# Determination of the percentile of r and r-squared, by correlation. Now designated "Abernethy's P-value"

### Description

Dr. Abernethy has devoted several decades to promoting the percentile of r and r-squared (prr) generated by pivotal Monte Carlo analysis to represent a goodness of fit measure of high merit. In recognition of this contribution to Weibull Analysis for reliability study, Project "Abernethy Reliability Methods" is attributing Dr. Abernethy's name to this measure.

### Usage

1 | ```
AbPval(F,R2,model="weibull")
``` |

### Arguments

`F` |
The quantity of complete failure data points under consideration. |

`R2` |
The square of the correlation coefficient derived from residuals of the linear model. |

`model` |
A string defining the distribution under consideration. Only a value of "lnorm" will be treated any differently from default of "weibull". |

### Details

The value returned is derived from a correlation developed from previously run pivotal analysis with 10^8 random samples. Project "Abernethy Reliability Methods" has judged that only the prr derived from 2 parameter models to have usefullness in comparitive analysis. This is seen from the "Detect Power" presentations in Appendix D of "The New Weibull Handbook, Fifth Edition". For validity of a 3rd parameter optimization on a given model over its 2 parameter fit, only the Likelihood Ratio Test will be applied.

### Value

Returns a vector containing the Abernethy P-value and the square of CCC (for comparison with R squared).

### References

Dr. Robert B. Abernethy, (2008) "The New Weibull Handbook, Fifth Edition"

### Examples

1 | ```
AbernethyPvalue<-AbPval(50, 0.996, "lnorm")
``` |

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