g01eef

g01eef © Numerical Algorithms Group, 2002.

Purpose

G01EEF Computes upper and lower tail probabilities and probability density function for the beta distribution

Synopsis

[p,q,pdf,ifail] = g01eef(x,a,b<,tol,ifail>)

Description

 
 The probability density function of the beta distribution with 
 parameters a and b is:
 
                          (Gamma)(a+b)     a-1     b-1
            f(B:a,b)= --------------------B   (1-B)   ,
                      (Gamma)(a)(Gamma)(b)            
 
 0<=B<=1 ; a,b>0.
 
 The lower tail probability, P(B<=(beta):a,b) is defined by
 
 
                                        (beta)              
                       (Gamma)(a+b)     /      a-1     b-1  
 P(B<=(beta):a,b)= -------------------- |     B   (1-B)   dB
                   (Gamma)(a)(Gamma)(b) /                   
                                        0                   
         
         
 =I      (a,b),
   (beta)
         
 
 0<=(beta)<=1 ; a,b>0.
 
 The function I (a,b) is also known as the incomplete beta 
               x                                          
 function.

Parameters

g01eef

Required Input Arguments:

x                                     real
a                                     real
b                                     real

Optional Input Arguments:                       <Default>

tol                                   real     10*eps
ifail                                 integer  -1

Output Arguments:

p                                     real
q                                     real
pdf                                   real
ifail                                 integer