mu,), loc=0, lb=None, ub=None, conditional=False) - Expected value of a function (of one argument) with respect to the distribution. - median(mu, loc=0) - Median of the distribution. - mean(mu, loc=0) - Mean of the distribution. - var(mu, loc=0) - Variance of the distribution. - std(mu, loc=0) - Standard deviation of the distribution. - interval(confidence, mu, loc=0) - Confidence interval with equal areas around the median.