Some useful NAG routines:

Discrete distributions:
Uniform distribution POINT=(easy to calculate) GEN=G05DYF
Binomial distribution POINT=G01BJF GEN=G05EDF
Geometric distribution POINT= GEN=
Poisson distribution POINT=G01BKF GEN=G05DRF/G05ECF

Continuous distributions:
Uniform distribution DENS=(easy to calculate) GEN=G05FAF
Normal distribution DENS= GEN=G05FDF
Multinomial distribution DENS= GEN=
Exponential distribution DENS= GEN=G05FBF
Binormal distribution DENS= GEN=
Lognormal distribution DENS= GEN=G05DEF
Gamma distribution DENS= GEN=G05FFF
Beta distribution DENS=G05FEF
Dirichlet distribution DENS= GEN=

POINT=which subroutine computes the point probablity function
DENS=which subroutine computes the density function
GEN=which subroutine generates random numbers


G01 – Simple Calculations on Statistical Data

G01BJF Binomial distribution function
- G01BJF returns the lower tail, upper tail and point probabilities associated with a Binomial distribution.

SUBROUTINE G01BJF(N,P,K,PLEK,PGTK,PEQK,IFAIL)
INTEGER N,K,IFAIL
real P,PLEK,PGTK,PEQK

Here N,P are the parameters of the binomial distribution
(N = number of tries, P = success prob)
K is the point in which we are interested,
PLEK, PGTK, PEQK are probabilities of 
X < K, X > K and X = K, respectively.


G01BKF Poisson distribution function 
- G01BKF returns the lower tail, upper tail and point probabilities associated with a Poisson distribution.

SUBROUTINE G01BKF(RLAMDA,K,PLEK,PGTK,PEQK,IFAIL)
INTEGER K,IFAIL
real RLAMDA,PLEK,PGTK,PEQK

Here RLAMDA is the parameter of the Poisson distribution P(RLAMDA)
K is the point in which we are interested,
PLEK, PGTK, PEQK are probabilities of 
X < K, X > K and X = K, respectively.


G01EEF Computes upper and lower tail probabilities and probability density function for the beta distribution 
- G01EEF computes the upper and lower tail probabilities and the probability density function of the beta
distribution with parameters a and b.

SUBROUTINE G01EEF(X,A,B,TOL,P,Q,PDF,IFAIL)
INTEGER IFAIL
real X,A,B,TOL,P,Q,PDF

Here A and B are the parameters of the distribution Beta(A, B)
TOL is the tolerance for error; the smallest number that must be able to express
P and Q are the probabilities
P(B =< X) and P(B >= X), respectively.
PDF is the probability density function Beta(X: A, B)



G01EFF Computes probabilities for the gamma distribution 
- G01EFF returns the lower or upper tail probability of the gamma distribution, with parameters a and b, via
the routine name.
- Note: No density function included!

real FUNCTION G01EFF(TAIL,G,A,B,IFAIL)
INTEGER IFAIL
real G,A,B
CHARACTER *1 TAIL



G05LAF(Mark 20) Generates a vector of random numbers from a Normal distribution, seeds and generator number passed explicitly 
- G05LAF generates a vector of pseudo-random numbers taken from a Normal (Gaussian) distribution with
mean XMU and variance VAR. 

SUBROUTINE G05LAF(XMU,VAR,N,X,IGEN,ISEED,IFAIL)
INTEGER N,IGEN,ISEED(4),IFAIL
real XMU,VAR,X(*)

G05LEF(Mark 20) Generates a vector of random numbers from a beta distribution, seeds and generator number passed explicitly  


G05DBF Pseudo-random real numbers, (negative) exponential distribution 
G05DEF Pseudo-random real numbers, log-normal distribution 
G05EBF Set up reference vector for generating pseudo-random integers, uniform distribution