MLE of continuous univariate distributions defined on the real line
MLE of continuous univariate distributions defined on the real line.
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)
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. |
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.
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. |
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis <papadakm95@gmail.com>.
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
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)
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