# pbetaRv1

##### Pure R Implementation of Old pbeta()

`pbetaRv1()`

is an implementation of the original
(“version 1” `pbeta()`

function in R (versions <=
2.2.x), before we started using TOMS 708 `bratio()`

instead, see
that help page also for references.

`pbetaRv1()`

is basically a manual translation from C to R of the
underlying `pbeta_raw()`

C function, see in R's source tree at
https://svn.r-project.org/R/branches/R-2-2-patches/src/nmath/pbeta.c

For consistency within R, we are using R's argument names
`(q, shape1, shape2)`

instead of C code's
`(x, pin, qin )`

.

It is only for the *central* beta distribution.

- Keywords
- distribution, math

##### Usage

```
pbetaRv1(q, shape1, shape2, lower.tail = TRUE,
eps = 0.5 * .Machine$double.eps,
sml = .Machine$double.xmin,
verbose = 0)
```

##### Arguments

- q, shape1, shape2
non-negative numbers, q in \([0,1]\), see

`pbeta`

.- lower.tail
indicating if \(F(q; *)\) should be returned or the upper tail probability \(1 - F(q)\).

- eps
the tolerance used to determine congerence.

`eps`

has been hard coded in C code to`0.5 * .Machine$double.eps`

which is equal to \(2^{-53}\) or`1.110223e-16`

.- sml
the smallest positive number on the typical platform. The default

`.Machine$double.xmin`

is hard coded in the C code (as`DBL_MIN`

), and this is equal to \(2^{-1022}\) or`2.225074e-308`

on all current platforms.- verbose
integer indicating the amount of verbosity of diagnostic output,

`0`

means no output,`1`

more, etc.

##### Value

a number.

##### Note

The C code contains *
This routine is a translation into C of a Fortran subroutine
by W. Fullerton of Los Alamos Scientific Laboratory.*

##### References

(From the C code:)

Nancy E. Bosten and E.L. Battiste (1974).
Remark on Algorithm 179 (S14): Incomplete Beta Ratio.
*Communications of the ACM*, **17**(3), 156--7.

##### See Also

##### Examples

```
# NOT RUN {
all.equal(pbetaRv1(1/4, 2, 3),
pbeta (1/4, 2, 3))
set.seed(101)
N <- 1000
x <- sample.int(7, N, replace=TRUE) / 8
a <- rlnorm(N)
b <- 5*rlnorm(N)
pbt <- pbeta(x, a, b)
for(i in 1:N) {
stopifnot(all.equal(pbetaRv1(x[i], a[i], b[i]), pbt[i]))
cat(".", if(i %% 20 == 0) paste0(i, "\n"))
}
# }
```

*Documentation reproduced from package DPQ, version 0.3-3, License: GPL (>= 2)*