g05sr generates a vector of pseudorandom numbers from a von Mises distribution with concentration parameter $\kappa$.

# Syntax

C#
```public static void g05sr(
int n,
double vk,
G05..::..G05State g05state,
double[] x,
out int ifail
)```
Visual Basic
```Public Shared Sub g05sr ( _
n As Integer, _
vk As Double, _
g05state As G05..::..G05State, _
x As Double(), _
<OutAttribute> ByRef ifail As Integer _
)```
Visual C++
```public:
static void g05sr(
int n,
double vk,
G05..::..G05State^ g05state,
array<double>^ x,
[OutAttribute] int% ifail
)```
F#
```static member g05sr :
n : int *
vk : float *
g05state : G05..::..G05State *
x : float[] *
ifail : int byref -> unit
```

#### Parameters

n
Type: System..::..Int32
On entry: $n$, the number of pseudorandom numbers to be generated.
Constraint: ${\mathbf{n}}\ge 0$.
vk
Type: System..::..Double
On entry: $\kappa$, the concentration parameter of the required von Mises distribution.
Constraint: $0.0<{\mathbf{vk}}\le \sqrt{{\mathbf{x02al}}}/2.0$.
g05state
Type: NagLibrary..::..G05..::..G05State
An Object of type G05.G05State.
x
Type: array<System..::..Double>[]()[][]
An array of size [n]
On exit: the $n$ pseudorandom numbers from the specified von Mises distribution.
ifail
Type: System..::..Int32%
On exit: ${\mathbf{ifail}}={0}$ unless the method detects an error or a warning has been flagged (see [Error Indicators and Warnings]).

# Description

The von Mises distribution is a symmetric distribution used in the analysis of circular data. The PDF (probability density function) of this distribution on the circle with mean direction ${\mu }_{0}=0$ and concentration parameter $\kappa$, can be written as:
 $fθ=eκcos θ2πI0κ,$
where $\theta$ is reduced modulo $2\pi$ so that $-\pi \le \theta <\pi$ and $\kappa \ge 0$. For very small $\kappa$ the distribution is almost the uniform distribution, whereas for $\kappa \to \infty$ all the probability is concentrated at one point.
The $n$ variates, ${\theta }_{1},{\theta }_{2},\dots ,{\theta }_{n}$, are generated using an envelope rejection method with a wrapped Cauchy target distribution as proposed by Best and Fisher (1979) and described by Dagpunar (1988).
One of the initialization methods (G05KFF not in this release) (for a repeatable sequence if computed sequentially) or (G05KGF not in this release) (for a non-repeatable sequence) must be called prior to the first call to g05sr.

# References

Best D J and Fisher N I (1979) Efficient simulation of the von Mises distribution Appl. Statist. 28 152–157
Dagpunar J (1988) Principles of Random Variate Generation Oxford University Press
Mardia K V (1972) Statistics of Directional Data Academic Press

# Error Indicators and Warnings

Errors or warnings detected by the method:
${\mathbf{ifail}}=1$
On entry, ${\mathbf{n}}<0$.
${\mathbf{ifail}}=2$
 On entry, ${\mathbf{vk}}\le 0.0$, or ${\mathbf{vk}}>\sqrt{{\mathbf{x02al}}\left(\right)}/2.0$.
${\mathbf{ifail}}=3$
 On entry, state vector was not initialized or has been corrupted.
${\mathbf{ifail}}=-9000$
An error occured, see message report.
${\mathbf{ifail}}=-8000$
Negative dimension for array $〈\mathit{\text{value}}〉$
${\mathbf{ifail}}=-6000$
Invalid Parameters $〈\mathit{\text{value}}〉$

Not applicable.

# Parallelism and Performance

None.

For a given number of random variates the generation time increases slightly with increasing $\kappa$.