g05th generates a vector of pseudorandom integers from the discrete negative binomial distribution with parameter $m$ and probability $p$ of success at a trial.

# Syntax

C# |
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public static void g05th( int mode, int n, int m, double p, double[] r, G05..::..G05State g05state, int[] x, out int ifail ) |

Visual Basic |
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Public Shared Sub g05th ( _ mode As Integer, _ n As Integer, _ m As Integer, _ p As Double, _ r As Double(), _ g05state As G05..::..G05State, _ x As Integer(), _ <OutAttribute> ByRef ifail As Integer _ ) |

Visual C++ |
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public: static void g05th( int mode, int n, int m, double p, array<double>^ r, G05..::..G05State^ g05state, array<int>^ x, [OutAttribute] int% ifail ) |

F# |
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static member g05th : mode : int * n : int * m : int * p : float * r : float[] * g05state : G05..::..G05State * x : int[] * ifail : int byref -> unit |

#### Parameters

- mode
- Type: System..::..Int32
*On entry*: a code for selecting the operation to be performed by the method.- ${\mathbf{mode}}=0$
- Set up reference vector only.
- ${\mathbf{mode}}=1$
- Generate variates using reference vector set up in a prior call to g05th.
- ${\mathbf{mode}}=2$
- Set up reference vector and generate variates.
- ${\mathbf{mode}}=3$
- Generate variates without using the reference vector.

*Constraint*: ${\mathbf{mode}}=0$, $1$, $2$ or $3$.

- n
- Type: System..::..Int32
*On entry*: $n$, the number of pseudorandom numbers to be generated.*Constraint*: ${\mathbf{n}}\ge 0$.

- m
- Type: System..::..Int32
*On entry*: $m$, the number of failures of the distribution.*Constraint*: ${\mathbf{m}}\ge 0$.

- p
- Type: System..::..Double
*On entry*: $p$, the parameter of the negative binomial distribution representing the probability of success at a single trial.*Constraint*: $0.0\le {\mathbf{p}}<1.0$.

- r
- Type: array<System..::..Double>[]()[][]An array of size [lr]
*On entry*: if ${\mathbf{mode}}=1$, the reference vector from the previous call to g05th.If ${\mathbf{mode}}=3$, r is not referenced.*On exit*: if ${\mathbf{mode}}\ne 3$, the reference vector.

- g05state
- Type: NagLibrary..::..G05..::..G05StateAn Object of type G05.G05State.

- x
- Type: array<System..::..Int32>[]()[][]An array of size [n]
*On exit*: the $n$ pseudorandom numbers from the specified negative binomial 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

g05th generates $n$ integers ${x}_{i}$ from a discrete negative binomial distribution, where the probability of ${x}_{i}=I$ ($I$ successes before $m$ failures) is

$$P\left({x}_{i}=I\right)=\frac{\left(m+I-1\right)!}{I!\left(m-1\right)!}\times {p}^{I}\times {\left(1-p\right)}^{m}\text{, \hspace{1em}}I=0,1,\dots \text{.}$$ |

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 g05th with the same parameter value can then use this reference vector to generate further variates.

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 g05th.

# References

Knuth D E (1981)

*The Art of Computer Programming (Volume 2)*(2nd Edition) Addison–Wesley# Error Indicators and Warnings

Errors or warnings detected by the method:

- ${\mathbf{ifail}}=1$
- On entry, ${\mathbf{mode}}\ne 0$, $1$, $2$ or $3$.

- ${\mathbf{ifail}}=2$
- On entry, ${\mathbf{n}}<0$.

- ${\mathbf{ifail}}=3$
- On entry, ${\mathbf{m}}<0$.

- ${\mathbf{ifail}}=4$
On entry, ${\mathbf{p}}<0.0$, or ${\mathbf{p}}\ge 1.0$.

- ${\mathbf{ifail}}=5$
- On entry, p or m is not the same as when r was set up in a previous call to g05th with ${\mathbf{mode}}=0$ or $2$.On entry, the r vector was not initialized correctly, or has been corrupted.

- ${\mathbf{ifail}}=6$

- ${\mathbf{ifail}}=7$
On entry, state vector was not initialized or has been corrupted.

# Accuracy

Not applicable.

# Parallelism and Performance

None.

# Further Comments

None.