The Bivariate Chi-bar-squared Distribution

Density, distribution function, and random generation for the bivariate chi-bar-squared distribution with mixing weights (conic intrinsic volumes) v.

dbichibarsq(x, v)

pbichibarsq(x, v)

rbichibarsq(n, v)

Arguments

x

two-entry vectors or two-column matrices.
v

vector of mixing weights (conic intrinsic volumes).
n

number of observations.

Value

The output of dbichibarsq(x, v) is either a number, if x is a vector of length 2, or a vector of length dim(x)[1] such that the entries are the values of the density of the bivariate chi-bar-squared distribution with weights v in the corresponding entry (row) of x.

The output of pbichibarsq(x, v) is either a number, if x is a vector of length 2, or a vector of length dim(x)[1] such that the entries are the values of the cdf of the bivariate chi-bar-squared distribution with weights v in the corresponding entry (row) of x.

The output of rbichibarsq(n, v) is either a number, if n==1, or a two-column matrix with n rows such that the rows are iid samples from the bivariate chi-bar-squared distribution with weights v.

Functions

  • dbichibarsq: Evaluates the density of the bivariate chi-bar-squared distribution.

  • pbichibarsq: Evaluates the cdf of the bivariate chi-bar-squared distribution.

  • rbichibarsq: Samples from the bivariate chi-bar-squared distribution.

See also

dchibarsq, pchibarsq, rchibarsq, dchisq, pchisq, qchisq, rchisq

Package: conivol

Examples

dbichibarsq(c(2,3),c(0.1,0.6,0.3))
#> [1] 0.003200071
dbichibarsq(matrix(c(2,3,4,5),2,2),c(0.1,0.6,0.3))
#> [1] 0.0016809041 0.0004515936

pbichibarsq(c(2,3),c(0.1,0.6,0.3))
#> [1] 0.5619684
pbichibarsq(matrix(c(2,3,4,5),2,2),c(0.1,0.6,0.3))
#> [1] 0.2761026 0.3248525

rbichibarsq(10,c(0.1,0.6,0.3))
#>             [,1]        [,2]
#>  [1,] 2.42851423 0.831476280
#>  [2,] 0.73513904 0.000000000
#>  [3,] 0.19940087 0.000000000
#>  [4,] 0.02584938 0.559404408
#>  [5,] 0.27859713 0.002207469
#>  [6,] 0.79216544 2.167001067
#>  [7,] 0.01192337 0.191516046
#>  [8,] 0.91097694 1.265104123
#>  [9,] 1.37431459 0.000000000
#> [10,] 4.61400034 0.000000000