scipy.stats.rdist#
- scipy.stats.rdist = <scipy.stats._continuous_distns.rdist_gen object>[source]#
An R-distributed (symmetric beta) continuous random variable.
As an instance of the
rv_continuous
class,rdist
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
rdist
is:\[f(x, c) = \frac{(1-x^2)^{c/2-1}}{B(1/2, c/2)}\]for \(-1 \le x \le 1\), \(c > 0\).
rdist
is also called the symmetric beta distribution: if B has abeta
distribution with parameters (c/2, c/2), then X = 2*B - 1 follows a R-distribution with parameter c.rdist
takesc
as a shape parameter for \(c\).This distribution includes the following distribution kernels as special cases:
c = 2: uniform c = 3: `semicircular` c = 4: Epanechnikov (parabolic) c = 6: quartic (biweight) c = 8: triweight
The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the
loc
andscale
parameters. Specifically,rdist.pdf(x, c, loc, scale)
is identically equivalent tordist.pdf(y, c) / scale
withy = (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.Examples
>>> from scipy.stats import rdist >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)
Calculate the first four moments:
>>> c = 1.6 >>> mean, var, skew, kurt = rdist.stats(c, moments='mvsk')
Display the probability density function (
pdf
):>>> x = np.linspace(rdist.ppf(0.01, c), ... rdist.ppf(0.99, c), 100) >>> ax.plot(x, rdist.pdf(x, c), ... 'r-', lw=5, alpha=0.6, label='rdist 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 = rdist(c) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
Check accuracy of
cdf
andppf
:>>> vals = rdist.ppf([0.001, 0.5, 0.999], c) >>> np.allclose([0.001, 0.5, 0.999], rdist.cdf(vals, c)) True
Generate random numbers:
>>> r = rdist.rvs(c, 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(c, loc=0, scale=1, size=1, random_state=None)
Random variates.
pdf(x, c, loc=0, scale=1)
Probability density function.
logpdf(x, c, loc=0, scale=1)
Log of the probability density function.
cdf(x, c, loc=0, scale=1)
Cumulative distribution function.
logcdf(x, c, loc=0, scale=1)
Log of the cumulative distribution function.
sf(x, c, loc=0, scale=1)
Survival function (also defined as
1 - cdf
, but sf is sometimes more accurate).logsf(x, c, loc=0, scale=1)
Log of the survival function.
ppf(q, c, loc=0, scale=1)
Percent point function (inverse of
cdf
— percentiles).isf(q, c, loc=0, scale=1)
Inverse survival function (inverse of
sf
).moment(order, c, loc=0, scale=1)
Non-central moment of the specified order.
stats(c, loc=0, scale=1, moments=’mv’)
Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
entropy(c, 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=(c,), 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(c, loc=0, scale=1)
Median of the distribution.
mean(c, loc=0, scale=1)
Mean of the distribution.
var(c, loc=0, scale=1)
Variance of the distribution.
std(c, loc=0, scale=1)
Standard deviation of the distribution.
interval(confidence, c, loc=0, scale=1)
Confidence interval with equal areas around the median.