| Type: | Package |
| Title: | Left-Truncated Mixtures of Gamma, Weibull, and Lognormal Distributions |
| Version: | 0.2.2 |
| Author: | Martin Blostein <martin.blostein@gmail.com> and Tatjana Miljkovic <miljkot@miamioh.edu> |
| Maintainer: | Martin Blostein <martin.blostein@gmail.com> |
| Description: | Mixture modelling of one-dimensional data using combinations of left-truncated Gamma, Weibull, and Lognormal Distributions. Blostein, Martin & Miljkovic, Tatjana. (2019) <doi:10.1016/j.insmatheco.2018.12.001>. |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 7.3.1 |
| Imports: | gtools, pracma |
| Depends: | R (≥ 3.5.0) |
| NeedsCompilation: | no |
| Packaged: | 2024-02-12 03:57:26 UTC; martin |
| Repository: | CRAN |
| Date/Publication: | 2024-02-23 13:20:02 UTC |
Create an ltmm model object given data and parameters
Description
This function is useful for omparing models produced using the ltmix package to models fit using other, or for computing fit criteria and risk measures for a known set of parameters.
Usage
createLtmmObj(x, distributions, trunc, Pars, Pi, npars = NULL)
Arguments
x |
data vector |
distributions |
densities to combine |
trunc |
left truncation point (optional) |
Pars |
list of length G of parameter values |
Pi |
vector of length G of component proportions |
npars |
Can optionally be used to overwrite the number of free parameters (used in the calculation of AIC & BIC), if the model has additional constraints |
Value
An ltmm model object
ltmix: Left-Truncated Mixtures of Gamma, Weibull, and Lognormal Distributions
Description
Mixture modelling of one-dimensional data using combinations of left-truncated Gamma, Weibull, and Lognormal Distributions.
Fit a Left-truncated mixture model (LTMM)
Description
This function generates a mixture model combining left-truncated lognormal, gamma, and weibull distributions
Usage
ltmm(
x,
G,
distributions,
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
)
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? |
Value
An ltmm model object, with the following properties:
- x
Copy of the input data
- distributions
The selected distributions
- trunc
The left truncation value, if specified
- fitted_pdf
The probability density function of the fitted model
- fitted_cfd
The cumulative density function of the fitted model
- VaR
The value-at-risk of the fitted model (function with p taken as onl yargument)
- ES
The expected shortfall of the fitted model (function with p taken as onl yargument)
- G
The number of components in the model
- Pi
The estimated probabilites of component membership
- Pars
The estimated model parameters
- ll
The log-likelihood of the fitted model
- bic
The BIC of the fitted model
- aic
The AIC of the fitted model
- id
The MAP component membership for each observation
- iter
The number of iterations until convergence for the EM algorithm
- npars
The total number of model parameters for the fitted model
- ll.history
The value of log-likelihood at each iteration of the EM algorithm
Examples
x <- secura$Loss
fit <- ltmm(x, G = 2, distributions = c('gamma', 'gamma', 'weibull'), trunc = 1.2e6)
summary(fit)
plot(fit)
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)
The Secura Belgian Re Data
Description
"The Secura Belgian Re data set contains automobile claims from 1988 until 2001, which are at least as large as 1,200,000 Euros." (Beirlant, Goegebeur, Segers & Teugels, 2004).
Usage
secura
Format
An object of class data.frame with 371 rows and 2 columns.
References
Beirlant, J., Goegebeur Y., Segers, J., & Teugels, J. Statistics of extremes : theory and applications. Hoboken, NJ: Wiley, 2004. Print.