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

## Usage

llikBinom(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 llikBinom() but you have to use all arguments. You can also get the derivative of prob with llikBinomDprob()

## Author

Matthew L. Fidler

## Examples

# \donttest{
llikBinom(46:54, 100, 0.5)
#>          fx dProb
#> 1 -2.848030   -16
#> 2 -2.709193   -12
#> 3 -2.610102    -8
#> 4 -2.550679    -4
#> 5 -2.530876     0
#> 6 -2.550679     4
#> 7 -2.610102     8
#> 8 -2.709193    12
#> 9 -2.848030    16

llikBinom(46:54, 100, 0.5, TRUE)
#>    x size prob        fx dProb
#> 1 46  100  0.5 -2.848030   -16
#> 2 47  100  0.5 -2.709193   -12
#> 3 48  100  0.5 -2.610102    -8
#> 4 49  100  0.5 -2.550679    -4
#> 5 50  100  0.5 -2.530876     0
#> 6 51  100  0.5 -2.550679     4
#> 7 52  100  0.5 -2.610102     8
#> 8 53  100  0.5 -2.709193    12
#> 9 54  100  0.5 -2.848030    16

# In rxode2 you can use:

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

model <- function() {
model({
fx <- llikBinom(time, size, prob)
dProb <- llikBinomDprob(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 -2.85   -16   100   0.5
#> 2    47 -2.71   -12   100   0.5
#> 3    48 -2.61    -8   100   0.5
#> 4    49 -2.55    -4   100   0.5
#> 5    50 -2.53     0   100   0.5
#> 6    51 -2.55     4   100   0.5
#> # ℹ 3 more rows
# }