# rp: Signed log-likelihood ratio statistic In ProbYX: Inference for the Stress-Strength Model R = P(Y<X)

## Description

Compute the 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

 `1` ```rp(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 `distr` are "exp" (default) for the one-parameter exponential, "norm_EV" and "norm_DV" for the Gaussian distribution with, respectively, equal or unequal variances assumed for the two random variables.

## Details

The two independent random variables Y and X with given distribution `distr` are measurements of the diagnostic marker on the diseased and non-diseased subjects, respectively. 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

Value of the signed log-likelihood ratio statistic r_p.

## Note

The r_p values can be also used for testing statistical hypotheses on the probability R.

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.

`wald`, `rpstar`, `MLEs`, `Prob`
 ```1 2 3 4 5 6``` ``` # 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} rp(Y, X, 0.9,"norm_DV") ```