Description Usage Arguments Details Value Author(s) References See Also Examples

Skewness and an asymmetry coefficient 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.

1 2 3 |

`p3, p4` |
tails weights ( |

`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.

`BMTskew`

gives the Pearson's skewness and `BMTasymm`

the
proposed asymmetry coefficient 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`

.

Camilo Jose Torres-Jimenez [aut,cre] [email protected]

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.

`BMTcentral`

, `BMTdispersion`

,
`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 | ```
# BMT on [0,1] with left tail weight equal to 0.25 and
# right tail weight equal to 0.75
BMTskew(0.25, 0.75, "t w")
BMTasymm(0.25, 0.75, "t w")
# BMT on [0,1] with asymmetry coefficient equal to 0.5 and
# steepness coefficient equal to 0.75
BMTskew(0.5, 0.5, "a-s")
BMTasymm(0.5, 0.5, "a-s")
# domain or location-scale parameters do not affect
# the skewness and the asymmetry coefficient
# BMT on [-1.783489,3.312195] with
# left tail weight equal to 0.25 and
# right tail weight equal to 0.75
BMTskew(0.25, 0.75, "t w", -1.783489, 3.312195, "c-d")
BMTasymm(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
BMTskew(0.5, 0.5, "a-s", 0, 1, "l-s")
BMTasymm(0.5, 0.5, "a-s", 0, 1, "l-s")
``` |

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