# Modified signed log-likelihood ratio statistic

### 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

1 | ```
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 |

### 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 |

`rp_star` |
Value of the modified signed log-likelihood ratio statistic |

### 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

1 2 3 4 5 6 7 |