# pcbinom: A continuous version of the binomial cdf In Smisc: Sego Miscellaneous

## Description

Uses the incomplete beta function to calculate a continuous version of the binomial cumulative distribution function.

## Usage

 `1` ```pcbinom(x, n, p, lower.tail = TRUE, log.p = FALSE) ```

## Arguments

 `x` Real valued vector of the number of successes. `n` Real valued vector, all elements in `[0, Inf)`, of the number of trials. `p` Real valued vector, all elements in `[0,1]`, of the probability of success. `lower.tail` logical; if `TRUE`, the probabilities are ```P[X <= x]```, otherwise, `P[X > x]`. `log.p` logical; if `TRUE`, probabilities `p` are returned as `log(p)`.

## Details

`pcbinom` is equivalent to `pbinom` for integer values of `n` and `x`.

Note that `pcbinom` does not recycle vectors in the usual fashion. Each of the arguments `x`, `n`, and `p` should have the same length, or, one or more of them can have the same length, so long as the other arguments have length 1. See examples below.

## Value

Returns a continuous version of the binomial distribution function.

## Note

This function was based on `binom.c` in the R source code.

## Author(s)

Landon Sego

`pbinom`, `pbeta`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```x <- c( 2, 3, 5, 5.2, 5) n <- c( 4, 5, 7, 7, 7.2) p <- c(0.2, 0.1, 0.8, 0.8, 0.7) pcbinom(x, n, p) pbinom(x, n, p) # These will work pcbinom(c(7.3, 7.8), 12, 0.7) pcbinom(c(7.3, 7.8), c(12,13), 0.7) pcbinom(12.1, c(14.2,14.3), 0.6) # But these won't try(pcbinom(c(7.3, 7.8), c(12, 14, 16), 0.7)) try(pcbinom(c(7.3, 7.8), c(12, 14, 16), c(0.7, 0.8))) ```