scipy.stats.exponpow#
- scipy.stats.exponpow = <scipy.stats._continuous_distns.exponpow_gen object>[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:\[f(x, b) = b x^{b-1} \exp(1 + x^b - \exp(x^b))\]for \(x \ge 0\), \(b > 0\). 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
takesb
as a shape parameter for \(b\).The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the
loc
andscale
parameters. Specifically,exponpow.pdf(x, b, loc, scale)
is identically equivalent toexponpow.pdf(y, 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.References
http://www.math.wm.edu/~leemis/chart/UDR/PDFs/Exponentialpower.pdf
Examples
>>> import numpy as np >>> from scipy.stats import exponpow >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)
Calculate the first four 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
andppf
:>>> 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, 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(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(order, b, loc=0, scale=1)
Non-central moment of the specified order.
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)
Parameter estimates for generic data. See scipy.stats.rv_continuous.fit for detailed documentation of the keyword arguments.
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(confidence, b, loc=0, scale=1)
Confidence interval with equal areas around the median.