scipy.stats.skewnorm#
- scipy.stats.skewnorm = <scipy.stats._continuous_distns.skewnorm_gen object>[source]#
A skew-normal random variable.
As an instance of the
rv_continuous
class,skewnorm
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 pdf is:
skewnorm.pdf(x, a) = 2 * norm.pdf(x) * norm.cdf(a*x)
skewnorm
takes a real number \(a\) as a skewness parameter Whena = 0
the distribution is identical to a normal distribution (norm
). rvs implements the method of [1].The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the
loc
andscale
parameters. Specifically,skewnorm.pdf(x, a, loc, scale)
is identically equivalent toskewnorm.pdf(y, a) / 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.References
[1]A. Azzalini and A. Capitanio (1999). Statistical applications of the multivariate skew-normal distribution. J. Roy. Statist. Soc., B 61, 579-602. arXiv:0911.2093
Examples
>>> import numpy as np >>> from scipy.stats import skewnorm >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)
Calculate the first four moments:
>>> a = 4 >>> mean, var, skew, kurt = skewnorm.stats(a, moments='mvsk')
Display the probability density function (
pdf
):>>> x = np.linspace(skewnorm.ppf(0.01, a), ... skewnorm.ppf(0.99, a), 100) >>> ax.plot(x, skewnorm.pdf(x, a), ... 'r-', lw=5, alpha=0.6, label='skewnorm 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 = skewnorm(a) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
Check accuracy of
cdf
andppf
:>>> vals = skewnorm.ppf([0.001, 0.5, 0.999], a) >>> np.allclose([0.001, 0.5, 0.999], skewnorm.cdf(vals, a)) True
Generate random numbers:
>>> r = skewnorm.rvs(a, 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(a, loc=0, scale=1, size=1, random_state=None)
Random variates.
pdf(x, a, loc=0, scale=1)
Probability density function.
logpdf(x, a, loc=0, scale=1)
Log of the probability density function.
cdf(x, a, loc=0, scale=1)
Cumulative distribution function.
logcdf(x, a, loc=0, scale=1)
Log of the cumulative distribution function.
sf(x, a, loc=0, scale=1)
Survival function (also defined as
1 - cdf
, but sf is sometimes more accurate).logsf(x, a, loc=0, scale=1)
Log of the survival function.
ppf(q, a, loc=0, scale=1)
Percent point function (inverse of
cdf
— percentiles).isf(q, a, loc=0, scale=1)
Inverse survival function (inverse of
sf
).moment(order, a, loc=0, scale=1)
Non-central moment of the specified order.
stats(a, loc=0, scale=1, moments=’mv’)
Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
entropy(a, 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=(a,), 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(a, loc=0, scale=1)
Median of the distribution.
mean(a, loc=0, scale=1)
Mean of the distribution.
var(a, loc=0, scale=1)
Variance of the distribution.
std(a, loc=0, scale=1)
Standard deviation of the distribution.
interval(confidence, a, loc=0, scale=1)
Confidence interval with equal areas around the median.