Determination of the percentile of r and r-squared, by correlation. Now designated "Abernethy's P-value"
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.
The quantity of complete failure data points under consideration.
The square of the correlation coefficient derived from residuals of the linear model.
A string defining the distribution under consideration. Only a value of "lnorm" will be treated any differently from default of "weibull".
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.
Returns a vector containing the Abernethy P-value and the square of CCC (for comparison with R squared).
Dr. Robert B. Abernethy, (2008) "The New Weibull Handbook, Fifth Edition"
AbernethyPvalue<-AbPval(50, 0.996, "lnorm")