ltmmCombo {ltmix}

Fit a Left-truncated mixture model (LTMM)

Description

This function fits a family of finite mixture models using every combination of the left-truncated lognormal, gamma, and weibull distributions.

Usage

ltmmCombo(
  x,
  G,
  distributions = c("lognormal", "gamma", "weibull"),
  trunc = NULL,
  EM_init_method = "emEM",
  EM_starts = 5,
  init_pars = NULL,
  init_pi = NULL,
  init_classes = NULL,
  one_group_reps = 50,
  eps = 1e-06,
  max.it = 1000,
  verbose = FALSE,
  parallel = FALSE,
  cores = NULL,
  save_each_fit = FALSE
)

Arguments

x

data vector

G

number of components

distributions

densities to combine

trunc

left truncation point (optional)

EM_init_method

initialization method for EM algorithm

EM_starts

number of random starts for initialization of EM algorithm. (only for G > 1)

init_pars

initial parameter values (list of length G)

init_pi

manually specified initial component proportions (for init_method=specified)

init_classes

manually specified initial classes. will overwrite init_pars and init_pi

one_group_reps

number of random starts for each numerical optimization in 1-component model

eps

stopping tolerance for EM algoithm

max.it

maximum number of iterations of EM algorithm

verbose

print information as fitting progresses?

parallel

fit models in parallel?

cores

number of processes used for parallel computation. if NULL detect.cores() used

save_each_fit

save each model as it is produced, in a time-stamped directory (safer)

Value

An ltmmCombo model object, with the following properties:

x

Copy of the input data

distributions

The selected distributions

combos

List of all combinations of distributions considered

all.fits

List of all ltmm fit objects

all.bic

Vector of BIC values for each model

best.bic.fit

The best ltmm fit by BIC

best.bic

The best BIC value of all fits

best.bic.combo

The combination of distributions used for the best fit by BIC

all.aic

Vector of AIC value for each model

best.aic.fit

The best ltmm fit by AIC

best.aic

The best AIC value of all fits

best.aic.combo

The combination of distributions used for the best fit by AIC

all.ll

Vector of log-likelihood value for each model

summary_table

Table summarizing the AIC, BIC, LL, and risk measures for each fitted model

References

Blostein, Martin & Miljkovic, Tatjana. (2019). On modeling left-truncated loss data using mixtures of distributions. Insurance Mathematics and Economics. 85. 35-46. 10.1016/j.insmatheco.2018.12.001.

Examples

x <- secura$Loss

fits_GL <- ltmmCombo(x, G = 2, distributions = c('gamma', 'lognormal'), trunc = 1.2e6)
summary(fits_GL)