Probability Density Function

Access a copula's probability density function (pdf).

Usage

eval_density(copula, u, v, strict = TRUE)

enframe_density(..., u, v, fn_prefix = "density", sep = "_", strict = TRUE)

Arguments

copula, ...

A copula, or possibly multiple copulas in the case of ....

u, v

Vectors of values to evaluate the copula at.

strict

Only evaluate when the density exists? TRUE if so; if FALSE, evaluates the derivative of the cdf.

fn_prefix

For enframe_, name of the function to appear in the column(s).

sep

When enframe'ing more than one copula, the character that will be separating the fn_name and the copula name.

Value

The evaluated density in vector form (for eval_) and data frame or tibble form (for enframe_).

See also

Other distributional representations: eval_cdf(), eval_pmf(), eval_survival()

Examples

d1 <- cop_ig(20, 4)
d2 <- cop_igl(1.1)
eval_density(d1, u = 0.4, v = 1:9 / 10)
#> [1] 0.9690656 1.0757272 1.1908119 1.2939665 1.3688790 1.3790318 1.2426071
#> [8] 0.8194615 0.1685303
enframe_density(d1, u = 0.4, v = 1:9 / 10)
#> # A tibble: 9 × 3
#>      .u    .v density
#>   <dbl> <dbl>   <dbl>
#> 1   0.4   0.1   0.969
#> 2   0.4   0.2   1.08 
#> 3   0.4   0.3   1.19 
#> 4   0.4   0.4   1.29 
#> 5   0.4   0.5   1.37 
#> 6   0.4   0.6   1.38 
#> 7   0.4   0.7   1.24 
#> 8   0.4   0.8   0.819
#> 9   0.4   0.9   0.169
enframe_density(d1, d2, u = 1:9 / 10, v = 1:9 / 10)
#> # A tibble: 9 × 4
#>      .u    .v density_d1 density_d2
#>   <dbl> <dbl>      <dbl>      <dbl>
#> 1   0.1   0.1       1.80       1.76
#> 2   0.2   0.2       1.62       1.52
#> 3   0.3   0.3       1.42       1.36
#> 4   0.4   0.4       1.29       1.26
#> 5   0.5   0.5       1.25       1.23
#> 6   0.6   0.6       1.27       1.28
#> 7   0.7   0.7       1.39       1.47
#> 8   0.8   0.8       1.66       2.00
#> 9   0.9   0.9       2.37       3.89