scipy.stats.rice¶
-
scipy.stats.
rice
(*args, **kwds) = <scipy.stats._continuous_distns.rice_gen object>[source]¶ A Rice continuous random variable.
As an instance of the
rv_continuous
class,rice
object 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
rice
is:\[f(x, b) = x \exp(- \frac{x^2 + b^2}{2}) I_0(x b)\]for \(x >= 0\), \(b > 0\). \(I_0\) is the modified Bessel function of order zero (
scipy.special.i0
).rice
takesb
as a shape parameter for \(b\).The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the
loc
andscale
parameters. Specifically,rice.pdf(x, b, loc, scale)
is identically equivalent torice.pdf(y, b) / scale
withy = (x - loc) / scale
.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
>>> from scipy.stats import rice >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)
Calculate a few first 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
cdf
andppf
:>>> 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, histtype='stepfilled', alpha=0.2) >>> 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(n, b, loc=0, scale=1)
Non-central moment of order n
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(alpha, b, loc=0, scale=1)
Endpoints of the range that contains alpha percent of the distribution