| BMTfit.mqde {BMT} | R Documentation |
Minimum Quantile Distance Fit of the BMT Distribution to Non-censored Data.
Description
Fit of the BMT distribution to non-censored data by minimum quantile distance (mqde), which can also be called maximum quantile goodness-of-fit.
Usage
BMTfit.mqde(data, probs = (1:length(data) - 0.5)/length(data), qtype = 5,
dist = "euclidean", 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,
weights = NULL, silent = TRUE, ...)
Arguments
data |
A numeric vector with the observed values for non-censored data. |
probs |
A numeric vector of the probabilities for which the minimum
quantile distance estimation is done. |
qtype |
The quantile type used by the R |
dist |
The distance measure between observed and theoretical quantiles to be used. This must be one of "euclidean" (default), "maximum", or "manhattan". Any unambiguous substring can be given. |
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 |
weights |
an optional vector of weights to be used in the fitting process.
Should be |
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 minimum quantile distance
method.
BMTfit.mqde is based on the function mqdedist but it
focuses on the minimum quantile distance parameter estimation for the BMT
distribution (see BMT for details about the BMT distribution
and mqdedist for details about minimum quantile distance fit
of univariate distributions).
Given the close-form expression of the quantile
function, two optimization methods were added when the euclidean distance is
selected: Coordinate descend ("CD") and Newton-Rhapson ("NR").
Value
BMTfit.mqde 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. |
probs |
the probability vector on which observed and theoretical quantiles were calculated. |
dist |
the name of the distance between observed and theoretical quantiles used. |
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 mqdedist which in turn is based on
the function mledist 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.mle, BMTfit.mge,
BMTfit.mpse and BMTfit.qme 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 minimum quantile distance estimation
set.seed(1234)
x1 <- rBMT(n=100, p3=0.25, p4=0.75)
BMTfit.mqde(x1)
# (2) quantile matching is a particular case of minimum quantile distance
BMTfit.mqde(x1, probs=c(0.2,0.4,0.6,0.8), qtype=7)
# (3) maximum or manhattan instead of euclidean distance
BMTfit.mqde(x1, dist="maximum")
BMTfit.mqde(x1, dist="manhattan")
# (4) how to change the optimisation method?
BMTfit.mqde(x1, optim.method="L-BFGS-B")
BMTfit.mqde(x1, custom.optim="nlminb")
# (5) estimation of the tails weights parameters of the BMT
# distribution with domain fixed at [0,1]
BMTfit.mqde(x1, start=list(p3=0.5, p4=0.5), fix.arg=list(p1=0, p2=1))
# (6) estimation of the asymmetry-steepness parameters of the BMT
# distribution with domain fixed at [0,1]
BMTfit.mqde(x1, start=list(p3=0, p4=0.5), type.p.3.4 = "a-s",
fix.arg=list(p1=0, p2=1))