REBayes: Weibullmix – R documentation

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REBayes

Weibullmix

NPMLE for Weibull Mixtures

Description

Kiefer-Wolfowitz NPMLE for Weibull Mixtures of scale parameter

Usage

Weibullmix(x, v = 300, u = 300, alpha, lambda = 1, hist = FALSE,
  weights = NULL, ...)

Arguments

`x`	Survival times
`v`	Grid values for mixing distribution
`u`	Grid values for histogram bins, if needed
`alpha`	Shape parameter for Weibull distribution
`lambda`	Scale parameter for Weibull Distribution; must either have length 1, or length equal to `length(x)` the latter case accommodates the possibility of a linear predictor
`hist`	If TRUE aggregate to histogram counts
`weights`	replicate weights for x obervations, should sum to 1
`...`	optional parameters passed to KWDual to control optimization

Details

Kiefer Wolfowitz NPMLE density estimation for Weibull scale mixtures. The histogram option is intended for relatively large problems, say n > 1000, where reducing the sample size dimension is desirable. By default the grid for the binning is equally spaced on the support of the data. Parameterization: f(t|alpha, lambda) = alpha * exp(v) * (lambda * t )^(alpha-1) * exp(-(lambda * t)^alpha * exp(v)); shape = alpha; scale = lambda^(-1) * (exp(v))^(-1/alpha)

Value

An object of class density with components

`x`	points of evaluation on the domain of the density
`y`	estimated function values at the points x of the mixing density
`logLik`	Log likelihood value at the proposed solution
`dy`	Bayes Rule estimates of mixing parameter
`status`	exit code from the optimizer

Author(s)

Roger Koenker and Jiaying Gu

References

Kiefer, J. and J. Wolfowitz Consistency of the Maximum Likelihood Estimator in the Presence of Infinitely Many Incidental Parameters Ann. Math. Statist. Volume 27, Number 4 (1956), 887-906.

Koenker, R. and J. Gu, (2017) REBayes: An R Package for Empirical Bayes Mixture Methods, Journal of Statistical Software, 82, 1–26.