# asypow.noncent: Asymptotic Noncentrality Parameter In asypow: Calculate Power Utilizing Asymptotic Likelihood Ratio Methods

## Description

Given an information matrix, alternative hypothesis parameter values, and constraints that create the null hypothesis from the alternative, calculates noncentrality parameter, degrees of freedom and parameter value estimates under the null hypothesis.

## Usage

 ```1 2``` ``` asypow.noncent(theta.ha, info.mat, constraints, nobs.ell=1, get.ho=TRUE) ```

## Arguments

 `theta.ha` Array of parameter values under the alternative hypothesis. `info.mat` The information matrix, the second derivate matrix of the expected log likelihood under the alternative hypothesis. The negative of the hessian matrix. `constraints` The constraints which set the null hypothesis from the alternative hypothesis. They are in matrix form. CONSTRAINT[,1] is 1 for setting parameter to a value 2 for equality of two parameters CONSTRAINT[,2] is case on CONSTRAINT[,1] (1) Index of parameter to set to value (2) Index of one of two parameters to be set equal CONSTRAINT[,3] is case on CONSTRAINT[,1] (1) Value to which parameter is set (2) Index of other of two parameters to be set equal `nobs.ell` The number of observations used in computing the information matrix. That is, info.mat is that for nobs.ell observations. Default is 1, which is the correct value for all of the 'info.' routines supplied here. `get.ho` If TRUE, estimates of the parameter values under the null hypothesis are calculated and returned, otherwise not. Default is TRUE.

## Value

Returns a list including

 `w` The noncentrality parameter for 1 observation. `df` The degrees of freedom of the test `theta.ho` Estimates of the parameter values under the null hypothesis.

## References

Cox, D.R. and Hinkley, D.V. (1974). Theoretical Statistics Chapman and Hall, London.

`asypow.n`, `asypow.sig`, `asypow.power`
 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```# Three Sample Poisson Example : # Three independent Poisson processes produce events at # mean rates of 1, 2 and 3 per day. # Find the information matrix pois.mean <- c(1,2,3) info.pois <- info.poisson.kgroup(pois.mean,group.size=3) # Create the constraints matrix constraints <- matrix(c(2,1,2,2,2,3),ncol=3,byrow=TRUE) # Calculate noncentrality parameter, degrees of freedom and parameter # value estimates under the null hypothesis for the test. poisson.object <- asypow.noncent(pois.mean,info.pois,constraints) ```