scipy.stats.logser#
- scipy.stats.logser = <scipy.stats._discrete_distns.logser_gen object>[source]#
- A Logarithmic (Log-Series, Series) discrete random variable. - As an instance of the - rv_discreteclass,- logserobject 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 - logseris:\[f(k) = - \frac{p^k}{k \log(1-p)}\]- for \(k \ge 1\), \(0 < p < 1\) - logsertakes \(p\) 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,- logser.pmf(k, p, loc)is identically equivalent to- logser.pmf(k - loc, p).- Examples - >>> import numpy as np >>> from scipy.stats import logser >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) - Calculate the first four moments: - >>> p = 0.6 >>> mean, var, skew, kurt = logser.stats(p, moments='mvsk') - Display the probability mass function ( - pmf):- >>> x = np.arange(logser.ppf(0.01, p), ... logser.ppf(0.99, p)) >>> ax.plot(x, logser.pmf(x, p), 'bo', ms=8, label='logser pmf') >>> ax.vlines(x, 0, logser.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 = logser(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 = logser.cdf(x, p) >>> np.allclose(x, logser.ppf(prob, p)) True - Generate random numbers: - >>> r = logser.rvs(p, size=1000) - 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.