Beta {stats} | R Documentation |

Density, distribution function, quantile function and random
generation for the Beta distribution with parameters `shape1`

and
`shape2`

(and optional non-centrality parameter `ncp`

).

dbeta(x, shape1, shape2, ncp=0, log = FALSE) pbeta(q, shape1, shape2, ncp=0, lower.tail = TRUE, log.p = FALSE) qbeta(p, shape1, shape2, lower.tail = TRUE, log.p = FALSE) rbeta(n, shape1, shape2)

`x, q` |
vector of quantiles. |

`p` |
vector of probabilities. |

`n` |
number of observations. If `length(n) > 1` , the length
is taken to be the number required. |

`shape1, shape2` |
positive parameters of the Beta distribution. |

`ncp` |
non-centrality parameter. |

`log, log.p` |
logical; if TRUE, probabilities p are given as log(p). |

`lower.tail` |
logical; if TRUE (default), probabilities are
P[X <= x], otherwise, P[X > x]. |

The Beta distribution with parameters `shape1`

*= a* and
`shape2`

*= b* has density

*Gamma(a+b)/(Gamma(a)Gamma(b))x^(a-1)(1-x)^(b-1)*

for *a > 0*, *b > 0* and *0 <= x <= 1*
where the boundary values at *x=0* or *x=1* are defined as
by continuity (as limits).

The mean is *a/(a+b)* and the variance is *ab/((a+b)^2 (a+b+1))*.

`pbeta`

is closely related to the incomplete beta function. As
defined by Abramowitz and Stegun 6.6.1

*B_x(a,b) =
integral_0^x t^(a-1) (1-t)^(b-1) dt,*

and 6.6.2 *I_x(a,b) = B_x(a,b) / B(a,b)* where
*B(a,b) = B_1(a,b)* is the Beta function (`beta`

).

*I_x(a,b)* is `pbeta(x,a,b)`

.

`dbeta`

gives the density, `pbeta`

the distribution
function, `qbeta`

the quantile function, and `rbeta`

generates random deviates.

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
*The New S Language*.
Wadsworth & Brooks/Cole.

Abramowitz, M. and Stegun, I. A. (1972)
*Handbook of Mathematical Functions.* New York: Dover.
Chapter 6: Gamma and Related Functions.

`beta`

for the Beta function, and `dgamma`

for
the Gamma distribution.

x <- seq(0, 1, length=21) dbeta(x, 1, 1) pbeta(x, 1, 1)

[Package *stats* version 2.2.1 Index]