scipy.stats.moyal#
- scipy.stats.moyal = <scipy.stats._continuous_distns.moyal_gen object>[source]#
- A Moyal continuous random variable. - As an instance of the - rv_continuousclass,- moyalobject 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 density function for - moyalis:\[f(x) = \exp(-(x + \exp(-x))/2) / \sqrt{2\pi}\]- for a real number \(x\). - The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the - locand- scaleparameters. Specifically,- moyal.pdf(x, loc, scale)is identically equivalent to- moyal.pdf(y) / 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.- This distribution has utility in high-energy physics and radiation detection. It describes the energy loss of a charged relativistic particle due to ionization of the medium [1]. It also provides an approximation for the Landau distribution. For an in depth description see [2]. For additional description, see [3]. - References [1]- J.E. Moyal, “XXX. Theory of ionization fluctuations”, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol 46, 263-280, (1955). DOI:10.1080/14786440308521076 (gated) [2]- G. Cordeiro et al., “The beta Moyal: a useful skew distribution”, International Journal of Research and Reviews in Applied Sciences, vol 10, 171-192, (2012). http://www.arpapress.com/Volumes/Vol10Issue2/IJRRAS_10_2_02.pdf [3]- C. Walck, “Handbook on Statistical Distributions for Experimentalists; International Report SUF-PFY/96-01”, Chapter 26, University of Stockholm: Stockholm, Sweden, (2007). http://www.stat.rice.edu/~dobelman/textfiles/DistributionsHandbook.pdf - Added in version 1.1.0. - Examples - >>> import numpy as np >>> from scipy.stats import moyal >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) - Calculate the first four moments: - >>> mean, var, skew, kurt = moyal.stats(moments='mvsk') - Display the probability density function ( - pdf):- >>> x = np.linspace(moyal.ppf(0.01), ... moyal.ppf(0.99), 100) >>> ax.plot(x, moyal.pdf(x), ... 'r-', lw=5, alpha=0.6, label='moyal 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 = moyal() >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') - Check accuracy of - cdfand- ppf:- >>> vals = moyal.ppf([0.001, 0.5, 0.999]) >>> np.allclose([0.001, 0.5, 0.999], moyal.cdf(vals)) True - Generate random numbers: - >>> r = moyal.rvs(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()   - Methods - rvs(loc=0, scale=1, size=1, random_state=None) - Random variates. - pdf(x, loc=0, scale=1) - Probability density function. - logpdf(x, loc=0, scale=1) - Log of the probability density function. - cdf(x, loc=0, scale=1) - Cumulative distribution function. - logcdf(x, loc=0, scale=1) - Log of the cumulative distribution function. - sf(x, loc=0, scale=1) - Survival function (also defined as - 1 - cdf, but sf is sometimes more accurate).- logsf(x, loc=0, scale=1) - Log of the survival function. - ppf(q, loc=0, scale=1) - Percent point function (inverse of - cdf— percentiles).- isf(q, loc=0, scale=1) - Inverse survival function (inverse of - sf).- moment(order, loc=0, scale=1) - Non-central moment of the specified order. - stats(loc=0, scale=1, moments=’mv’) - Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). - entropy(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=(), 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(loc=0, scale=1) - Median of the distribution. - mean(loc=0, scale=1) - Mean of the distribution. - var(loc=0, scale=1) - Variance of the distribution. - std(loc=0, scale=1) - Standard deviation of the distribution. - interval(confidence, loc=0, scale=1) - Confidence interval with equal areas around the median.