Evaluates the incomplete beta function.
function betainc ( x : numeric, a : numeric, b : numeric ) return_val [dimsizes(x)] : typeof(x)
upper limit of integration. x may be of any dimensionality. x must be in (0,1) inclusive and can only be float or double.
first beta distribution parameter; must be > 0.0. It must be the same dimensionality as x.b
second beta distribution parameter; must be > 0.0. It must be the same dimensionality as x.
The variable returned will be the same type and dimensionality as x.
betainc calculates the incomplete beta function. The incomplete beta function ratio is the probability that a random variable from a beta distribution having parameters a and b will be less than or equal to x. The code used is from SLATEC (http://www.netlib.org/slatec/fnlib/). This returns the same answers as the Numerical Recipes [Cambridge Univ. Press, 1986] function betai.
This function is often used to determine probabilities.
Note: in NCL version 4.3.1, this function was updated to handle missing values. If any missing values are inputted, the output array will contain missing values in the same locations.
a = 0.5 b = 5.0 x = 0.2 alpha = betainc(x,a,b) print("alpha(x,a,b)="+alpha) x = 0.5 alpha = betainc(x,a,b) print("alpha(x,a,b)="+alpha)The result is:
alpha(x,a,b)= 0.85507 alpha(x,a,b)= 0.98988Example 2 - The betainc can be used as a p-Value calculator for the Student t-test. Let's say a calculation has been made where the degrees-of-freedom (df=20) and a Student-t value of 2.08 has been determined. A probability level may be determined via:
df = 20 tval = 2.08 prob = betainc( df/(df+tval^2), df/2.0, 0.5) print ("prob="+prob)The result is prob = 0.0506. This is a two-tailed probability. The one-tailed probability is 0.5*prob = 0.0253,
For plotting, users often prefer to plot the quantity:
prob = (1.-betainc(x,a,b))*100. ; probability in %