code: def lbetai(a,b,x):
      
      if (x<0.0 or x>1.0):
          raise ValueError('Bad x in lbetai')
      if (x==0.0 or x==1.0):
          bt = 0.0
      else:
          bt = math.exp(gammln(a+b)-gammln(a)-gammln(b)+a*math.log(x)+b*
                        math.log(1.0-x))
      if (x<(a+1.0)/(a+b+2.0)):
          return bt*betacf(a,b,x)/float(a)
      else:
          return 1.0-bt*betacf(b,a,1.0-x)/float(b)
docs: Returns the incomplete beta function:
  
      I-sub-x(a,b) = 1/B(a,b)*(Integral(0,x) of t^(a-1)(1-t)^(b-1) dt)
  
  where a,b>0 and B(a,b) = G(a)*G(b)/(G(a+b)) where G(a) is the gamma
  function of a.  The continued fraction formulation is implemented here,
  using the betacf function.  (Adapted from: Numerical Recipies in C.)
  
  Usage:   lbetai(a,b,x)