gkf {StressStrength}

Numerical solution for an equation involving noncentral T cdf

Description

It provides the solution of the equation F_t(q;df,x)=p, where F_t is the cdf (calculated in q) of a non-central Student r.v. with df degrees of freedom and unkwon noncentrality parameter x. In R code, gkf provides the solution of pt(q,df,x)=p.

Usage

gkf(p, q, df, eps = 1e-05)

Arguments

p

a probability

q

a real value

df

degrees of freedom of noncentral T

eps

tolerance

Details

This function is used for building Guo-Krishnamoorthy confidence intervals for R

Value

the noncentrality parameter x satisfying the equation F_t(q;df,x)=p

Author(s)

Alessandro Barbiero, Riccardo Inchingolo

References

Guo H, Krishnamoorthy K (2004) New approximate inferential methods for the reliability parameter in a stress-strength model: The normal case. Commun Stat Theory Methods 33:1715-1731

See Also

estSSR

Examples

p<-0.95
q<-5
df<-12
ncp<-gkf(p, q, df)
ncp
# check if the result is correct
pt(q, df, ncp)
# OK
# changing the tolerance
ncp<-gkf(p, q, df, eps=1e-10)
ncp
pt(q, df, ncp)