This is documentation for an old release of SciPy (version 0.7.). Read this page Search for this page in the documentation of the latest stable release (version 1.15.1).

scipy.stats.exponweib

scipy.stats.exponweib()

An exponentiated Weibull 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,c : 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 : string, 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’)

Methods:

exponweib.rvs(a,c,loc=0,scale=1,size=1) :

• random variates

exponweib.pdf(x,a,c,loc=0,scale=1) :

• probability density function

exponweib.cdf(x,a,c,loc=0,scale=1) :

• cumulative density function

exponweib.sf(x,a,c,loc=0,scale=1) :

• survival function (1-cdf — sometimes more accurate)

exponweib.ppf(q,a,c,loc=0,scale=1) :

• percent point function (inverse of cdf — percentiles)

exponweib.isf(q,a,c,loc=0,scale=1) :

• inverse survival function (inverse of sf)

exponweib.stats(a,c,loc=0,scale=1,moments=’mv’) :

• mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’)

exponweib.entropy(a,c,loc=0,scale=1) :

• (differential) entropy of the RV.

exponweib.fit(data,a,c,loc=0,scale=1) :

• Parameter estimates for exponweib data

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

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

rv = exponweib(a,c,loc=0,scale=1) :

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

Examples

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

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

Random number generation

>>> R = exponweib.rvs(a,c,size=100)

Exponentiated Weibull distribution

exponweib.pdf(x,a,c) = a*c*(1-exp(-x**c))**(a-1)*exp(-x**c)*x**(c-1) for x > 0, a, c > 0.