BMTchangepars {BMT}

The BMT Distribution Parameter Conversion.

Description

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.

Usage

BMTchangepars(p3, p4, type.p.3.4 = "t w", p1 = NULL, p2 = NULL,
  type.p.1.2 = NULL)

Arguments

p3, p4

tails weights (\kappa_l and \kappa_r) or asymmetry-steepness (\zeta and \xi) parameters of the BMT distribution.

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.

p1, p2

domain (minimum and maximum) or location-scale (mean and standard deviation) parameters of the BMT ditribution.

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.

Details

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.

Value

BMTchangepars reparametrizes 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.

Author(s)

Camilo Jose Torres-Jimenez [aut,cre] [e-mail] and Alvaro Mauricio Montenegro Diaz [ths]

References

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

BMT for the BMT density, distribution, quantile function and random deviates.

Examples

# 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