View source: R/BMTchangepars.R
BMTchangepars | R Documentation |
Parameter conversion for different parameterizations for the BMT
distribution, with p3
and p4
tails weights (\kappa_l
and \kappa_r
) or asymmetry-steepness parameters (\zeta
and
\xi
) and p1
and p2
domain (minimum and maximum) or
location-scale (mean and standard deviation) parameters.
BMTchangepars(
p3,
p4,
type.p.3.4 = "t w",
p1 = NULL,
p2 = NULL,
type.p.1.2 = NULL
)
p3 , p4 |
tails weights ( |
type.p.3.4 |
type of parametrization associated to p3 and p4. "t w" means tails weights parametrization (default) and "a-s" means asymmetry-steepness parametrization. |
p1 , p2 |
domain (minimum and maximum) or location-scale (mean and standard deviation) parameters of the BMT distribution. |
type.p.1.2 |
type of parametrization associated to p1 and p2. "c-d" means domain parametrization (default) and "l-s" means location-scale parametrization. |
The BMT coefficient of asymmetry -1 < \zeta < 1
is
\kappa_r - \kappa_l
The BMT coefficient of steepness 0 < \xi < 1
is
(\kappa_r +
\kappa_l - |\kappa_r - \kappa_l|) / (2 (1 - |\kappa_r - \kappa_l|))
for
|\kappa_r - \kappa_l| < 1
.
The BMT distribution has mean ( d - c ) BMTmean(\kappa_l, \kappa_r) +
c
and standard deviation ( d - c ) BMTsd(\kappa_l, \kappa_r)
From these equations, we can go back and forth with each parameterization.
BMTchangepars
reparametrize p3
, p4
, p1
,
p2
according to the alternative parameterizations from the given
type.p.3.4
and type.p.1.2
. BMTchangepars
returns a
list with the alternative arguments to those received.
The arguments are recycled to the length of the result. Only the first
elements of type.p.3.4
and type.p.1.2
are used.
If type.p.3.4 == "t w"
, p3 < 0
and p3 > 1
are errors
and return NaN
.
If type.p.3.4 == "a-s"
, p3 < -1
and p3 > 1
are errors
and return NaN
.
p4 < 0
and p4 > 1
are errors and return NaN
.
If type.p.1.2 == "c-d"
, p1 >= p2
is an error and returns
NaN
.
If type.p.1.2 == "l-s"
, p2 <= 0
is an error and returns
NaN
.
Camilo Jose Torres-Jimenez [aut,cre] cjtorresj@unal.edu.co and Alvaro Mauricio Montenegro Diaz [ths]
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.
BMT
for the BMT density, distribution, quantile
function and random deviates.
# BMT on [0,1] with left tail weight equal to 0.25 and
# right tail weight equal to 0.75
parameters <- BMTchangepars(0.25, 0.75, "t w")
parameters # Parameters of the BMT in the asymmetry-steepness parametrization
# BMT with mean equal to 0, standard deviation equal to 1,
# asymmetry coefficient equal to 0.5 and
# steepness coefficient equal to 0.75
parameters <- BMTchangepars(0.5, 0.5, "a-s", 0, 1, "l-s")
parameters # Parameters of the BMT in the tail weight and domain parametrization
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