# Inference on the stress-strength model R = P(Y
### Description

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

### Details

Package: ProbYX
Type: Package
Version: 1.1
Date: 2012-03-20
License: GPL-2
LazyLoad: yes

The package can be used for computing accurate confidence intervals and
point estimates for the stress-strength (reliability) model R = P(Y<X); maximum likelihood estimates, Wald statistic, signed
log-likelihood ratio statistic and its modified version ca be computed.

The main function is `Prob`

, which evaluates confidence intervals and
point estimates under different approaches and parametric assumptions.

### Author(s)

Giuliana Cortese

Maintainer: Giuliana Cortese <gcortese@stat.unipd.it>

### References

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

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

### Examples

1
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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)
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".

### Description

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

### Details

Package: | ProbYX |

Type: | Package |

Version: | 1.1 |

Date: | 2012-03-20 |

License: | GPL-2 |

LazyLoad: | yes |

The package can be used for computing accurate confidence intervals and
point estimates for the stress-strength (reliability) model R = P(Y<X); maximum likelihood estimates, Wald statistic, signed
log-likelihood ratio statistic and its modified version ca be computed.

The main function is `Prob`

, which evaluates confidence intervals and
point estimates under different approaches and parametric assumptions.

### Author(s)

Giuliana Cortese

Maintainer: Giuliana Cortese <gcortese@stat.unipd.it>

### References

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

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

### Examples

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".
``` |