NAG Library Function Document
nag_rand_geom (g05tcc) generates a vector of pseudorandom integers from the discrete geometric distribution with probability of success at a trial.
||nag_rand_geom (Nag_ModeRNG mode,
nag_rand_geom (g05tcc) generates
from a discrete geometric distribution, where the probability of
(a first success after
The variates can be generated with or without using a search table and index. If a search table is used then it is stored with the index in a reference vector and subsequent calls to nag_rand_geom (g05tcc) with the same parameter value can then use this reference vector to generate further variates. If the search table is not used (as recommended for small values of ) then a direct transformation of uniform variates is used.
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_geom (g05tcc).
Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley
mode – Nag_ModeRNGInput
: a code for selecting the operation to be performed by the function.
- Set up reference vector only.
- Generate variates using reference vector set up in a prior call to nag_rand_geom (g05tcc).
- Set up reference vector and generate variates.
- Generate variates without using the reference vector.
, , or .
n – IntegerInput
On entry: , the number of pseudorandom numbers to be generated.
p – doubleInput
On entry: the parameter of the geometric distribution representing the probability of success at a single trial.
(see nag_machine_precision (X02AJC)
r[lr] – doubleCommunication Array
, the reference vector from the previous call to nag_rand_geom (g05tcc).
is not referenced by nag_rand_geom (g05tcc).
On exit: the reference vector.
lr – IntegerInput
: the dimension of the array r
- if , approximately (see Section 8);
- otherwise .
- if or , ;
- if , lr should remain unchanged from the previous call to nag_rand_geom (g05tcc).
state – IntegerCommunication Array
the actual argument supplied must be the array state
supplied to the initialization functions 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] – IntegerOutput
On exit: the pseudorandom numbers from the specified geometric 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, lr
is too small when
, minimum length required
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.
is not the same as when r
was set up in a previous call.
Previous value of
On entry, .
is so small that lr
would have to be larger than the largest representable
On entry, some of the elements of the array r
have been corrupted or have not been initialized.
The time taken to set up the reference vector, if used, increases with the length of array r
. However, if the reference vector is used, the time taken to generate numbers decreases as the space allotted to the index part of r
increases. Nevertheless, there is a point, depending on the distribution, where this improvement becomes very small and the suggested value for the length of array r
is designed to approximate this point.
is very small then the storage requirements for the reference vector and the time taken to set up the reference vector becomes prohibitive. In this case it is recommended that the reference vector is not used. This is achieved by selecting
This example prints
pseudorandom integers from a geometric distribution with parameter
, generated by a single call to nag_rand_geom (g05tcc), after initialization by nag_rand_init_repeatable (g05kfc)
9.1 Program Text
Program Text (g05tcce.c)
9.2 Program Data
9.3 Program Results
Program Results (g05tcce.r)