R: Pearson's incomplete Beta Approximation to the Hyperbolic...

phyperIbeta {DPQ} | R Documentation

## Pearson's incomplete Beta Approximation to the Hyperbolic Distribution

### Description

Pearson's incomplete Beta function approximation to the cumulative hyperbolic distribution function `phyper(.)`.

Note that in R, `pbeta()` provides a version of the incomplete Beta function.

### Usage

    phyperIbeta(q, m, n, k)

### Arguments

`q` | vector of quantiles representing the number of white balls drawn without replacement from an urn which contains both black and white balls.
`m` | the number of white balls in the urn.
`n` | the number of black balls in the urn.
`k` | the number of balls drawn from the urn, hence must be in 0,1,…, m+n.

### Value

a numeric vector “like” `q` with values approximately equal to `phyper(q,m,n,k)`.

### Author(s)

Martin Maechler

### References

Johnson, Kotz & Kemp (1992): (6.90), p.260 – Bol'shev (1964)

### See Also

`phyper`.

### Examples

    ## The function is currently defined as
    function (q, m, n, k)
    {
        Np <- m
        N <- n + m
        n <- k
        x <- q
        p <- Np/N
        np <- n * p
        xi <- (n + Np - 1 - 2 * np)/(N - 2)
        d.c <- (N - n) * (1 - p) + np - 1
        cc <- n * (n - 1) * p * (Np - 1)/((N - 1) * d.c)
        lam <- (N - 2)^2 * np * (N - n) * (1 - p)/((N - 1) * d.c *
            (n + Np - 1 - 2 * np))
        pbeta(1 - xi, lam - x + cc, x - cc + 1)
      }

[Package DPQ version 0.5-2 Index]