Log likelihood for normal distribution
Arguments
- x
Observation
- mean
Mean for the likelihood
- sd
Standard deviation for the likelihood
- full
Add the data frame showing x, mean, sd as well as the fx and derivatives
Value
data frame with fx for the pdf value of with dMean and
dSd that has the derivatives with respect to the parameters at
the observation time-point
Details
In an rxode2() model, you can use llikNorm() but you have to
use all arguments. You can also get the derivatives with
llikNormDmean() and llikNormDsd()
Examples
# \donttest{
llikNorm(0)
#> fx dMean dSd
#> 1 -0.9189385 0 -1
llikNorm(seq(-2,2,length.out=10), full=TRUE)
#> x mean sd fx dMean dSd
#> 1 -2.0000000 0 1 -2.9189385 -2.0000000 3.0000000
#> 2 -1.5555556 0 1 -2.1288151 -1.5555556 1.4197531
#> 3 -1.1111111 0 1 -1.5362225 -1.1111111 0.2345679
#> 4 -0.6666667 0 1 -1.1411608 -0.6666667 -0.5555556
#> 5 -0.2222222 0 1 -0.9436299 -0.2222222 -0.9506173
#> 6 0.2222222 0 1 -0.9436299 0.2222222 -0.9506173
#> 7 0.6666667 0 1 -1.1411608 0.6666667 -0.5555556
#> 8 1.1111111 0 1 -1.5362225 1.1111111 0.2345679
#> 9 1.5555556 0 1 -2.1288151 1.5555556 1.4197531
#> 10 2.0000000 0 1 -2.9189385 2.0000000 3.0000000
# With rxode2 you can use:
et <- et(-3, 3, length.out=10)
et$mu <- 0
et$sigma <- 1
model <- function(){
model({
fx <- llikNorm(time, mu, sigma)
dMean <- llikNormDmean(time, mu, sigma)
dSd <- llikNormDsd(time, mu, sigma)
})
}
ret <- rxSolve(model, et)
#>
#>
#>
#>
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
ret
#> ── 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 dMean dSd mu sigma
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 -3 -5.42 -3 8 0 1
#> 2 -2.33 -3.64 -2.33 4.44 0 1
#> 3 -1.67 -2.31 -1.67 1.78 0 1
#> 4 -1 -1.42 -1 0 0 1
#> 5 -0.333 -0.974 -0.333 -0.889 0 1
#> 6 0.333 -0.974 0.333 -0.889 0 1
#> # ℹ 4 more rows
# }