lbeta
Beta Function and its Logarithm

### Description

Calculates the beta function or its logarithm.

### Usage

    beta(a, b)
    lbeta(a, b)

### Arguments

a | A numeric vector. The values should be non-negative.
b | A numeric vector. The values should be non-negative.

### Details

beta(a,b) can be defined mathematically as gamma(a)*gamma(b)/gamma(a+b). This version is defined only for non-negative real a and b. For large a and b, the mathematically correct value of beta(a,b) will be smaller than the smallest positive floating point number so this approximation will return 0. Use lbeta(a,b) to avoid this underflow problem.
beta(a,b) is computed using the Boost library. lbeta(a,b) is computed using Fullerton's (1977) code from http://netlib.org/fn.
Value
beta(a,b) returns an approximation to the beta function and lbeta(a,b) returns an approximation to its natural logarithm. They both return NaN for negative arguments and give an error if an argument is complex.
See Also
See Beta for functions related to the beta distribution. gamma and lgamma compute the gamma function and its logarithm.
Examples

    beta(10, 3) # 2/(10*(10+1)*(10+2))
    lbeta(10, 3) # its logarithm
    beta(1000, c(999, 1000)) # underflows to 0
    lbeta(1000, c(999, 1000)) # large negative logarithms

Package base version 6.1.5-18
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