MLEcontour: Likelihood Ratio Contour for Weibull and Lognormal Fitted...

In WeibullR: Weibull Analysis for Reliability Engineering

Likelihood Ratio Contour for Weibull and Lognormal Fitted Data

Description

MLEcontour This function generates points for a display of the likelihood contour at given confidence limit for the 2-parameter Weibull or lognormal distributions.

Usage

MLEcontour(x,  dist="weibull", CL=0.9,dof=1,MLLx=NULL, MLEfit=NULL,
              RadLimit=1e-5,ptDensity=120, debias="none", show=FALSE)

Arguments

x	A dataframe such as generated by mleframe with column names 'left', 'right' and optionally 'qty'. Exact failure data (occurrences) have same time entered in both 'left' and 'right' columns. Suspension data has last known life[time] entered in 'left' column and -1 entered in 'right' column. The left(early) interval bound for left-censored data must be entered as zero. (NA is not accepted).
dist	A string defining a distribution to be fit. Implemented distributions are "weibull" (default) and "lognormal".
CL	a confidence limit to be applied to the Chi square test.
dof	an integer value indicating degrees of freedom to apply to the Chi square test, which defaults to dof=1 for confidence interval bound use. Should be set to 2 for comparison of two models each with 2 parameters.
MLLx	an optional argument intended for 3p modelling so that the maximum log-likelihood from an optimized 3rd parameter fit can be used to generate subsequent contours with variation in the translation parameter.
MLEfit	an optional argument to use a fit made external to the function. Disaster awaits any mismatch between data entered and this fit. When provided, the MLEfit shall be a vector in the order of scale(or logmean), shape (or std dev) and Loglikelihood.
ptDensity	an integer value for the number of points to be plotted around the circumference of the contour.
RadLimit	a convergence limit for the contour radials based on specific units such as Eta/Eta_hat and Beta/Beta_hat.
debias	An optional string argument indicating the adjustment to be applied to the shape or standard deviation parameter of the fitted data. Recognized values are "rba", "mean", or "hrbu".
show	a logical value indicating whether a graphical output is desired (independent of wblr activity).

Details

The contour points (p1,p2) identified as satisfying the root of the equation, (log(ML(p1_hat,p2_hat))-log(RL(p1,p2)) - chisquare(CL,DF)/2=0,where ML is Maximum Likelihood for the data,and RL is Ratioed Likelihood for the data at selected points for the contour. The algorithm for this function (executed in compiled C++ code) uses a quinary search for the root optimization of each radial on a polar coordinate loop. It is believed to be unique from commercial implementations and appears to have improved stability for this notoriously challenging calculation.

Value

A dataframe of plotting points for the contour.

References

William Q. Meeker and Luis A. Escobar, (1998) "Statistical Methods for Reliability Data", Wiley-Interscience, New York

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

John I. McCool, (2012) "Using the Weibull Distribution: Reliability, Modeling and Inference"

Examples

fig3cF<-c(1500,2250,4000,4300,7000)
fig3cS<-c(1750,5000)
Contour<-MLEcontour(mleframe(fig3cF,fig3cS))

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