rpstar {ProbYX} | R Documentation |
Modified signed log-likelihood ratio statistic
Description
Compute the modified signed log-likelihood ratio statistic (r_p^*
) 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 r_p^*
is a modified version of r_p
which provides
more statistically accurate estimates.
The r_p^*
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".