R: Normal Approximation to cumulative Hyperbolic Distribution -...

phyperApprAS152 {DPQ} | R Documentation

## Normal Approximation to cumulative Hyperbolic Distribution – AS 152

### Description

Compute the normal approximation (via `pnorm(.)` from AS 152 to the cumulative hyperbolic distribution function `phyper()`.

### Usage

    phyperApprAS152(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 of the same length (etc) as `q`.

### Note

I have Fortran (and C code translated from Fortran) which says

       ALGORITHM AS R77  APPL. STATIST. (1989), VOL.38, NO.1
       Replaces AS 59 and AS 152
       Incorporates AS R86 from vol.40(2)

### Author(s)

Martin Maechler, 19 Apr 1999

### References

Lund, Richard E. (1980) Algorithm AS 152: Cumulative Hypergeometric Probabilities. Journal of the Royal Statistical Society. Series C (Applied Statistics), 29(2), 221–223. doi: 10.2307/2986315

Shea, B. (1989) Remark AS R77: A Remark on Algorithm AS 152: Cumulative Hypergeometric Probabilities. JRSS C (Applied Statistics), 38(1), 199–204. doi: 10.2307/2347696

Berger, R. (1991) Algorithm AS R86: A Remark on Algorithm AS 152: Cumulative Hypergeometric Probabilities. JRSS C (Applied Statistics), 40(2), 374–375. doi: 10.2307/2347606

### See Also

`phyper`

### Examples

    ##---- Should be DIRECTLY executable !! ----
    ##-- ==>  Define data, use random,
    ##--	or do  help(data=index)  for the standard data sets.

    ## The function is currently defined as
    function (q, m, n, k)
    {
        kk <- n
        nn <- m
        mm <- m + n
        ll <- q
        mean <- kk * nn/mm
        sig <- sqrt(mean * (mm - nn)/mm * (mm - kk)/(mm - 1))
        pnorm(ll + 1/2, mean = mean, sd = sig)
      }

[Package DPQ version 0.5-2 Index]