This is documentation for an old release of SciPy (version 1.8.1). Read this page in the documentation of the latest stable release (version 1.14.1).
scipy.stats.beta#
- scipy.stats.beta = <scipy.stats._continuous_distns.beta_gen object>[source]#
A beta continuous random variable.
As an instance of the
rv_continuous
class,beta
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
beta
is:\[f(x, a, b) = \frac{\Gamma(a+b) x^{a-1} (1-x)^{b-1}} {\Gamma(a) \Gamma(b)}\]for \(0 <= x <= 1\), \(a > 0\), \(b > 0\), where \(\Gamma\) is the gamma function (
scipy.special.gamma
).beta
takes \(a\) and \(b\) as shape parameters.The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the
loc
andscale
parameters. Specifically,beta.pdf(x, a, b, loc, scale)
is identically equivalent tobeta.pdf(y, a, b) / 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 beta >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)
Calculate the first four moments:
>>> a, b = 2.31, 0.627 >>> mean, var, skew, kurt = beta.stats(a, b, moments='mvsk')
Display the probability density function (
pdf
):>>> x = np.linspace(beta.ppf(0.01, a, b), ... beta.ppf(0.99, a, b), 100) >>> ax.plot(x, beta.pdf(x, a, b), ... 'r-', lw=5, alpha=0.6, label='beta 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 = beta(a, b) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
Check accuracy of
cdf
andppf
:>>> vals = beta.ppf([0.001, 0.5, 0.999], a, b) >>> np.allclose([0.001, 0.5, 0.999], beta.cdf(vals, a, b)) True
Generate random numbers:
>>> r = beta.rvs(a, 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(a, b, loc=0, scale=1, size=1, random_state=None)
Random variates.
pdf(x, a, b, loc=0, scale=1)
Probability density function.
logpdf(x, a, b, loc=0, scale=1)
Log of the probability density function.
cdf(x, a, b, loc=0, scale=1)
Cumulative distribution function.
logcdf(x, a, b, loc=0, scale=1)
Log of the cumulative distribution function.
sf(x, a, b, loc=0, scale=1)
Survival function (also defined as
1 - cdf
, but sf is sometimes more accurate).logsf(x, a, b, loc=0, scale=1)
Log of the survival function.
ppf(q, a, b, loc=0, scale=1)
Percent point function (inverse of
cdf
— percentiles).isf(q, a, b, loc=0, scale=1)
Inverse survival function (inverse of
sf
).moment(n, a, b, loc=0, scale=1)
Non-central moment of order n
stats(a, b, loc=0, scale=1, moments=’mv’)
Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
entropy(a, 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=(a, 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(a, b, loc=0, scale=1)
Median of the distribution.
mean(a, b, loc=0, scale=1)
Mean of the distribution.
var(a, b, loc=0, scale=1)
Variance of the distribution.
std(a, b, loc=0, scale=1)
Standard deviation of the distribution.
interval(alpha, a, b, loc=0, scale=1)
Endpoints of the range that contains fraction alpha [0, 1] of the distribution