Column-wise MLE of continuous univariate distributions defined on the real line {MLE}

Column-wise MLE of continuous univariate distributions defined on the real line

Description

Column-wise MLE of continuous univariate distributions defined on the real line.

Usage

colreal.mle(x, distr = "normal", tol = 1e-07, maxiters = 100, parallel = FALSE)

Arguments

x

A numerical vector with data.

distr

The distribution to fit, "normal" stands for the normal distribution, "cauchy" for the Cauchy, "laplace" is the Laplace distribution.

tol

The tolerance level to stop the iterative process of finding the MLEs.

maxiters

The maximum number of iterations to implement.

parallel

Should the computations take place in parallel?

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. The Laplace distribution is also called double exponential distribution.

Value

A matrix with two, columns. The first one contains the parameters of the distribution and the second columns contains the log-likelihood values.

Author(s)

Michail Tsagris and Sofia Piperaki.

R implementation and documentation: Michail Tsagris [e-mail] and Sofia Piperaki [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

positive.mle, circ.mle, disc.mle

Examples

x <- rnorm(1000, 10, 2)
a <- real.mle(x, distr = "normal")