MLEce {MLEce}

Calculating MLEces for three different distributions

Description

The closed-form estimators (MLEces) are calculated for three distributions: bivariate gamma, bivariate Weibull and multivariate Dirichlet.

Usage

MLEce(data, distname)

Arguments

data

a numeric matrix.

distname

a character indicating which distribution to be fitted. BiGam stands for the bivariate gamma distribution, BiWei stands for the bivariate Weibull distribution, and Dirichlet stands for the multivariate Dirichlet distribution.

Details

Based on root n-consistent estimators, the closed-form estimators (MLEces) are calculated for the parameters in bivariate gamma, bivariate Weibull and multivariate Dirichlet distributions whose maximum likelihood estimators (MLEs) are not in closed forms. The MLEces are strong consistent and asymptotic normally like the corresponding MLEs, but their calculation are much faster than MLEs. For the bivariate gamma and multivariate Dirichlet distribution, their root n-consistent estimators are the corresponding method of moments estimators (MMEs). The correlation-based estimators (CMEs) are applied as root n-consistent estimators in the bivariate Weibull distribution.

Value

MLEce returns an object of class "MLEce". The object class "MLEce" is a list containing the following components.

distribution

a character string of a distribution assuming that data set comes from and the data was fitted to.

estimation

the estimated values of parameters in assigned distribution.

References

Kim, H.-M., Jang, Y.-H., Arnold, B. C. and Zhao, J. (2023) New efficient estimators for the Weibull distribution. Communications in Statistics - Theory and Methods, 1-26.

Jang, Y.-H., Zhao, J., Kim, H.-M., Yu, K., Kwon, S.and Kim, S. (2023) New closed-form efficient estimator for the multivariate gamma distribution. Statistica Neerlandica, 1–18.

Chang, J. H., Lee, S. K. and Kim, H.-M. (2023) An asymptotically efficient closed–form estimator for the multivariate Dirichlet distribution. submitted.

Examples

#bivariate gamma distribution
data_BiGam <-  rBiGam(100, c(1,4,5))
res_BiGam  <- MLEce(data_BiGam, "BiGam")
print(res_BiGam)
data(flood)
est_BiGam <- MLEce(flood, "BiGam")
print(est_BiGam)
#bivariate Weibull distribution
data_BiWei <- rBiWei(n=30, c(4,3,3,4,0.6))
res_BiWei <- MLEce(data_BiWei, "BiWei")
print(res_BiWei)
#real data example
data(airquality)
air_data <- airquality[ ,3:4]
air_data[ ,2] <- air_data[ ,2]*0.1
est_BiWei <- MLEce(air_data, "BiWei")
print(est_BiWei)
#Dirichlet distribution
data_Diri <- LaplacesDemon::rdirichlet(n=60, c(1,2,3))
res_Diri <- MLEce(data_Diri, "Dirichlet")
print(res_Diri)
data(fossil_pollen) 
#real data example
fossil_data <- fossil_pollen/rowSums(fossil_pollen)
eps <- 1e-10
fossil_data <- (fossil_data +eps)/(1+2*eps)
est_fossil <- MLEce(fossil_data, "Dirichlet")
print(est_fossil)