NAG Library Function Document
nag_rngs_cauchy (g05llc) generates a vector of pseudorandom numbers from a Cauchy distribution with median and semi-interquartile range .
The distribution has PDF (probability density function)
nag_rngs_cauchy (g05llc) returns the value
are a pair of consecutive pseudorandom numbers from a uniform distribution over
, such that
One of the initialization functions nag_rngs_init_repeatable (g05kbc)
(for a repeatable sequence if computed sequentially) or nag_rngs_init_nonrepeatable (g05kcc)
(for a non-repeatable sequence) must be called prior to the first call to nag_rngs_cauchy (g05llc).
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
xmed – doubleInput
On entry: , the median of the distribution.
semiqr – doubleInput
On entry: , the semi-interquartile range of the distribution.
n – IntegerInput
On entry: , the number of pseudorandom numbers to be generated.
x[n] – doubleOutput
On exit: the pseudorandom numbers from the specified Cauchy distribution.
igen – IntegerInput
: must contain the identification number for the generator to be used to return a pseudorandom number and should remain unchanged following initialization by a prior call to nag_rngs_init_repeatable (g05kbc)
or nag_rngs_init_nonrepeatable (g05kcc)
iseed – IntegerCommunication Array
On entry: contains values which define the current state of the selected generator.
On exit: contains updated values defining the new state of the selected generator.
fail – NagError *Input/Output
The NAG error argument (see Section 3.6
in the Essential Introduction).
6 Error Indicators and Warnings
On entry, argument had an illegal value.
On entry, .
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG
On entry, .
This example prints the first five pseudorandom real numbers from a Cauchy distribution with median
and semi-interquartile range
, generated by a single call to nag_rngs_cauchy (g05llc), after initialization by nag_rngs_init_repeatable (g05kbc)
9.1 Program Text
Program Text (g05llce.c)
9.2 Program Data
9.3 Program Results
Program Results (g05llce.r)