AbPval: Determination of the percentile of r and r-squared, by...

In WeibullR: Weibull Analysis for Reliability Engineering

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

Description

The percentile of r and r-squared (prr) generated by pivotal Monte Carlo analysis has been promoted as a goodness of fit measure by Robert B. Abernethy.

Usage

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 entry of "lnorm", or "lognormal" will alter the default of "weibull".

Details

The value returned is derived from a correlation developed from previously run pivotal analysis with 10^8 random samples. Only the prr derived from 2 parameter models is judged to have usefullness in comparitive analysis. For validity of a 3rd parameter optimization on a given model over its 2 parameter fit, only the Likelihood Ratio Test should be considered.

Value

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

References

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

Wes Fulton, (2005) "Improved Goodness of Fit: P-value of the Correlation Coefficient"

Chi-Chao Lui, (1997) "A Comparison Between The Weibull And Lognormal Models Used To Analyse Reliability Data" (dissertation from University of Nottingham)

Examples

AbernethyPvalue<-AbPval(50, 0.996, "lnorm")

WeibullR documentation built on June 26, 2022, 1:06 a.m.