log likelihood of Cauchy distribution and it's derivatives (from stan)
Source:R/llik.R
llikCauchy.Rdlog likelihood of Cauchy distribution and it's derivatives (from stan)
Arguments
- x
Observation
- location, scale
location and scale parameters.
- full
Add the data frame showing x, mean, sd as well as the fx and derivatives
Value
data frame with fx for the log pdf value of with
dLocation and dScale that has the derivatives with respect to the parameters at
the observation time-point
Details
In an rxode2() model, you can use llikCauchy() but you have to
use all arguments. You can also get the derivative of location and scale with
llikCauchyDlocation() and llikCauchyDscale().
Examples
# \donttest{
x <- seq(-3, 3, length.out = 21)
llikCauchy(x, 0, 1)
#> fx dLocation dScale
#> 1 -3.447315 -0.6000000 0.8000000
#> 2 -3.259780 -0.6513872 0.7587455
#> 3 -3.055753 -0.7100592 0.7041420
#> 4 -2.832979 -0.7763401 0.6303142
#> 5 -2.589293 -0.8490566 0.5283019
#> 6 -2.323385 -0.9230769 0.3846154
#> 7 -2.036728 -0.9836066 0.1803279
#> 8 -1.738057 -0.9944751 -0.1049724
#> 9 -1.452215 -0.8823529 -0.4705882
#> 10 -1.230908 -0.5504587 -0.8348624
#> 11 -1.144730 0.0000000 -1.0000000
#> 12 -1.230908 0.5504587 -0.8348624
#> 13 -1.452215 0.8823529 -0.4705882
#> 14 -1.738057 0.9944751 -0.1049724
#> 15 -2.036728 0.9836066 0.1803279
#> 16 -2.323385 0.9230769 0.3846154
#> 17 -2.589293 0.8490566 0.5283019
#> 18 -2.832979 0.7763401 0.6303142
#> 19 -3.055753 0.7100592 0.7041420
#> 20 -3.259780 0.6513872 0.7587455
#> 21 -3.447315 0.6000000 0.8000000
llikCauchy(x, 3, 1, full=TRUE)
#> x location scale fx dLocation dScale
#> 1 -3.0 3 1 -4.755648 -0.3243243 0.9459459
#> 2 -2.7 3 1 -4.655977 -0.3404001 0.9402807
#> 3 -2.4 3 1 -4.551246 -0.3580902 0.9336870
#> 4 -2.1 3 1 -4.440937 -0.3776379 0.9259534
#> 5 -1.8 3 1 -4.324449 -0.3993344 0.9168053
#> 6 -1.5 3 1 -4.201087 -0.4235294 0.9058824
#> 7 -1.2 3 1 -4.070040 -0.4506438 0.8927039
#> 8 -0.9 3 1 -3.930358 -0.4811845 0.8766194
#> 9 -0.6 3 1 -3.780926 -0.5157593 0.8567335
#> 10 -0.3 3 1 -3.620428 -0.5550883 0.8317914
#> 11 0.0 3 1 -3.447315 -0.6000000 0.8000000
#> 12 0.3 3 1 -3.259780 -0.6513872 0.7587455
#> 13 0.6 3 1 -3.055753 -0.7100592 0.7041420
#> 14 0.9 3 1 -2.832979 -0.7763401 0.6303142
#> 15 1.2 3 1 -2.589293 -0.8490566 0.5283019
#> 16 1.5 3 1 -2.323385 -0.9230769 0.3846154
#> 17 1.8 3 1 -2.036728 -0.9836066 0.1803279
#> 18 2.1 3 1 -1.738057 -0.9944751 -0.1049724
#> 19 2.4 3 1 -1.452215 -0.8823529 -0.4705882
#> 20 2.7 3 1 -1.230908 -0.5504587 -0.8348624
#> 21 3.0 3 1 -1.144730 0.0000000 -1.0000000
et <- et(-3, 3, length.out=10)
et$location <- 0
et$scale <- 1
model <- function() {
model({
fx <- llikCauchy(time, location, scale)
dLocation <- llikCauchyDlocation(time, location, scale)
dScale <- llikCauchyDscale(time, location, scale)
})
}
rxSolve(model, et)
#>
#>
#>
#>
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
#> Warning:
#> with negative times, compartments initialize at first negative observed time
#> with positive times, compartments initialize at time zero
#> use 'rxSetIni0(FALSE)' to initialize at first observed time
#> this warning is displayed once per session
#> ── Solved rxode2 object ──
#> ── Parameters ($params): ──
#> # A tibble: 1 × 0
#> ── Initial Conditions ($inits): ──
#> named numeric(0)
#> ── First part of data (object): ──
#> # A tibble: 10 × 6
#> time fx dLocation dScale location scale
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 -3 -3.45 -0.6 0.8 0 1
#> 2 -2.33 -3.01 -0.724 0.690 0 1
#> 3 -1.67 -2.47 -0.882 0.471 0 1
#> 4 -1 -1.84 -1 0 0 1
#> 5 -0.333 -1.25 -0.6 -0.8 0 1
#> 6 0.333 -1.25 0.600 -0.8 0 1
#> # ℹ 4 more rows
# }