mle {estimators}

Maximum Likelihood Estimation

Description

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

Usage

mle(x, distr, ...)

## S4 method for signature 'ANY,character'
mle(x, distr, ...)

Arguments

x

numeric. A sample under estimation.

distr

A subclass of Distribution. The distribution family assumed.

...

extra arguments.

Value

numeric. The estimator produced by the sample.

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

See Also

estim, me, same

Examples

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

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

# 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")