rpstar | R Documentation |
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.
rpstar(ydat, xdat, psi, distr = "exp")
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 |
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
.
rp |
Value of the signed log-likelihood ratio statistic r_p. |
rp_star |
Value of the modified signed log-likelihood ratio statistic r_p^*. |
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.
Giuliana Cortese
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.
wald
, rp
, MLEs
, Prob
# 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".
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