naginterfaces.library.rand.dist_​cauchy

naginterfaces.library.rand.dist_cauchy(n, xmed, semiqr, statecomm)[source]

dist_cauchy generates a vector of pseudorandom numbers from a Cauchy distribution with median and semi-interquartile range .

For full information please refer to the NAG Library document for g05sc

https://www.nag.com/numeric/nl/nagdoc_27.1/flhtml/g05/g05scf.html

Parameters
nint

, the number of pseudorandom numbers to be generated.

xmedfloat

, the median of the distribution.

semiqrfloat

, the semi-interquartile range of the distribution.

statecommdict, RNG communication object, modified in place

RNG communication structure.

This argument must have been initialized by a prior call to init_repeat() or init_nonrepeat().

Returns
xfloat, ndarray, shape

The pseudorandom numbers from the specified Cauchy distribution.

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, [‘state’] vector has been corrupted or not initialized.

Notes

The distribution has PDF (probability density function)

dist_cauchy returns the value

where and are a pair of consecutive pseudorandom numbers from a uniform distribution over , such that

One of the initialization functions init_repeat() (for a repeatable sequence if computed sequentially) or init_nonrepeat() (for a non-repeatable sequence) must be called prior to the first call to dist_cauchy.

References

Kendall, M G and Stuart, A, 1969, The Advanced Theory of Statistics (Volume 1), (3rd Edition), Griffin

Knuth, D E, 1981, The Art of Computer Programming (Volume 2), (2nd Edition), Addison–Wesley