# Estimation of the stress-strength model R = P(Y
### 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<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-α)*.

### 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

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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 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 |

`method` |
character string specifying the methodological approach used for inference (confidence intervals and point estimates) on the AUC.
The argument |

`level` |
it is the |

### Value

`PROB` |
Point estimate of |

`C.Interval` |
Confidence interval of R at confidence level |

### 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

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".
``` |

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