minxent (version 0.01)

minxent.single: Minimum Cross Entropy Distribution under One Constraint

Description

minxent.single estimates the Minimum Cross Entropy Distribution (MinxEnt) under a single constraint for corresponding observed probabilities by using Kullback minimum cross entropy principle.

Usage

"minxent"(q, G, eta, lambda)

Arguments

q

a priori distribution.

G

matrix of moment vector function.

eta

vector of one moment constraint.

lambda

initial point for langrangian multiplier.

Value

returns an estimate of Lagrange multipliers and minimum cross entropy distribution under single constraint which is specified by user.

Details

If "minxent" is obtained under single constraint arising from the knowledge of the mean of the system and taking a priori distribution to be a uniform distribution then this distribution is equivalent to Maxwell-Boltzmann distribution which has importance in statistical mechanics (Kapur&Kesavan, 1992). One can also use different moment constraint and obtain different MinxEnt distributions.

References

Kapur, J.N. and Kesavan, H.K.(1992), Entropy Optimization Principle with Applications, Academic Pres.

See Also

minxent.multiple

Examples

q <- c(0.05,0.10,0.15,0.20,0.22,0.28) # a priori distribution
G <- matrix(c(rep(1,6),1:6),byrow=TRUE,nrow=2) # matrix of moment vector function of observed data
eta <- c(1,4.5) # vector of moment constraints
minxent.single(q=q,G=G,eta=eta,c(0)) # estimate of lagrangian multipliers and Kullback minimimum cross entropy distribution