NAG Library Function Document
nag_rand_cauchy (g05scc) generates a vector of pseudorandom numbers from a Cauchy distribution with median and semi-interquartile range .
||nag_rand_cauchy (Integer n,
The distribution has PDF (probability density function)
nag_rand_cauchy (g05scc) returns the value
are a pair of consecutive pseudorandom numbers from a uniform distribution over
, such that
One of the initialization functions nag_rand_init_repeatable (g05kfc)
(for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeatable (g05kgc)
(for a non-repeatable sequence) must be called prior to the first call to nag_rand_cauchy (g05scc).
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
n – IntegerInput
On entry: , the number of pseudorandom numbers to be generated.
xmed – doubleInput
On entry: , the median of the distribution.
semiqr – doubleInput
On entry: , the semi-interquartile range of the distribution.
state – IntegerCommunication Array
, of this array is dictated by the requirements of associated functions that must have been previously called. This array MUST be the same array passed as argument state
in the previous call to nag_rand_init_repeatable (g05kfc)
or nag_rand_init_nonrepeatable (g05kgc)
On entry: contains information on the selected base generator and its current state.
On exit: contains updated information on the state of the generator.
x[n] – doubleOutput
On exit: the pseudorandom numbers from the specified Cauchy distribution.
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, state
vector has been corrupted or not initialized.
On entry, .
8 Parallelism and Performance
nag_rand_cauchy (g05scc) is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
Please consult the Users' Note
for your implementation for any additional implementation-specific information.
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_rand_cauchy (g05scc), after initialization by nag_rand_init_repeatable (g05kfc)
10.1 Program Text
Program Text (g05scce.c)
10.2 Program Data
10.3 Program Results
Program Results (g05scce.r)