# Prob: Estimation of the stress-strength model R = P(Y<X) In ProbYX: Inference for the Stress-Strength Model R = P(Y<X)

## Description

Compute confidence intervals and point estimates for the probability R, under parametric model assumptions for Y and X. Y and X are two independent continuous random variable from two different populations.

## Usage

 1 Prob(ydat, xdat, distr = "exp", method = "RPstar", level = 0.05) 

## Arguments

 ydat data vector of the sample measurements from Y. xdat data vector of the sample measurements from X. 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. method character string specifying the methodological approach used for inference (confidence intervals and point estimates) on the AUC. The argument method can be set equal to "Wald", "RP" or RPstar" (default), according as inference is based on the Wald statistic, the signed log-likelihood ratio statistic (directed likelihhod, r_p) or the modified signed log-likelihood ratio statistic (modified directed likelihood, r_p^*), respectively. level it is the α that supplies the nominal level (1-α) chosen for the confidence interval.

## Value

 PROB Point estimate of R = P(Y

Giuliana Cortese

## References

Cortese G., Ventura L. (2013). Accurate higher-order likelihood inference on R=P(Y<X). Computational Statistics, 28:1035-1059.

wald, rp, rpstar
 1 2 3 4 5 6 7 8 9  # 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) level <- 0.01 ## \eqn{\alpha} level # estimate and confidence interval under the assumption of two # normal variables with different variances. Prob(Y, X, "norm_DV", "RPstar", level) # method has to be set equal to "RPstar".