scipy.stats.genexpon¶
-
scipy.stats.
genexpon
= <scipy.stats._continuous_distns.genexpon_gen object>[source]¶ A generalized exponential continuous random variable.
As an instance of the
rv_continuous
class,genexpon
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
genexpon
is:\[f(x, a, b, c) = (a + b (1 - \exp(-c x))) \exp(-a x - b x + \frac{b}{c} (1-\exp(-c x)))\]for \(x \ge 0\), \(a, b, c > 0\).
genexpon
takes \(a\), \(b\) and \(c\) 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,genexpon.pdf(x, a, b, c, loc, scale)
is identically equivalent togenexpon.pdf(y, a, b, c) / scale
withy = (x - loc) / scale
.References
H.K. Ryu, “An Extension of Marshall and Olkin’s Bivariate Exponential Distribution”, Journal of the American Statistical Association, 1993.
N. Balakrishnan, “The Exponential Distribution: Theory, Methods and Applications”, Asit P. Basu.
Examples
>>> from scipy.stats import genexpon >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)
Calculate a few first moments:
>>> a, b, c = 9.13, 16.2, 3.28 >>> mean, var, skew, kurt = genexpon.stats(a, b, c, moments='mvsk')
Display the probability density function (
pdf
):>>> x = np.linspace(genexpon.ppf(0.01, a, b, c), ... genexpon.ppf(0.99, a, b, c), 100) >>> ax.plot(x, genexpon.pdf(x, a, b, c), ... 'r-', lw=5, alpha=0.6, label='genexpon 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 = genexpon(a, b, c) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
Check accuracy of
cdf
andppf
:>>> vals = genexpon.ppf([0.001, 0.5, 0.999], a, b, c) >>> np.allclose([0.001, 0.5, 0.999], genexpon.cdf(vals, a, b, c)) True
Generate random numbers:
>>> r = genexpon.rvs(a, b, c, 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, c, loc=0, scale=1, size=1, random_state=None)
Random variates.
pdf(x, a, b, c, loc=0, scale=1)
Probability density function.
logpdf(x, a, b, c, loc=0, scale=1)
Log of the probability density function.
cdf(x, a, b, c, loc=0, scale=1)
Cumulative distribution function.
logcdf(x, a, b, c, loc=0, scale=1)
Log of the cumulative distribution function.
sf(x, a, b, c, loc=0, scale=1)
Survival function (also defined as
1 - cdf
, but sf is sometimes more accurate).logsf(x, a, b, c, loc=0, scale=1)
Log of the survival function.
ppf(q, a, b, c, loc=0, scale=1)
Percent point function (inverse of
cdf
— percentiles).isf(q, a, b, c, loc=0, scale=1)
Inverse survival function (inverse of
sf
).moment(n, a, b, c, loc=0, scale=1)
Non-central moment of order n
stats(a, b, c, loc=0, scale=1, moments=’mv’)
Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
entropy(a, b, c, loc=0, scale=1)
(Differential) entropy of the RV.
fit(data, a, b, c, loc=0, scale=1)
Parameter estimates for generic data.
expect(func, args=(a, b, c), 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, c, loc=0, scale=1)
Median of the distribution.
mean(a, b, c, loc=0, scale=1)
Mean of the distribution.
var(a, b, c, loc=0, scale=1)
Variance of the distribution.
std(a, b, c, loc=0, scale=1)
Standard deviation of the distribution.
interval(alpha, a, b, c, loc=0, scale=1)
Endpoints of the range that contains alpha percent of the distribution