Modified signed log-likelihood ratio statistic

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Description

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.

Usage

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rpstar(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 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.

Value

rp

Value of the signed log-likelihood ratio statistic r_p.

rp_star

Value of the modified signed log-likelihood ratio statistic r_p^*.

Note

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.

Author(s)

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.

See Also

wald, rp, MLEs, Prob

Examples

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	# 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".