Prob {ProbYX}

Estimation of 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

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 \alpha that supplies the nominal level (1-\alpha) chosen for the confidence interval.

Value

PROB

Point estimate of R = P(Y<X). This value corresponds to the maximum likelihoos estimate if method "Wald" or "RP" is chosen; otherwise, when method "RPstar" is selected, estimate is obtained from the estimating equaltion r_p^* = 0.

C.Interval

Confidence interval of R at confidence level (1-\alpha).

Author(s)

Giuliana Cortese

References

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

See Also

wald, rp, rpstar

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)     
    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".