Log likelihood for normal distribution

Log likelihood for normal distribution

Usage

llikNorm(x, mean = 0, sd = 1, full = FALSE)

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()

Author

Matthew L. Fidler

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)
#>  
#>  
#> ℹ parameter labels from comments are typically ignored in non-interactive mode
#> ℹ Need to run with the source intact to parse comments
#>  
#>  
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
ret
#> ── Solved rxode2 object ──
#> ── Parameters (value$params): ──
#> # A tibble: 1 × 0
#> ── Initial Conditions (value$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
# }