rpstar {ProbYX} | R Documentation |
Modified signed log-likelihood ratio statistic
Description
Compute the modified signed log-likelihood ratio statistic () for a given value
of the stress strength R = P(Y<X), that is the parameter of interest,
under given parametric model assumptions.
Usage
rpstar(ydat, xdat, psi, distr = "exp")
Arguments
ydat |
data vector of the sample measurements from Y. |
xdat |
data vector of the sample measurements from X. |
psi |
scalar for the parameter of interest. It is the value of R, treated as a parameter under the parametric model construction. |
distr |
character string specifying the type of distribution assumed for Y and X.
Possible choices for |
Details
The two independent random variables Y and X with given distribution
distr
are measurements from two different populations.
For the relationship of the parameter of interest (R) and nuisance parameters with
the original parameters of distr
, look at the details in loglik
.
Value
rp |
Value of the signed log-likelihood ratio statistic |
rp_star |
Value of the modified signed log-likelihood ratio statistic |
Note
The statistic is a modified version of
which provides
more statistically accurate estimates.
The
values can be also used for testing statistical hypotheses on the probability R.
Author(s)
Giuliana Cortese
References
Cortese G., Ventura L. (2013). Accurate higher-order likelihood inference on P(Y<X). Computational Statistics, 28:1035-1059.
Severini TA. (2000). Likelihood Methods in Statistics. Oxford University Press, New York.
Brazzale AR., Davison AC., Reid N. (2007). Applied Asymptotics. Case-Studies in Small Sample Statistics. Cambridge University Press, Cambridge.
See Also
Examples
# data from the first population
Y <- rnorm(15, mean=5, sd=1)
# data from the second population
X <- rnorm(10, mean=7, sd=1.5)
# value of \eqn{r_p^*} for \code{psi=0.9}
rpstar(Y, X, 0.9,"norm_DV")
# method has be set equal to "RPstar".