prob

# Module Prob

Ignacy Misztal and Deukhwan Lee, University of Georgia
04/29/99-04/19/2001

Module Prob is a collection of random number generators / probabilities / truncated distributions useful for Gibbs sampling and for threshold models. The module uses features of Fortran 90 to simplify programnming and high-level optimization to reduce running time, with simplicity being as important as efficiency. To understand the module fully, please read the documentation on SPARSEM and on BLUPF90.

Module prob uses high-quality generators from public domain package RANLIB for random number generators. Some low level code is from Luis Varona.

### Subroutines/functions

call set_seed(n)
Sets seed for random number generator to integer n. If this subroutine is not called, the seed will be selected by the system.

x=gen_uniform(a,b)
a,b - both real (r*) or both integers or both missing.
If a,b are missing, generates samples from uniform(0,1) distribution
If a,b are real (r8), generates samples from uniform(a,b) distribution
If a,b are integers, generates random integer between a and b

x=gen_normal(mean,var)
mean - (r8) scalar or vector
var - (r8) scalar or square matrix
x - (r8) scalar or square matrix

Generates x=N(mean,Var) when mean and var are scalars, or x=MVN(mean,Var) when mean is a vector and Var is a matrix. Arguments mean and var are optional. If they are missing, sampling is from N(0,1)

x=gen_invwishart(inv_q_form,df)
inv_q_form - (r8) scalar or square matrix containing inverse of quadratic form
df - an integer containing degrees of freedom

Generates samples from inverted chi square or inverted Wishart distributions.

y=normal(x)
x - real(r8) scalar
y - real (r8) contains density(X) for N(0,1)

y=normal_cdf(x)
x - real (r8) scalar
y - real (r8) cumulative distribution function for N(0,1)

y=normal_invcdf(x)
x - real (r8) scalar in the range of <0,1>
y - real (r8) as in: x=normal_cdf(y)

y=generate_trunc_normal(a,b,mean,var)
y - real (r8) scalar or vector
a,b - real (r8) lower and upper bound of random samples
mean - real(r8) scalar or vectors of mean, optional if scalar
var - real(r8) variance or covariance matrix, optional if scalar

If mean and var are missing, generates random samples from N(0,1) distribution truncated to interval <a,b>.

If mean and var are scalars, generates random samples from N(mean,var) distribution truncated to interval <a,b>.

If mean is a vector and var is a matrix, generates random samples from MVN(mean,var) distribution with first dimension truncated to interval <a,b>.

#### Other functions/subroutines

New functions/subroutines are added to Module prob periodically. Please see program prob.f90 for details.