scipy.stats.planck#
- scipy.stats.planck = <scipy.stats._discrete_distns.planck_gen object>[source]#
- A Planck discrete exponential random variable. - As an instance of the - rv_discreteclass,- planckobject 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(lambda_, loc=0, size=1, random_state=None) - Random variates. - pmf(k, lambda_, loc=0) - Probability mass function. - logpmf(k, lambda_, loc=0) - Log of the probability mass function. - cdf(k, lambda_, loc=0) - Cumulative distribution function. - logcdf(k, lambda_, loc=0) - Log of the cumulative distribution function. - sf(k, lambda_, loc=0) - Survival function (also defined as - 1 - cdf, but sf is sometimes more accurate).- logsf(k, lambda_, loc=0) - Log of the survival function. - ppf(q, lambda_, loc=0) - Percent point function (inverse of - cdf— percentiles).- isf(q, lambda_, loc=0) - Inverse survival function (inverse of - sf).- stats(lambda_, loc=0, moments=’mv’) - Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). - entropy(lambda_, loc=0) - (Differential) entropy of the RV. - expect(func, args=(lambda_,), loc=0, lb=None, ub=None, conditional=False) - Expected value of a function (of one argument) with respect to the distribution. - median(lambda_, loc=0) - Median of the distribution. - mean(lambda_, loc=0) - Mean of the distribution. - var(lambda_, loc=0) - Variance of the distribution. - std(lambda_, loc=0) - Standard deviation of the distribution. - interval(confidence, lambda_, loc=0) - Confidence interval with equal areas around the median. - See also - Notes - The probability mass function for - planckis:\[f(k) = (1-\exp(-\lambda)) \exp(-\lambda k)\]- for \(k \ge 0\) and \(\lambda > 0\). - plancktakes \(\lambda\) as shape parameter. The Planck distribution can be written as a geometric distribution (- geom) with \(p = 1 - \exp(-\lambda)\) shifted by- loc = -1.- The probability mass function above is defined in the “standardized” form. To shift distribution use the - locparameter. Specifically,- planck.pmf(k, lambda_, loc)is identically equivalent to- planck.pmf(k - loc, lambda_).- Examples - >>> import numpy as np >>> from scipy.stats import planck >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) - Get the support: - >>> lambda_ = 0.51 >>> lb, ub = planck.support(lambda_) - Calculate the first four moments: - >>> mean, var, skew, kurt = planck.stats(lambda_, moments='mvsk') - Display the probability mass function ( - pmf):- >>> x = np.arange(planck.ppf(0.01, lambda_), ... planck.ppf(0.99, lambda_)) >>> ax.plot(x, planck.pmf(x, lambda_), 'bo', ms=8, label='planck pmf') >>> ax.vlines(x, 0, planck.pmf(x, lambda_), 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 = planck(lambda_) >>> 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 = planck.cdf(x, lambda_) >>> np.allclose(x, planck.ppf(prob, lambda_)) True - Generate random numbers: - >>> r = planck.rvs(lambda_, size=1000)