NAG Library Manual, Mark 27.3

Interfaces: FL CL CPP AD

NAG CL Interface Introduction

G01 (Stat) Chapter Contents

G01 (Stat) Chapter Introduction

g01eu: FL CL CPP AD

NAG CL Interface
g01euc (prob_vavilov)

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NAG Library Manual, Mark 27.3

Interfaces: FL CL CPP AD

NAG CL Interface Introduction

G01 (Stat) Chapter Contents

G01 (Stat) Chapter Introduction

g01eu: FL CL CPP AD

▸▿ Contents

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

8 Parallelism and Performance

9 Further Comments

▸▿ 10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

© The Numerical Algorithms Group Ltd. 2021

CL Name Style:
Short (a00aac)
Long (impl_details)
Full (nag_info_impl_details)

1 Purpose

g01euc returns the value of the Vavilov distribution function

Φ_{V} (λ; κ, β^{2})

.

It is intended to be used after a call to g01zuc.

2 Specification

#include <nag.h>

double

g01euc (double x, const double comm_arr[])

The function may be called by the names: g01euc, nag_stat_prob_vavilov or nag_prob_vavilov.

3 Description

g01euc evaluates an approximation to the Vavilov distribution function

Φ_{V} (λ; κ, β^{2})

given by

Φ_{V} (λ; κ, β^{2}) = \int_{- \infty}^{λ} ϕ_{V} (λ; κ, β^{2}) d λ,

where

ϕ (λ)

is described in g01muc. The method used is based on Fourier expansions. Further details can be found in Schorr (1974).

4 References

Schorr B (1974) Programs for the Landau and the Vavilov distributions and the corresponding random numbers Comp. Phys. Comm. 7 215–224

5 Arguments

1: $x$ – double Input: On entry: the argument $λ$ of the function.
2: $comm_arr [322]$ – const double Communication Array: On entry: this must be the same argument comm_arr as returned by a previous call to g01zuc.

6 Error Indicators and Warnings

None.

7 Accuracy

At least five significant digits are usually correct.

8 Parallelism and Performance

g01euc is not threaded in any implementation.

9 Further Comments

g01euc can be called repeatedly with different values of

λ

provided that the values of

κ

and

β^{2}

remain unchanged between calls. Otherwise, g01zuc must be called again.

10 Example

This example evaluates

Φ_{V} (λ; κ, β^{2})

at

λ = 0.1

,

κ = 2.5

and

β^{2} = 0.7

, and prints the results.

10.1 Program Text

Program Text (g01euce.c)

10.2 Program Data

Program Data (g01euce.d)

10.3 Program Results

Program Results (g01euce.r)

NAG Library Manual, Mark 27.3

Interfaces: FL CL CPP AD

NAG CL Interface Introduction

G01 (Stat) Chapter Contents

G01 (Stat) Chapter Introduction

g01eu: FL CL CPP AD

© The Numerical Algorithms Group Ltd. 2021