MLE of continuous univariate distributions defined on the real line {Rfast}

MLE of continuous univariate distributions defined on the real line

Description

MLE of continuous univariate distributions defined on the real line.

Usage

normal.mle(x) 
gumbel.mle(x, tol = 1e-09)
cauchy.mle(x, tol = 1e-09)
logistic.mle(x, tol = 1e-07)
ct.mle(x, tol = 1e-09)
tmle(x, v = 5, tol = 1e-08)
wigner.mle(x, tol = 1e-09)
laplace.mle(x)

Arguments

x

A numerical vector with data.

v

The degrees of freedom of the t distribution.

tol

The tolerance level up to which the maximisation stops set to 1e-09 by default.

Details

Instead of maximising the log-likelihood via a numerical optimiser we have used a Newton-Raphson algorithm which is faster. See wikipedia for the equation to be solved. For the t distribution we need the degrees of freedom and estimate the location and scatter parameters.

The Cauchy is the t distribution with 1 degree of freedom. If you want to fit such a distribution used the cauchy.mle and not the t.mle with 1 degree of freedom as it's faster. The Laplace distribution is also called double exponential distribution.

The wigner.mle refers to the wigner semicircle distribution.

Value

Usually a list with three elements, but this is not for all cases.

iters

The number of iterations required for the Newton-Raphson to converge.

loglik

The value of the maximised log-likelihood.

param

The vector of the parameters.

Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris <[e-mail]> and Manos Papadakis <[e-mail]>.

References

Johnson, Norman L. Kemp, Adrianne W. Kotz, Samuel (2005). Univariate Discrete Distributions (third edition). Hoboken, NJ: Wiley-Interscience.

https://en.wikipedia.org/wiki/Wigner_semicircle_distribution

See Also

zip.mle, gammamle, vm.mle

Examples

x <- rt(1000,10)
a <- ct.mle(x)
res<-tmle(x, v = a$nu)
res<-cauchy.mle(x)
res<-normal.mle(x)
res<-logistic.mle(x)
res<-gumbel.mle(x)