NAG Library Routine Document
G05SCF generates a vector of pseudorandom numbers from a Cauchy distribution with median and semi-interquartile range .
||N, STATE(*), IFAIL
||XMED, SEMIQR, X(N)
The distribution has PDF (probability density function)
G05SCF returns the value
are a pair of consecutive pseudorandom numbers from a uniform distribution over
, such that
One of the initialization routines G05KFF
(for a repeatable sequence if computed sequentially) or G05KGF
(for a non-repeatable sequence) must be called prior to the first call to G05SCF.
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
- 1: N – INTEGERInput
On entry: , the number of pseudorandom numbers to be generated.
- 2: XMED – REAL (KIND=nag_wp)Input
On entry: , the median of the distribution.
- 3: SEMIQR – REAL (KIND=nag_wp)Input
On entry: , the semi-interquartile range of the distribution.
- 4: STATE() – INTEGER arrayCommunication Array
the actual argument supplied must be the array STATE
supplied to the initialization routines G05KFF
On entry: contains information on the selected base generator and its current state.
On exit: contains updated information on the state of the generator.
- 5: X(N) – REAL (KIND=nag_wp) arrayOutput
On exit: the pseudorandom numbers from the specified Cauchy distribution.
- 6: IFAIL – INTEGERInput/Output
must be set to
. If you are unfamiliar with this parameter you should refer to Section 3.3
in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value
is recommended. If the output of error messages is undesirable, then the value
is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is
. When the value is used it is essential to test the value of IFAIL on exit.
unless the routine detects an error or a warning has been flagged (see Section 6
6 Error Indicators and Warnings
If on entry
, explanatory error messages are output on the current error message unit (as defined by X04AAF
Errors or warnings detected by the routine:
On entry, .
On entry, .
|On entry,||STATE vector was not initialized or has been corrupted.|
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 G05SCF, after initialization by G05KFF
9.1 Program Text
Program Text (g05scfe.f90)
9.2 Program Data
Program Data (g05scfe.d)
9.3 Program Results
Program Results (g05scfe.r)