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  1. "File PROBABIL.MTH, copyright (c) 1990-2000 by Texas Instruments Incorporated"
  2.  
  3. POCHHAMMER(a,x):=PERM(x+a-1,x)
  4.  
  5. DIGAMMA_PSI(z):=LN(z)-1/(2*z)-2*INT(t_/((t_^2+z^2)*(#e^(2*pi*t_)-1)),t_,0,inf)
  6.  
  7. POLYGAMMA(n,z):=IF(n=-1,LN(GAMMA(z)),IF(n=0,DIGAMMA(z),(-1)^(n+1)*n!*ZETA(n+1,~
  8. z)))
  9.  
  10. INCOMPLETE_GAMMA(z,w):=1/GAMMA(z)*(w^z/z+INT((#e^(-t_)-1)*t_^(z-1),t_,0,w))
  11.  
  12. INCOMPLETE_GAMMA_SERIES(z,w,m):=#e^(-w)*w^z*SUM(w^(m-n_)/GAMMA(z+m-n_+1),n_,0,~
  13. m)
  14.  
  15. EULER_BETA(z,w):=GAMMA(z)*GAMMA(w)/GAMMA(z+w)
  16.  
  17. INCOMPLETE_BETA(x,z,w):=(x^z/z+(1-(1-x)^w)/w+INT(t_^(z-1)*((1-t_)^(w-1)-1)-(1-~
  18. t_)^(w-1),t_,0,x))/EULER_BETA(z,w)
  19.  
  20. POISSON_DENSITY(k,t):=#e^(-t)*t^k/k!
  21.  
  22. POISSON_DISTRIBUTION(k,t):=SUM(POISSON_DENSITY(m_,t),m_,0,k)
  23.  
  24. BINOMIAL_DENSITY(k,n,p):=COMB(n,k)*p^k*(1-p)^(n-k)
  25.  
  26. BINOMIAL_DISTRIBUTION(k,n,p):=SUM(BINOMIAL_DENSITY(m_,n,p),m_,0,MIN(k,n))
  27.  
  28. HYPERGEOMETRIC_DENSITY(k,n,m,j):=COMB(m,k)*COMB(j-m,n-k)/COMB(j,n)
  29.  
  30. HYPERGEOMETRIC_DISTRIBUTION(k,n,m,j):=SUM(HYPERGEOMETRIC_DENSITY(l_,n,m,j),l_,~
  31. MAX(0,n-j+m),MIN(k,n,m))
  32.  
  33. STUDENT(t,v):=1-INCOMPLETE_BETA(v/(v+t^2),v/2,1/2)
  34.  
  35. F_DISTRIBUTION(f_,v1,v2):=INCOMPLETE_BETA(v2/(v2+v1*f_),v2/2,v1/2)
  36.  
  37. CHI_SQUARE(x2,v):=INCOMPLETE_GAMMA(v/2,x2/2)
  38.