scipy.stats.alpha

scipy.stats.alpha

A alpha continuous random variable.

Continuous random variables are defined from a standard form and may require some shape parameters to complete its specification. Any optional keyword parameters can be passed to the methods of the RV object as given below:

Parameters :

x : array-like

quantiles

q : array-like

lower or upper tail probability

a : array-like

shape parameters

loc : array-like, optional

location parameter (default=0)

scale : array-like, optional

scale parameter (default=1)

size : int or tuple of ints, optional

shape of random variates (default computed from input arguments )

moments : str, optional

composed of letters [‘mvsk’] specifying which moments to compute where ‘m’ = mean, ‘v’ = variance, ‘s’ = (Fisher’s) skew and ‘k’ = (Fisher’s) kurtosis. (default=’mv’)

Alternatively, the object may be called (as a function) to fix the shape, :

location, and scale parameters returning a “frozen” continuous RV object: :

rv = alpha(a, loc=0, scale=1) :

• Frozen RV object with the same methods but holding the given shape, location, and scale fixed.

Notes

Alpha distribution

alpha.pdf(x,a) = 1/(x**2*Phi(a)*sqrt(2*pi)) * exp(-1/2 * (a-1/x)**2) where Phi(alpha) is the normal CDF, x > 0, and a > 0.

Examples

>>> import matplotlib.pyplot as plt
>>> numargs = alpha.numargs
>>> [ a ] = [0.9,] * numargs
>>> rv = alpha(a)

Display frozen pdf

>>> x = np.linspace(0, np.minimum(rv.dist.b, 3))
>>> h = plt.plot(x, rv.pdf(x))

Check accuracy of cdf and ppf

>>> prb = alpha.cdf(x, a)
>>> h = plt.semilogy(np.abs(x - alpha.ppf(prb, a)) + 1e-20)

Random number generation

>>> R = alpha.rvs(a, size=100)

(Source code)

Methods

rvs(a, loc=0, scale=1, size=1)	Random variates.
pdf(x, a, loc=0, scale=1)	Probability density function.
cdf(x, a, loc=0, scale=1)	Cumulative density function.
sf(x, a, loc=0, scale=1)	Survival function (1-cdf — sometimes more accurate).
ppf(q, a, loc=0, scale=1)	Percent point function (inverse of cdf — percentiles).
isf(q, a, loc=0, scale=1)	Inverse survival function (inverse of sf).
stats(a, loc=0, scale=1, moments=’mv’)	Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
entropy(a, loc=0, scale=1)	(Differential) entropy of the RV.
fit(data, a, loc=0, scale=1)	Parameter estimates for generic data.