exp1st {EQUIVNONINF}R Documentation

Critical constants and power against the null alternative of the UMP test for equivalence of the hazard rate of a single exponential distribution to some given reference value

Description

The function computes the critical constants defining the uniformly most powerful test for the problem σ ≤ 1/(1 + \varepsilon) or σ≥ (1 + \varepsilon) versus 1/(1 + \varepsilon) < σ < (1 + \varepsilon), with σ denoting the scale parameter [\equiv reciprocal hazard rate] of an exponential distribution.

Usage

exp1st(alpha,tol,itmax,n,eps) 

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

n

sample size

eps

margin determining the hypothetical equivalence range symmetrically on the log-scale

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

n

sample size

eps

margin determining the hypothetical equivalence range symmetrically on the log-scale

IT

number of iteration steps performed until reaching the stopping criterion corresponding to TOL

C1

left-hand limit of the critical interval for T =∑_{i=1}^n X_i

C2

right-hand limit of the critical interval for T =∑_{i=1}^n X_i

ERR1

deviation of the rejection probability from α under σ = 1/(1 + \varepsilon)

POW0

power of the randomized UMP test against the alternative σ = 1

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. 4.2.

Examples

exp1st(0.05,1.0e-10,100,80,0.3)

[Package EQUIVNONINF version 1.0.2 Index]