scipy.stats.nct

scipy.stats.nct = <scipy.stats.distributions.nct_gen object at 0x4acb510>

A non-central Student’s T 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

df, nc : 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 = nct(df, nc, loc=0, scale=1) :

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

Notes

The probability density function for nct is:

                                    df**(df/2) * gamma(df+1)
nct.pdf(x, df, nc) = ----------------------------------------------------
                     2**df*exp(nc**2/2) * (df+x**2)**(df/2) * gamma(df/2)

for df > 0, nc > 0.

Examples

>>> from scipy.stats import nct
>>> numargs = nct.numargs
>>> [ df, nc ] = [0.9,] * numargs
>>> rv = nct(df, nc)

Display frozen pdf

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

Here, rv.dist.b is the right endpoint of the support of rv.dist.

Check accuracy of cdf and ppf

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

Random number generation

>>> R = nct.rvs(df, nc, size=100)

Methods

rvs(df, nc, loc=0, scale=1, size=1)	Random variates.
pdf(x, df, nc, loc=0, scale=1)	Probability density function.
logpdf(x, df, nc, loc=0, scale=1)	Log of the probability density function.
cdf(x, df, nc, loc=0, scale=1)	Cumulative density function.
logcdf(x, df, nc, loc=0, scale=1)	Log of the cumulative density function.
sf(x, df, nc, loc=0, scale=1)	Survival function (1-cdf — sometimes more accurate).
logsf(x, df, nc, loc=0, scale=1)	Log of the survival function.
ppf(q, df, nc, loc=0, scale=1)	Percent point function (inverse of cdf — percentiles).
isf(q, df, nc, loc=0, scale=1)	Inverse survival function (inverse of sf).
moment(n, df, nc, loc=0, scale=1)	Non-central moment of order n
stats(df, nc, loc=0, scale=1, moments=’mv’)	Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
entropy(df, nc, loc=0, scale=1)	(Differential) entropy of the RV.
fit(data, df, nc, loc=0, scale=1)	Parameter estimates for generic data.
expect(func, df, nc, 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(df, nc, loc=0, scale=1)	Median of the distribution.
mean(df, nc, loc=0, scale=1)	Mean of the distribution.
var(df, nc, loc=0, scale=1)	Variance of the distribution.
std(df, nc, loc=0, scale=1)	Standard deviation of the distribution.
interval(alpha, df, nc, loc=0, scale=1)	Endpoints of the range that contains alpha percent of the distribution