scipy.stats.rice#
- scipy.stats.rice = <scipy.stats._continuous_distns.rice_gen object>[source]#
- A Rice continuous random variable. - As an instance of the - rv_continuousclass,- riceobject 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 - riceis:\[f(x, b) = x \exp(- \frac{x^2 + b^2}{2}) I_0(x b)\]- for \(x >= 0\), \(b > 0\). \(I_0\) is the modified Bessel function of order zero ( - scipy.special.i0).- ricetakes- bas a shape parameter for \(b\).- The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the - locand- scaleparameters. Specifically,- rice.pdf(x, b, loc, scale)is identically equivalent to- rice.pdf(y, b) / 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.- The Rice distribution describes the length, \(r\), of a 2-D vector with components \((U+u, V+v)\), where \(U, V\) are constant, \(u, v\) are independent Gaussian random variables with standard deviation \(s\). Let \(R = \sqrt{U^2 + V^2}\). Then the pdf of \(r\) is - rice.pdf(x, R/s, scale=s).- Examples - >>> import numpy as np >>> from scipy.stats import rice >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) - Calculate the first four moments: - >>> b = 0.775 >>> mean, var, skew, kurt = rice.stats(b, moments='mvsk') - Display the probability density function ( - pdf):- >>> x = np.linspace(rice.ppf(0.01, b), ... rice.ppf(0.99, b), 100) >>> ax.plot(x, rice.pdf(x, b), ... 'r-', lw=5, alpha=0.6, label='rice 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 = rice(b) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') - Check accuracy of - cdfand- ppf:- >>> vals = rice.ppf([0.001, 0.5, 0.999], b) >>> np.allclose([0.001, 0.5, 0.999], rice.cdf(vals, b)) True - Generate random numbers: - >>> r = rice.rvs(b, 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(b, loc=0, scale=1, size=1, random_state=None) - Random variates. - pdf(x, b, loc=0, scale=1) - Probability density function. - logpdf(x, b, loc=0, scale=1) - Log of the probability density function. - cdf(x, b, loc=0, scale=1) - Cumulative distribution function. - logcdf(x, b, loc=0, scale=1) - Log of the cumulative distribution function. - sf(x, b, loc=0, scale=1) - Survival function (also defined as - 1 - cdf, but sf is sometimes more accurate).- logsf(x, b, loc=0, scale=1) - Log of the survival function. - ppf(q, b, loc=0, scale=1) - Percent point function (inverse of - cdf— percentiles).- isf(q, b, loc=0, scale=1) - Inverse survival function (inverse of - sf).- moment(order, b, loc=0, scale=1) - Non-central moment of the specified order. - stats(b, loc=0, scale=1, moments=’mv’) - Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). - entropy(b, 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=(b,), 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(b, loc=0, scale=1) - Median of the distribution. - mean(b, loc=0, scale=1) - Mean of the distribution. - var(b, loc=0, scale=1) - Variance of the distribution. - std(b, loc=0, scale=1) - Standard deviation of the distribution. - interval(confidence, b, loc=0, scale=1) - Confidence interval with equal areas around the median.