me: Moment Estimation

Description

Calculates the ME under the assumption the sample observations are independent and identically distributed (iid) according to a specified family of distributions.

Usage

me(x, distr, ...)
# S4 method for ANY,character
me(x, distr, ...)
# S4 method for numeric,Beta
me(x, distr)
# S4 method for numeric,Binom
me(x, distr)
# S4 method for matrix,Dirichlet
me(x, distr)
# S4 method for numeric,Exp
me(x, distr)
# S4 method for numeric,Gammad
me(x, distr)
# S4 method for matrix,MGamma
me(x, distr, dirich = FALSE)
# S4 method for numeric,Norm
me(x, distr)
# S4 method for numeric,Pois
me(x, distr)

Value

numeric. The estimator produced by the sample.

Arguments

x: numeric. A sample under estimation.
distr: A subclass of Distribution. The distribution family assumed.
...: extra arguments.
dirich: logical. Should the Dirichlet-based estimator be calculated instead? Applies only to the Multivariate Gamma distribution.

References

Ye, Z.-S. & Chen, N. (2017), Closed-form estimators for the gamma distribution derived from likelihood equations, The American Statistician 71(2), 177–181.

Van der Vaart, A. W. (2000), Asymptotic statistics, Vol. 3, Cambridge university press.

Tamae, H., Irie, K. & Kubokawa, T. (2020), A score-adjusted approach to closed-form estimators for the gamma and beta distributions, Japanese Journal of Statistics and Data Science 3, 543–561.

Mathal, A. & Moschopoulos, P. (1992), A form of multivariate gamma distribution, Annals of the Institute of Statistical Mathematics 44, 97–106.

Oikonomidis, I. & Trevezas, S. (2023), Moment-Type Estimators for the Dirichlet and the Multivariate Gamma Distributions, arXiv, https://arxiv.org/abs/2311.15025

Examples

Run this code

# -------------------------------------------
# Beta Distribution Example
# -------------------------------------------

# Simulation
set.seed(1)
shape1 <- 1
shape2 <- 2
x <- rbeta(100, shape1, shape2)

library(distr)
D <- Beta(shape1, shape2)

# Likelihood - The ll Functions

llbeta(x, shape1, shape2)
ll(x, c(shape1, shape2), D)
ll(x, c(shape1, shape2), "beta")

# Point Estimation - The e Functions

ebeta(x, type = "mle")
ebeta(x, type = "me")
ebeta(x, type = "same")

mle(x, D)
me(x, D)
same(x, D)

estim(x, D, type = "mle")

# Asymptotic Variance - The v Functions

vbeta(shape1, shape2, type = "mle")
vbeta(shape1, shape2, type = "me")
vbeta(shape1, shape2, type = "same")

avar_mle(D)
avar_me(D)
avar_same(D)

avar(D, type = "mle")