log likelihood and derivatives for Gamma distribution

## Usage

llikGamma(x, shape, rate, full = FALSE)

## Arguments

x

variable that is distributed by gamma distribution

shape

this is the distribution's shape parameter. Must be positive.

rate

this is the distribution's rate parameters. Must be positive.

full

Add the data frame showing x, mean, sd as well as the fx and derivatives

## Value

data frame with fx for the log pdf value of with dProb

that has the derivatives with respect to the prob parameters at the observation time-point

## Details

In an rxode2() model, you can use llikGamma() but you have to use the x and rate arguments. You can also get the derivative of shape or rate with llikGammaDshape() and llikGammaDrate().

## Author

Matthew L. Fidler

## Examples

# \donttest{

llikGamma(1, 1, 10)
#>          fx   dShape dRate
#> 1 -7.697415 2.879801  -0.9

# You can use this in rxode2 too:

et  <- et(seq(0.001, 1, length.out=10))
et$shape <- 1 et$rate <- 10

model <- function() {
model({
fx <- llikGamma(time, shape, rate)
dShape<- llikGammaDshape(time, shape, rate)
dRate <- llikGammaDrate(time, shape, rate)
})
}

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: 10 × 6
#>    time      fx dShape  dRate  rate shape
#>   <dbl>   <dbl>  <dbl>  <dbl> <dbl> <dbl>
#> 1 0.001  2.29   -4.03   0.099    10     1
#> 2 0.112  1.18    0.691 -0.012    10     1
#> 3 0.223  0.0726  1.38  -0.123    10     1
#> 4 0.334 -1.04    1.78  -0.234    10     1
#> 5 0.445 -2.15    2.07  -0.345    10     1
#> 6 0.556 -3.26    2.29  -0.456    10     1
#> # ℹ 4 more rows
# }