Calculate the log likelihood of the negative binomial function (and its derivatives)

Usage

llikNbinomMu(x, size, mu, full = FALSE)

Arguments

x: Number of successes
size: Size of trial
mu: mu parameter for negative binomial
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 dProb that has the derivatives with respect to the parameters at the observation time-point

Details

In an rxode2() model, you can use llikNbinomMu() but you have to use all arguments. You can also get the derivative of mu with llikNbinomMuDmu()

Author

Matthew L. Fidler

Examples

# \donttest{
llikNbinomMu(46:54, 100, 40)
#>          fx       dMu
#> 1 -3.326828 0.1071429
#> 2 -3.446132 0.1250000
#> 3 -3.579663 0.1428571
#> 4 -3.727034 0.1607143
#> 5 -3.887874 0.1785714
#> 6 -4.061827 0.1964286
#> 7 -4.248554 0.2142857
#> 8 -4.447728 0.2321429
#> 9 -4.659037 0.2500000

llikNbinomMu(46:54, 100, 40, TRUE)
#>    x size mu        fx       dMu
#> 1 46  100 40 -3.326828 0.1071429
#> 2 47  100 40 -3.446132 0.1250000
#> 3 48  100 40 -3.579663 0.1428571
#> 4 49  100 40 -3.727034 0.1607143
#> 5 50  100 40 -3.887874 0.1785714
#> 6 51  100 40 -4.061827 0.1964286
#> 7 52  100 40 -4.248554 0.2142857
#> 8 53  100 40 -4.447728 0.2321429
#> 9 54  100 40 -4.659037 0.2500000

et <- et(46:54)
et$size <- 100
et$mu <- 40

model <- function() {
  model({
    fx <- llikNbinomMu(time, size, mu)
    dProb <- llikNbinomMuDmu(time, size, mu)
  })
}

rxSolve(model, et)
#>  
#>  
#>  
#>  
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
#> ── Solved rxode2 object ──
#> ── Parameters ($params): ──
#> # A tibble: 1 × 0
#> ── Initial Conditions ($inits): ──
#> named numeric(0)
#> ── First part of data (object): ──
#> # A tibble: 9 × 5
#>    time    fx dProb  size    mu
#>   <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1    46 -3.33 0.107   100    40
#> 2    47 -3.45 0.125   100    40
#> 3    48 -3.58 0.143   100    40
#> 4    49 -3.73 0.161   100    40
#> 5    50 -3.89 0.179   100    40
#> 6    51 -4.06 0.196   100    40
#> # ℹ 3 more rows
# }