BMTfit.mge {BMT} | R Documentation |
Maximum Goodness-of-fit Fit of the BMT Distribution to Non-censored Data.
Description
Fit of the BMT distribution to non-censored data by maximum goodness-of-fit estimation (mge), also known as minimum distance estimation.
Usage
BMTfit.mge(data, gof = "CvM", start = list(p3 = 0.5, p4 = 0.5, p1 =
min(data) - 0.1, p2 = max(data) + 0.1), fix.arg = NULL,
type.p.3.4 = "t w", type.p.1.2 = "c-d", optim.method = "Nelder-Mead",
custom.optim = NULL, silent = TRUE, ...)
Arguments
data |
A numeric vector with the observed values for non-censored data. |
gof |
A character string coding for the name of the goodness-of-fit distance used : "CvM" for Cramer-von Mises distance,"KS" for Kolmogorov-Smirnov distance, "AD" for Anderson-Darling distance, "ADR", "ADL", "AD2R", "AD2L" and "AD2" for variants of Anderson-Darling distance described by Luceno (2006). |
start |
A named list giving the initial values of parameters of the BMT
distribution or a function of data computing initial values and returning a
named list. (see the 'details' section of
|
fix.arg |
An optional named list giving the values of fixed parameters of
the BMT distribution or a function of data computing (fixed) parameter
values and returning a named list. Parameters with fixed value are thus NOT
estimated. (see the 'details' section of
|
type.p.3.4 |
Type of parametrization asociated to p3 and p4. "t w" means tails weights parametrization (default) and "a-s" means asymmetry-steepness parametrization. |
type.p.1.2 |
Type of parametrization asociated to p1 and p2. "c-d" means domain parametrization (default) and "l-s" means location-scale parametrization. |
optim.method |
|
custom.optim |
A function carrying the optimization (see the 'details'
section of |
silent |
A logical to remove or show warnings when bootstraping. |
... |
Further arguments to be passed to generic functions or to the
function |
Details
This function is not intended to be called directly but is internally
called in BMTfit
when used with the maximum goodness-of-fit
method.
BMTfit.mge
is based on the function mgedist
but it
focuses on the maximum goodness-of-fit parameter estimation for the BMT
distribution (see BMT
for details about the BMT distribution
and mgedist
for details about maximum goodness-of-fit fit of
univariate distributions).
Value
BMTfit.mge
returns a list with following components,
estimate |
the parameter estimates. |
convergence |
an integer code for the convergence of
|
value |
the value of the corresponding objective function of the estimation method at the estimate. |
hessian |
a symmetric matrix computed by |
loglik |
the log-likelihood value. |
gof |
the code of the goodness-of-fit distance maximized. |
optim.function |
the name of the optimization function used for maximum product of spacing. |
optim.method |
when |
fix.arg |
the named list giving the values of parameters of the named
distribution that must kept fixed rather than estimated or |
fix.arg.fun |
the function used to set the value of |
weights |
the vector of weigths used in the estimation process or
|
counts |
A two-element integer vector giving the number of calls to the
log-likelihood function and its gradient respectively. This excludes those
calls needed to compute the Hessian, if requested, and any calls to
log-likelihood function to compute a finite-difference approximation to the
gradient. |
optim.message |
A character string giving any additional information
returned by the optimizer, or |
Author(s)
Camilo Jose Torres-Jimenez [aut,cre] cjtorresj@unal.edu.co
Source
Based on the function mgedist
of the R package:
fitdistrplus
Delignette-Muller ML and Dutang C (2015), fitdistrplus: An R Package for Fitting Distributions. Journal of Statistical Software, 64(4), 1-34.
References
Torres-Jimenez, C. J. (2017, September), Comparison of estimation methods for the BMT distribution. ArXiv e-prints.
Torres-Jimenez, C. J. (2018), The BMT Item Response Theory model: A new skewed distribution family with bounded domain and an IRT model based on it, PhD thesis, Doctorado en ciencias - Estadistica, Universidad Nacional de Colombia, Sede Bogota.
See Also
See BMT
for the BMT density, distribution, quantile
function and random deviates. See BMTfit.mme
,
BMTfit.qme
, BMTfit.mle
,
BMTfit.mpse
and BMTfit.mqde
for other estimation
methods. See optim
and constrOptim
for
optimization routines. See BMTfit
and fitdist
for functions that return an objetc of class "fitdist"
.
Examples
# (1) basic fit by maximum goodness-of-fit estimation
set.seed(1234)
x1 <- rBMT(n=100, p3 = 0.25, p4 = 0.75)
BMTfit.mge(x1)
# (2) how to change the goodness-of-fit statistic/distance?
BMTfit.mge(x1, gof="KS")
BMTfit.mge(x1, gof="AD2R")
# (3) how to change the optimisation method?
BMTfit.mge(x1, optim.method="L-BFGS-B")
BMTfit.mge(x1, custom.optim="nlminb")
# (4) estimation of the tails weights parameters of the BMT
# distribution with domain fixed at [0,1]
BMTfit.mge(x1, start=list(p3=0.5, p4=0.5), fix.arg=list(p1=0, p2=1))
# (5) estimation of the asymmetry-steepness parameters of the BMT
# distribution with domain fixed at [0,1]
BMTfit.mge(x1, start=list(p3=0, p4=0.5), type.p.3.4 = "a-s",
fix.arg=list(p1=0, p2=1))