pNonCentralChiSquare

pNonCentralChiSquare(*args)

Cumulative distribution function of a NonCentralChiSquare.

Parameters:
nufloat, \nu > 0

The \nu parameter.

lambdafloat, \lambda \geq 0

The \lambda parameter.

xfloat

Location.

tailbool, optional

Tail flag. Default value is False. If True, the complementary CDF is computed.

precisionfloat, optional

The precision of the evaluation.

maxInterint, optional

The maximum number of iterations of the algorithm.

Returns:
pfloat

The CDF or the complementary CDF at x.

Notes

The probability density function is defined as:

f_X(x) = \sum_{j=0}^{\infty} e^{-\lambda} \frac{\lambda^j}{j!}p_{\chi^2(\nu + 2j)}(x), \quad x \in [0; +\infty[

where p_{\chi^2(q)} is the probability density function of a \chi^2(q) random variate.

We use Benton and Krishnamoorthy’s algorithm described in [benton2003].

Examples

>>> import openturns as ot
>>> cdf = ot.DistFunc.pNonCentralChiSquare(2.5, 2.7, 3.0, True, 0.001, 100)
>>> cdf = ot.DistFunc.pNonCentralChiSquare(2.5, 2.7, 3.0, False, 0.001, 100)