scipy.stats.burr¶
-
scipy.stats.
burr
= <scipy.stats._continuous_distns.burr_gen object>[source]¶ A Burr (Type III) continuous random variable.
As an instance of the
rv_continuous
class,burr
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
burr
is:\[f(x, c, d) = c d x^{-c-1} (1+x^{-c})^{-d-1}\]for \(x > 0\) and \(c, d > 0\).
burr
takes \(c\) and \(d\) as shape parameters.This is the PDF corresponding to the third CDF given in Burr’s list; specifically, it is equation (11) in Burr’s paper [1].
The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the
loc
andscale
parameters. Specifically,burr.pdf(x, c, d, loc, scale)
is identically equivalent toburr.pdf(y, c, d) / scale
withy = (x - loc) / scale
.References
[1] (1, 2) Burr, I. W. “Cumulative frequency functions”, Annals of Mathematical Statistics, 13(2), pp 215-232 (1942). Examples
>>> from scipy.stats import burr >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)
Calculate a few first moments:
>>> c, d = 10.5, 4.3 >>> mean, var, skew, kurt = burr.stats(c, d, moments='mvsk')
Display the probability density function (
pdf
):>>> x = np.linspace(burr.ppf(0.01, c, d), ... burr.ppf(0.99, c, d), 100) >>> ax.plot(x, burr.pdf(x, c, d), ... 'r-', lw=5, alpha=0.6, label='burr 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 = burr(c, d) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
Check accuracy of
cdf
andppf
:>>> vals = burr.ppf([0.001, 0.5, 0.999], c, d) >>> np.allclose([0.001, 0.5, 0.999], burr.cdf(vals, c, d)) True
Generate random numbers:
>>> r = burr.rvs(c, d, 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, d, loc=0, scale=1, size=1, random_state=None) Random variates. pdf(x, c, d, loc=0, scale=1) Probability density function. logpdf(x, c, d, loc=0, scale=1) Log of the probability density function. cdf(x, c, d, loc=0, scale=1) Cumulative distribution function. logcdf(x, c, d, loc=0, scale=1) Log of the cumulative distribution function. sf(x, c, d, loc=0, scale=1) Survival function (also defined as 1 - cdf
, but sf is sometimes more accurate).logsf(x, c, d, loc=0, scale=1) Log of the survival function. ppf(q, c, d, loc=0, scale=1) Percent point function (inverse of cdf
— percentiles).isf(q, c, d, loc=0, scale=1) Inverse survival function (inverse of sf
).moment(n, c, d, loc=0, scale=1) Non-central moment of order n stats(c, d, loc=0, scale=1, moments=’mv’) Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). entropy(c, d, loc=0, scale=1) (Differential) entropy of the RV. fit(data, c, d, loc=0, scale=1) Parameter estimates for generic data. expect(func, args=(c, d), 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, d, loc=0, scale=1) Median of the distribution. mean(c, d, loc=0, scale=1) Mean of the distribution. var(c, d, loc=0, scale=1) Variance of the distribution. std(c, d, loc=0, scale=1) Standard deviation of the distribution. interval(alpha, c, d, loc=0, scale=1) Endpoints of the range that contains alpha percent of the distribution