# 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

 ```1 2``` ```## 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.

Senay Asma

## References

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

`minxent.multiple`
 ```1 2 3 4``` ```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 ```