ProbYX (version 1.1-0.1)

MLEs: Maximum likelihood estimates of the stress-strength model R = P(Y<X).

Description

Compute maximum likelihood estimates of R, considered as the parameter of interest. Maximum likelihood estimates of the nuisance parameter are also supplied.

Usage

MLEs(ydat, xdat, distr)

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.

Value

Vector of estimetes of the nuisance parameters and the R quantity (parameter of interest), respectively.

Details

The two independent random variables Y and X with given distribution distr are measurements of a certain characteristics on 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.

References

Kotz S, Lumelskii Y, Pensky M. (2003). The Stress-Strength Model and its Generalizations. Theory and Applications. World Scientific, Singapore.

See Also

loglik, Prob

Examples

# NOT RUN {
	# 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)      
    # vector of MLEs for the nuisance parameters and the quantity R
    MLEs(Y, X, "norm_DV")  
# }