scipy.stats.exponpow¶
- scipy.stats.exponpow = <scipy.stats._continuous_distns.exponpow_gen object at 0x2b2318c03b50>[source]¶
An exponential power continuous random variable.
As an instance of the rv_continuous class, exponpow 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 exponpow is:
exponpow.pdf(x, b) = b * x**(b-1) * exp(1 + x**b - exp(x**b))
for x >= 0, b > 0. Note that this is a different distribution from the exponential power distribution that is also known under the names “generalized normal” or “generalized Gaussian”.
exponpow takes b as a shape parameter.
The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the loc and scale parameters. Specifically, exponpow.pdf(x, b, loc, scale) is identically equivalent to exponpow.pdf(y, b) / scale with y = (x - loc) / scale.
References
http://www.math.wm.edu/~leemis/chart/UDR/PDFs/Exponentialpower.pdf
Examples
>>> from scipy.stats import exponpow >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)
Calculate a few first moments:
>>> b = 2.7 >>> mean, var, skew, kurt = exponpow.stats(b, moments='mvsk')
Display the probability density function (pdf):
>>> x = np.linspace(exponpow.ppf(0.01, b), ... exponpow.ppf(0.99, b), 100) >>> ax.plot(x, exponpow.pdf(x, b), ... 'r-', lw=5, alpha=0.6, label='exponpow 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 = exponpow(b) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
Check accuracy of cdf and ppf:
>>> vals = exponpow.ppf([0.001, 0.5, 0.999], b) >>> np.allclose([0.001, 0.5, 0.999], exponpow.cdf(vals, b)) True
Generate random numbers:
>>> r = exponpow.rvs(b, size=1000)
And compare the histogram:
>>> ax.hist(r, normed=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, b, loc=0, scale=1) Parameter estimates for generic data. 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