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Chapter Contents
Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_rand_dist_exp (g05sf)

Purpose

nag_rand_dist_exp (g05sf) generates a vector of pseudorandom numbers from a (negative) exponential distribution with mean a$a$.

Syntax

[state, x, ifail] = g05sf(n, a, state)
[state, x, ifail] = nag_rand_dist_exp(n, a, state)

Description

The exponential distribution has PDF (probability density function):
 f(x) = 1/a e − x / a if ​x ≥ 0, f(x) = 0 otherwise.
$f(x) = 1a e -x/a if ​x≥0, f(x)=0 otherwise.$
nag_rand_dist_exp (g05sf) returns the values
 xi = − a lnyi $xi = -a ln⁡yi$
where yi${y}_{i}$ are the next n$n$ numbers generated by a uniform (0,1]$\left(0,1\right]$ generator.
One of the initialization functions nag_rand_init_repeat (g05kf) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeat (g05kg) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_dist_exp (g05sf).

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

Parameters

Compulsory Input Parameters

1:     n – int64int32nag_int scalar
n$n$, the number of pseudorandom numbers to be generated.
Constraint: n0${\mathbf{n}}\ge 0$.
2:     a – double scalar
a$a$, the mean of the distribution.
Constraint: a > 0.0${\mathbf{a}}>0.0$.
3:     state( : $:$) – int64int32nag_int array
Note: the actual argument supplied must be the array state supplied to the initialization routines nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg).
Contains information on the selected base generator and its current state.

None.

None.

Output Parameters

1:     state( : $:$) – int64int32nag_int array
Note: the actual argument supplied must be the array state supplied to the initialization routines nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg).
Contains updated information on the state of the generator.
2:     x(n) – double array
The n$n$ pseudorandom numbers from the specified exponential distribution.
3:     ifail – int64int32nag_int scalar
${\mathrm{ifail}}={\mathbf{0}}$ unless the function detects an error (see [Error Indicators and Warnings]).

Error Indicators and Warnings

Errors or warnings detected by the function:
ifail = 1${\mathbf{ifail}}=1$
On entry, n < 0${\mathbf{n}}<0$.
ifail = 2${\mathbf{ifail}}=2$
On entry, a0.0${\mathbf{a}}\le 0.0$.
ifail = 3${\mathbf{ifail}}=3$
 On entry, state vector was not initialized or has been corrupted.

Not applicable.

None.

Example

```function nag_rand_dist_exp_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
n = int64(5);
a = 1;
% Initialize the generator to a repeatable sequence
[state, ifail] = nag_rand_init_repeat(genid, subid, seed);
[state, x, ifail] = nag_rand_dist_exp(n, a, state)
```
```

state =

17
1234
1
0
4110
11820
23399
29340
17917
13895
19930
8
0
1234
1
1
1234

x =

0.4520
2.2398
0.2930
0.2253
2.2577

ifail =

0

```
```function g05sf_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
n = int64(5);
a = 1;
% Initialize the generator to a repeatable sequence
[state, ifail] = g05kf(genid, subid, seed);
[state, x, ifail] = g05sf(n, a, state)
```
```

state =

17
1234
1
0
4110
11820
23399
29340
17917
13895
19930
8
0
1234
1
1
1234

x =

0.4520
2.2398
0.2930
0.2253
2.2577

ifail =

0

```