BMTfit.qme {BMT}  R Documentation 
Fit of the BMT distribution to noncensored data by quantile matching estimation (qme).
BMTfit.qme(data, probs = c(0.2, 0.4, 0.6, 0.8), qtype = 7, 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 = "cd", optim.method = "NelderMead", custom.optim = NULL, silent = TRUE, ...)
data 
A numeric vector with the observed values for noncensored data. 
probs 
A numeric vector of the probabilities for which the quantile matching is done. The length of this vector must be equal to the number of parameters to estimate. 
qtype 
The quantile type used by the R 
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 "as" means asymmetrysteepness parametrization. 
type.p.1.2 
Type of parametrization asociated to p1 and p2. "cd" means domain parametrization (default) and "ls" means locationscale 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 
This function is not intended to be called directly but is internally
called in BMTfit
when used with the quantile matching method.
BMTfit.qme
is based on the function qmedist
but it
focuses on the quantile matching parameter estimation for the BMT
distribution (see BMT
for details about the BMT distribution
and qmedist
for details about quantile matching fit of
univariate distributions).
BMTfit.qme
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 loglikelihood value. 
probs 
the probability vector on which quantiles are matched. 
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 twoelement integer vector giving the number of calls to the
loglikelihood function and its gradient respectively. This excludes those
calls needed to compute the Hessian, if requested, and any calls to
loglikelihood function to compute a finitedifference approximation to the
gradient. 
optim.message 
A character string giving any additional information
returned by the optimizer, or 
Camilo Jose TorresJimenez [aut,cre] cjtorresj@unal.edu.co
Based on the function qmedist
of the R package:
fitdistrplus
DelignetteMuller ML and Dutang C (2015), fitdistrplus: An R Package for Fitting Distributions. Journal of Statistical Software, 64(4), 134.
TorresJimenez, C. J. (2017, September), Comparison of estimation methods for the BMT distribution. ArXiv eprints.
TorresJimenez, 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 BMT
for the BMT density, distribution, quantile
function and random deviates. See BMTfit.mme
,
BMTfit.mle
, BMTfit.mge
,
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"
.
# (1) basic fit by quantile matching estimation set.seed(1234) x1 < rBMT(n=100, p3 = 0.25, p4 = 0.75) BMTfit.qme(x1) # (2) changing the probability vector on which quantiles are matched BMTfit.qme(x1, probs=c(0.1,0.3,0.5,0.75)) # (3) how to change the optimisation method? BMTfit.qme(x1, optim.method="LBFGSB") BMTfit.qme(x1, custom.optim="nlminb") # (4) estimation of the tails weights parameters of the BMT # distribution with domain fixed at [0,1] BMTfit.qme(x1, start=list(p3=0.5, p4=0.5), fix.arg=list(p1=0, p2=1), probs=c(1/3,2/3)) # (5) estimation of the asymmetrysteepness parameters of the BMT # distribution with domain fixed at [0,1] BMTfit.qme(x1, start=list(p3=0, p4=0.5), type.p.3.4 = "as", fix.arg=list(p1=0, p2=1), probs=c(1/3,2/3))