# BMTcentral: The BMT Distribution Descriptive Measures - Central Tendency. In BMT: The BMT Distribution

## Description

Mean, median and mode for the BMT distribution, with `p3` and `p4` tails weights (κ_l and κ_r) or asymmetry-steepness parameters (ζ and ξ) and `p1` and `p2` domain (minimum and maximum) or location-scale (mean and standard deviation) parameters.

## Usage

 ```1 2 3 4 5 6``` ```BMTmean(p3, p4, type.p.3.4 = "t w", p1 = 0, p2 = 1, type.p.1.2 = "c-d") BMTmedian(p3, p4, type.p.3.4 = "t w", p1 = 0, p2 = 1, type.p.1.2 = "c-d") BMTmode(p3, p4, type.p.3.4 = "t w", p1 = 0, p2 = 1, type.p.1.2 = "c-d") ```

## Arguments

 `p3, p4` tails weights (κ_l and κ_r) or asymmetry-steepness (ζ and ξ) 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.

See References.

## Value

`BMTmean` gives the mean, `BMTmedian` the median and `BMTmode` the mode for the BMT distribution.

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] cjtorresj@unal.edu.co

## References

Torres-Jimenez, C. J. and Montenegro-Diaz, A. M. (2017, September), An alternative to continuous univariate distributions supported on a bounded interval: 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.

`BMTdispersion`, `BMTskewness`, `BMTkurtosis`, `BMTmoments` for other descriptive measures or moments.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25``` ```# BMT on [0,1] with left tail weight equal to 0.25 and # right tail weight equal to 0.75 BMTmean(0.25, 0.75, "t w") BMTmedian(0.25, 0.75, "t w") BMTmode(0.25, 0.75, "t w") # BMT on [0,1] with asymmetry coefficient equal to 0.5 and # steepness coefficient equal to 0.75 BMTmean(0.5, 0.5, "a-s") BMTmedian(0.5, 0.5, "a-s") BMTmode(0.5, 0.5, "a-s") # BMT on [-1.783489,3.312195] with # left tail weight equal to 0.25 and # right tail weight equal to 0.75 BMTmean(0.25, 0.75, "t w", -1.783489, 3.312195, "c-d") BMTmedian(0.25, 0.75, "t w", -1.783489, 3.312195, "c-d") BMTmode(0.25, 0.75, "t w", -1.783489, 3.312195, "c-d") # BMT with mean equal to 0, standard deviation equal to 1, # asymmetry coefficient equal to 0.5 and # steepness coefficient equal to 0.75 BMTmean(0.5, 0.5, "a-s", 0, 1, "l-s") BMTmedian(0.5, 0.5, "a-s", 0, 1, "l-s") BMTmode(0.5, 0.5, "a-s", 0, 1, "l-s") ```