y = beta(z,w)
y = betainc(x,a,b)
y = betaln(z,w)
y = beta(z,w)
is the beta function
or equivalently gamma(z)
*gamma(w)./gamma(z+w)
. If both z
and w
are vectors or matrices, they must be the same size.
y = betainc(x,z,w)
is the incomplete beta function
y = betaln(z,w)
is the natural logarithm of the beta function, log(beta(z,w)),
computed without computing beta(z,w)
. Since the beta
function can range over very large or very small values, its logarithm is sometimes more useful. If both z
and w
are vectors or matrices, they must be the same size.
In this case, with integer arguments,format rat
beta((0:10)',3)
ans =
1/0
1/3
1/12
1/30
1/60
1/105
1/168
1/252
1/360
1/495
1/660
is the ratio of fairly small integers and the rational format is able to recover the exact result.beta(n,3)
= (n-1)!
*2!/(n+2)!
= 2/(n
*(n+1)
*(n+2))
For x = 510
, betaln(x,x) = -708.8616
, which, on a computer with IEEE arithmetic, is slightly less than log(realmin)
. Here beta(x,x)
would underflow (or be denormal).
beta(z,w) = exp(gammaln(z)+gammaln(w)-gammaln(z+w))
betaln(z,w) = gammaln(z)+gammaln(w)-gammaln(z+w)
(c) Copyright 1994 by The MathWorks, Inc.