alaplafit {Rsubbotools} | R Documentation |
Fit an Asymmetric Laplace Distribution via maximum likelihood
Description
alaplafit
returns the parameters, standard errors. negative
log-likelihood and covariance matrix of the Asymmetric Laplace Distribution
for a sample. See details below.
Usage
alaplafit(data, verb = 0L, interv_step = 10L, provided_m_ = NULL)
Arguments
data |
(NumericVector) - the sample used to fit the distribution. |
verb |
(int) - the level of verbosity. Select one of:
|
interv_step |
int - the number of intervals to be explored after the last minimum was found in the interval optimization. Default is 10. |
provided_m_ |
NumericVector - if NULL, the m parameter is estimated by the routine. If numeric, the estimation fixes m to the given value. |
Details
The Asymmetric Laplace distribution is a distribution controlled by three parameters, with formula:
f(x;a_l,a_r,m) = \frac{1}{A} e^{-|\frac{x-m}{a_l}| }, x < m
f(x;a_l,a_r,m) = \frac{1}{A} e^{-|\frac{x-m}{a_r}| }, x > m
with:
A = a_l + a_r
where a*
are scale parameters, and m
is a location parameter.
It is basically derived from the Asymmetric Exponential Power distribution
by setting b_l = b_r = b
.
The estimations are produced by maximum likelihood, where
analytical formulas are available for the a*
parameters.
The m
parameter is found by an iterative method, using the median as
the initial guess. The method explore intervals around the last minimum
found, similar to the subboafit
routine.
Details on the method can be found on the package vignette.
Value
a list containing the following items:
"dt" - dataset containing parameters estimations and standard deviations.
"log-likelihood" - negative log-likelihood value.
"matrix" - the covariance matrix for the parameters.
Examples
sample_subbo <- rpower(1000, 1, 1)
alaplafit(sample_subbo)