scipy.stats.boltzmann#
- scipy.stats.boltzmann = <scipy.stats._discrete_distns.boltzmann_gen object>[source]#
- A Boltzmann (Truncated Discrete Exponential) random variable. - As an instance of the - rv_discreteclass,- boltzmannobject 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_, N, loc=0, size=1, random_state=None) - Random variates. - pmf(k, lambda_, N, loc=0) - Probability mass function. - logpmf(k, lambda_, N, loc=0) - Log of the probability mass function. - cdf(k, lambda_, N, loc=0) - Cumulative distribution function. - logcdf(k, lambda_, N, loc=0) - Log of the cumulative distribution function. - sf(k, lambda_, N, loc=0) - Survival function (also defined as - 1 - cdf, but sf is sometimes more accurate).- logsf(k, lambda_, N, loc=0) - Log of the survival function. - ppf(q, lambda_, N, loc=0) - Percent point function (inverse of - cdf— percentiles).- isf(q, lambda_, N, loc=0) - Inverse survival function (inverse of - sf).- stats(lambda_, N, loc=0, moments=’mv’) - Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). - entropy(lambda_, N, loc=0) - (Differential) entropy of the RV. - expect(func, args=(lambda_, N), loc=0, lb=None, ub=None, conditional=False) - Expected value of a function (of one argument) with respect to the distribution. - median(lambda_, N, loc=0) - Median of the distribution. - mean(lambda_, N, loc=0) - Mean of the distribution. - var(lambda_, N, loc=0) - Variance of the distribution. - std(lambda_, N, loc=0) - Standard deviation of the distribution. - interval(confidence, lambda_, N, loc=0) - Confidence interval with equal areas around the median. - Notes - The probability mass function for - boltzmannis:\[f(k) = (1-\exp(-\lambda)) \exp(-\lambda k) / (1-\exp(-\lambda N))\]- for \(k = 0,..., N-1\). - boltzmanntakes \(\lambda > 0\) and \(N > 0\) as shape parameters.- The probability mass function above is defined in the “standardized” form. To shift distribution use the - locparameter. Specifically,- boltzmann.pmf(k, lambda_, N, loc)is identically equivalent to- boltzmann.pmf(k - loc, lambda_, N).- Examples - >>> import numpy as np >>> from scipy.stats import boltzmann >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) - Get the support: - >>> lambda_, N = 1.4, 19 >>> lb, ub = boltzmann.support(lambda_, N) - Calculate the first four moments: - >>> mean, var, skew, kurt = boltzmann.stats(lambda_, N, moments='mvsk') - Display the probability mass function ( - pmf):- >>> x = np.arange(boltzmann.ppf(0.01, lambda_, N), ... boltzmann.ppf(0.99, lambda_, N)) >>> ax.plot(x, boltzmann.pmf(x, lambda_, N), 'bo', ms=8, label='boltzmann pmf') >>> ax.vlines(x, 0, boltzmann.pmf(x, lambda_, N), 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 = boltzmann(lambda_, N) >>> 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 = boltzmann.cdf(x, lambda_, N) >>> np.allclose(x, boltzmann.ppf(prob, lambda_, N)) True - Generate random numbers: - >>> r = boltzmann.rvs(lambda_, N, size=1000)