minxent.single: Minimum Cross Entropy Distribution under One Constraint

In minxent: Entropy Optimization Distributions

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

## S3 method for class 'single'
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.

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.

Value

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

Author(s)

Senay Asma

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

Example output

$Langrangians
[1]  0.4460205 -0.1015608

$Estimates
[1] 0.03543016 0.07843508 0.13022935 0.19220067 0.23402102 0.32968372

minxent documentation built on May 2, 2019, 5:45 a.m.