NPMLE for Weibull Mixtures

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Description

Kiefer-Wolfowitz NPMLE for Weibull Mixtures of scale parameter

Usage

1
2
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.

See Also

Gompertzmix

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