scipy.stats.exponnorm#
- scipy.stats.exponnorm = <scipy.stats._continuous_distns.exponnorm_gen object>[source]#
- An exponentially modified Normal continuous random variable. - Also known as the exponentially modified Gaussian distribution [1]. - As an instance of the - rv_continuousclass,- exponnormobject 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(K, loc=0, scale=1, size=1, random_state=None) - Random variates. - pdf(x, K, loc=0, scale=1) - Probability density function. - logpdf(x, K, loc=0, scale=1) - Log of the probability density function. - cdf(x, K, loc=0, scale=1) - Cumulative distribution function. - logcdf(x, K, loc=0, scale=1) - Log of the cumulative distribution function. - sf(x, K, loc=0, scale=1) - Survival function (also defined as - 1 - cdf, but sf is sometimes more accurate).- logsf(x, K, loc=0, scale=1) - Log of the survival function. - ppf(q, K, loc=0, scale=1) - Percent point function (inverse of - cdf— percentiles).- isf(q, K, loc=0, scale=1) - Inverse survival function (inverse of - sf).- moment(order, K, loc=0, scale=1) - Non-central moment of the specified order. - stats(K, loc=0, scale=1, moments=’mv’) - Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). - entropy(K, loc=0, scale=1) - (Differential) entropy of the RV. - fit(data) - Parameter estimates for generic data. See scipy.stats.rv_continuous.fit for detailed documentation of the keyword arguments. - expect(func, args=(K,), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds) - Expected value of a function (of one argument) with respect to the distribution. - median(K, loc=0, scale=1) - Median of the distribution. - mean(K, loc=0, scale=1) - Mean of the distribution. - var(K, loc=0, scale=1) - Variance of the distribution. - std(K, loc=0, scale=1) - Standard deviation of the distribution. - interval(confidence, K, loc=0, scale=1) - Confidence interval with equal areas around the median. - Notes - The probability density function for - exponnormis:\[f(x, K) = \frac{1}{2K} \exp\left(\frac{1}{2 K^2} - x / K \right) \text{erfc}\left(-\frac{x - 1/K}{\sqrt{2}}\right)\]- where \(x\) is a real number and \(K > 0\). - It can be thought of as the sum of a standard normal random variable and an independent exponentially distributed random variable with rate - 1/K.- The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the - locand- scaleparameters. Specifically,- exponnorm.pdf(x, K, loc, scale)is identically equivalent to- exponnorm.pdf(y, K) / scalewith- y = (x - loc) / scale. Note that shifting the location of a distribution does not make it a “noncentral” distribution; noncentral generalizations of some distributions are available in separate classes.- An alternative parameterization of this distribution (for example, in the Wikipedia article [1]) involves three parameters, \(\mu\), \(\lambda\) and \(\sigma\). - In the present parameterization this corresponds to having - locand- scaleequal to \(\mu\) and \(\sigma\), respectively, and shape parameter \(K = 1/(\sigma\lambda)\).- Added in version 0.16.0. - References [1] (1,2)- Exponentially modified Gaussian distribution, Wikipedia, https://en.wikipedia.org/wiki/Exponentially_modified_Gaussian_distribution - Examples - >>> import numpy as np >>> from scipy.stats import exponnorm >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) - Get the support: - >>> K = 1.5 >>> lb, ub = exponnorm.support(K) - Calculate the first four moments: - >>> mean, var, skew, kurt = exponnorm.stats(K, moments='mvsk') - Display the probability density function ( - pdf):- >>> x = np.linspace(exponnorm.ppf(0.01, K), ... exponnorm.ppf(0.99, K), 100) >>> ax.plot(x, exponnorm.pdf(x, K), ... 'r-', lw=5, alpha=0.6, label='exponnorm pdf') - Alternatively, the distribution object can be called (as a function) to fix the shape, location and scale parameters. This returns a “frozen” RV object holding the given parameters fixed. - Freeze the distribution and display the frozen - pdf:- >>> rv = exponnorm(K) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') - Check accuracy of - cdfand- ppf:- >>> vals = exponnorm.ppf([0.001, 0.5, 0.999], K) >>> np.allclose([0.001, 0.5, 0.999], exponnorm.cdf(vals, K)) True - Generate random numbers: - >>> r = exponnorm.rvs(K, size=1000) - And compare the histogram: - >>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2) >>> ax.set_xlim([x[0], x[-1]]) >>> ax.legend(loc='best', frameon=False) >>> plt.show() 