censored Weibull MLE for Type I right-censored data

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Description

Calculate the censored Weibull (two parameter, shape and scale) MLE for the Type I censored data with the algorithm described in ASTM 5457(2004). Return the estimates of the shape and scale parameters. A comprehesive description of this algorithm can be found in Liu (2012).

Usage

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cenWbMLE.T1(dat, Cx=NULL, useC = FALSE, conCr = 1e-09, nIter = 1000)

Arguments

dat

A vector of the data, should not contain any negative observations, but NA is allowed. The NA's and observations larger than the censoring threshold Cx will be censored in the calculation. The algorithm will decide the original sample size (before censoring) from the length of this vector.

Cx

The censoring threshold of Type I right-censoring. If NULL, the complete (uncensored MLE) will be calculated.

useC

Default to be false and use the R routine to calculate estimates. If true, the function will use the C routine, which is much faster than the R routine, but harder for the user to identify the numerical issues (if there is any).

conCr

In terms of the relative change in the negative log-likelihood. The algorithm is viewed as converged if the relative change is smaller than conCr

nIter

The maximum numer of iterations allowed in the function.

Value

convergence

an integer indicating why the algorithm terminated

  • 0, successfully converged;

  • 1, Numerical over/under-flow, maybe the shape parameter diverges to infinity;

  • 2, Iteration limit reached;

  • 3, Shape parameter becomes negative;

  • 4, Shape parameter diverges to infinity.

estimates

Shape and scale parameter estimates

Note

Please report the numerical problems and inconvenience when using this function to the author.

Author(s)

Yang (Seagle) Liu <yang.liu@stat.ubc.ca>

References

ASTM (2004). Standard specfication for computing reference resistance of wood-based materials and structural connections for load and resistance factor design D5457. American Society for Testing Materials, Philadephia, Pa.

Liu Y. (2012). Lower Quantile Estimation of Wood Strength Data. Master Thesis, Department of Statistics, UBC. Downloadable here.

See Also

rweibull, cenWbMLE.T2, emCenWbMix.T1

Examples

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set.seed(1)
y <- sort(rweibull(100, 7, 7)) ##Generate the data
cenWbMLE.T1(y) #The MLE for the complete data
cenWbMLE.T1(y, 5) #Censor the data at 5 and calculate the censored MLE
##Or
newy <- rep(NA, 100)
newy[y<=5] <- y[y<=5] #Censor the data at 5
fit <- cenWbMLE.T1(newy, 5) #Calculate the censored MLE
qweibull(0.05, fit$estimates[1], fit$estimates[2]) 
#Calculate the 5% quantile of the fitted distribution.