weibulltools (version 1.0.1)

mixture_em_cpp: EM-Algorithm using Newton-Raphson Method

Description

This method uses the EM-Algorithm to estimate the parameters of a univariate mixture model. Until now, the mixture model can consist of k two-parametric Weibull distributions. The Weibull distributions are parameterized with scale \(\eta\) and shape \(\beta\). In M-step these parameters are estimated using Newton-Raphson. This function is implemented in c++ and is called in function mixmod_em.

Usage

mixture_em_cpp(x, event, post, distribution = "weibull", k = 2L,
  method = "EM", n_iter = 100L, conv_limit = 1e-06)

Arguments

x

a numeric vector which consists of lifetime data. Lifetime data could be every characteristic influencing the reliability of a product, e.g. operating time (days/months in service), mileage (km, miles), load cycles.

event

a vector of binary data (0 or 1) indicating whether unit i is a right censored observation (= 0) or a failure (= 1).

post

a numeric matrix specifiying initial a-posteriori probabilities. The number of rows have to be in line with observations x and the number of columns must equal the mixture components k.

distribution

supposed distribution of mixture model components. The value must be "weibull". Other distributions have not been implemented yet.

k

integer of mixture components, default is 2.

method

default method is "EM". Other methods have not been implemented yet.

n_iter

integer defining the maximum number of iterations.

conv_limit

numeric value defining the convergence limit.

Value

Returns a list with the following components:

• coefficients : A matrix with estimated Weibull parameters. In the first row the estimated scale parameters \(\eta\) and in the second the estimated shape parameters \(\beta\) are provided. The first column belongs to the first mixture component and so forth.

• posteriori : A matrix with estimated a-posteriori probabilities.

• priori : A vector with estimated a-priori probabilities.

• logL : The value of the complete log-likelihood.

References

Doganaksoy, N.; Hahn, G.; Meeker, W. Q., Reliability Analysis by Failure Mode, Quality Progress, 35(6), 47-52, 2002

Examples

# NOT RUN {
# Data is taken from given reference:
hours <- c(2, 28, 67, 119, 179, 236, 282, 317, 348, 387, 3, 31, 69, 135,
          191, 241, 284, 318, 348, 392, 5, 31, 76, 144, 203, 257, 286,
          320, 350, 412, 8, 52, 78, 157, 211, 261, 298, 327, 360, 446,
          13, 53, 104, 160, 221, 264, 303, 328, 369, 21, 64, 113, 168,
          226, 278, 314, 328, 377)
state <- c(1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1,
         1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0,
         1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
         0, 1, 1, 1, 1, 1, 1)
post_dirichlet <- LearnBayes::rdirichlet(n = length(hours),
                                         par = rep(.1, 2))
mix_mod_em <- mixture_em_cpp(x = hours,
                             event = state,
                             post = post_dirichlet,
                             distribution = "weibull",
                             k = 2,
                             method = "EM",
                             n_iter = 150)

# }