alaplafit returns the parameters, standard errors. negative
log-likelihood and covariance matrix of the Asymmetric Laplace Distribution
for a sample. See details below.
alaplafit(data, verb = 0L, interv_step = 10L, provided_m_ = NULL)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.
(NumericVector) - the sample used to fit the distribution.
(int) - the level of verbosity. Select one of:
0 just the final result
1 details of optim. routine
int - the number of intervals to be explored after the last minimum was found in the interval optimization. Default is 10.
NumericVector - if NULL, the m parameter is estimated by the routine. If numeric, the estimation fixes m to the given value.
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.
sample_subbo <- rpower(1000, 1, 1)
alaplafit(sample_subbo)
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