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

Usage

llikNbinom(x, size, prob, full = FALSE)

Arguments

x: Number of successes
size: Size of trial
prob: probability of success
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 llikNbinom() but you have to use all arguments. You can also get the derivative of prob with llikNbinomDprob()

Author

Matthew L. Fidler

Examples

# \donttest{
llikNbinom(46:54, 100, 0.5)
#>          fx dProb
#> 1 -13.25200   108
#> 2 -12.81168   106
#> 3 -12.38560   104
#> 4 -11.97335   102
#> 5 -11.57458   100
#> 6 -11.18892    98
#> 7 -10.81603    96
#> 8 -10.45559    94
#> 9 -10.10728    92

llikNbinom(46:54, 100, 0.5, TRUE)
#>    x size prob        fx dProb
#> 1 46  100  0.5 -13.25200   108
#> 2 47  100  0.5 -12.81168   106
#> 3 48  100  0.5 -12.38560   104
#> 4 49  100  0.5 -11.97335   102
#> 5 50  100  0.5 -11.57458   100
#> 6 51  100  0.5 -11.18892    98
#> 7 52  100  0.5 -10.81603    96
#> 8 53  100  0.5 -10.45559    94
#> 9 54  100  0.5 -10.10728    92

# In rxode2 you can use:

et <- et(46:54)
et$size <- 100
et$prob <-0.5

model <- function() {
  model({
    fx <- llikNbinom(time, size, prob)
    dProb <- llikNbinomDprob(time, size, prob)
  })
}

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  prob
#>   <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1    46 -13.3   108   100   0.5
#> 2    47 -12.8   106   100   0.5
#> 3    48 -12.4   104   100   0.5
#> 4    49 -12.0   102   100   0.5
#> 5    50 -11.6   100   100   0.5
#> 6    51 -11.2    98   100   0.5
#> # ℹ 3 more rows
# }