fstretch {EQUIVNONINF} R Documentation

## Critical constants and power of the UMPI (uniformly most powerful invariant) test for dispersion equivalence of two Gaussian distributions

### Description

The function computes the critical constants defining the optimal test for the problem σ^2/τ^2 ≤ \varrho_1 or σ^2/τ^2 ≥ \varrho_2 versus \varrho_1 < σ^2/τ^2 < \varrho_2, with (\varrho_1,\varrho_2) as a fixed nonempty interval around unity.

### Usage

fstretch(alpha,tol,itmax,ny1,ny2,rho1,rho2)


### Arguments

 alpha significance level tol tolerable deviation from α of the rejection probability at either boundary of the hypothetical equivalence interval itmax maximum number of iteration steps ny1 number of degrees of freedom of the estimator of σ^2 ny2 number of degrees of freedom of the estimator of τ^2 rho1 lower equivalence limit to σ^2/τ^2 rho2 upper equivalence limit to σ^2/τ^2

### Value

 alpha significance level tol tolerable deviation from α of the rejection probability at either boundary of the hypothetical equivalence interval itmax maximum number of iteration steps ny1 number of degrees of freedom of the estimator of σ^2 ny2 number of degrees of freedom of the estimator of τ^2 rho1 lower equivalence limit to σ^2/τ^2 rho2 upper equivalence limit to σ^2/τ^2 IT number of iteration steps performed until reaching the stopping criterion corresponding to TOL C1 left-hand limit of the critical interval for T = \frac{n-1}{m-1} ∑_{i=1}^m (X_i-\overline{X})^2 / ∑_{j=1}^{n-1} (Y_j-\overline{Y})^2 C2 right-hand limit of the critical interval for T = \frac{n-1}{m-1} ∑_{i=1}^m (X_i-\overline{X})^2 / ∑_{j=1}^{n-1} (Y_j-\overline{Y})^2 ERR deviation of the rejection probability from α under σ^2/τ^2 = \varrho_1 POW0 power of the UMPI test against the alternative σ^2/τ^2 = 1

### Note

If the two independent samples under analysis are from exponential rather than Gaussian distributions, the critical constants computed by means of fstretch with ν_1 = 2m, ν_2 = 2n, can be used for testing for equivalence with respect to the ratio of hazard rates. The only difference is that the ratio of sample means rather than variances has to be used as the test statistic then.

### Author(s)

Stefan Wellek <stefan.wellek@zi-mannheim.de>
Peter Ziegler <peter.ziegler@zi-mannheim.de>

### References

Wellek S: Testing statistical hypotheses of equivalence and noninferiority. Second edition. Boca Raton: Chapman & Hall/CRC Press, 2010, Par. 6.5.

### Examples

fstretch(0.05, 1.0e-10, 50,40,45,0.5625,1.7689)


[Package EQUIVNONINF version 1.0.2 Index]