Log likelihood of T and it's derivatives (from stan)

## Usage

llikT(x, df, mean = 0, sd = 1, full = FALSE)

## Arguments

x

Observation

df

degrees of freedom ($$> 0$$, maybe non-integer). df = Inf is allowed.

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 log pdf value of with dDf

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 llikT() but you have to use all arguments. You can also get the derivative of df, mean and sd with llikTDdf(), llikTDmean() and llikTDsd().

## Author

Matthew L. Fidler

## Examples


# \donttest{
x <- seq(-3, 3, length.out = 21)

llikT(x, 7, 0, 1)
#>            fx          dDf      dMean        dSd
#> 1  -4.2612484 -0.086858773 -1.5000000  3.5000000
#> 2  -3.8091335 -0.060260433 -1.5115465  3.0811756
#> 3  -3.3561547 -0.037201674 -1.5047022  2.6112853
#> 4  -2.9088542 -0.018379169 -1.4723926  2.0920245
#> 5  -2.4761000 -0.004340221 -1.4062500  1.5312500
#> 6  -2.0693878  0.004691380 -1.2972973  0.9459459
#> 7  -1.7028228  0.009010785 -1.1374408  0.3649289
#> 8  -1.3925134  0.009569214 -0.9218950 -0.1702945
#> 9  -1.1551333  0.007927361 -0.6521739 -0.6086957
#> 10 -1.0056349  0.005918024 -0.3385049 -0.8984485
#> 11 -0.9545342  0.005051942  0.0000000 -1.0000000
#> 12 -1.0056349  0.005918024  0.3385049 -0.8984485
#> 13 -1.1551333  0.007927361  0.6521739 -0.6086957
#> 14 -1.3925134  0.009569214  0.9218950 -0.1702945
#> 15 -1.7028228  0.009010785  1.1374408  0.3649289
#> 16 -2.0693878  0.004691380  1.2972973  0.9459459
#> 17 -2.4761000 -0.004340221  1.4062500  1.5312500
#> 18 -2.9088542 -0.018379169  1.4723926  2.0920245
#> 19 -3.3561547 -0.037201674  1.5047022  2.6112853
#> 20 -3.8091335 -0.060260433  1.5115465  3.0811756
#> 21 -4.2612484 -0.086858773  1.5000000  3.5000000

llikT(x, 15, 0, 1, full=TRUE)
#>            fx           dDf      dMean        dSd
#> 1  -4.6956220 -0.0338931511 -2.0000000  5.0000000
#> 2  -4.1042965 -0.0225073150 -1.9380888  4.2328398
#> 3  -3.5354158 -0.0134033865 -1.8497110  3.4393064
#> 4  -2.9974985 -0.0065857823 -1.7310665  2.6352396
#> 5  -2.5001272 -0.0019378861 -1.5789474  1.8421053
#> 6  -2.0536885  0.0007929097 -1.3913043  1.0869565
#> 7  -1.6689304  0.0019903977 -1.1678832  0.4014599
#> 8  -1.3563325  0.0021369166 -0.9108159 -0.1802657
#> 9  -1.1253251  0.0017504002 -0.6250000 -0.6250000
#> 10 -0.9834495  0.0012985422 -0.3180915 -0.9045726
#> 11 -0.9355929  0.0011086635  0.0000000 -1.0000000
#> 12 -0.9834495  0.0012985422  0.3180915 -0.9045726
#> 13 -1.1253251  0.0017504002  0.6250000 -0.6250000
#> 14 -1.3563325  0.0021369166  0.9108159 -0.1802657
#> 15 -1.6689304  0.0019903977  1.1678832  0.4014599
#> 16 -2.0536885  0.0007929097  1.3913043  1.0869565
#> 17 -2.5001272 -0.0019378861  1.5789474  1.8421053
#> 18 -2.9974985 -0.0065857823  1.7310665  2.6352396
#> 19 -3.5354158 -0.0134033865  1.8497110  3.4393064
#> 20 -4.1042965 -0.0225073150  1.9380888  4.2328398
#> 21 -4.6956220 -0.0338931511  2.0000000  5.0000000

et <- et(-3, 3, length.out=10)
et$nu <- 7 et$mean <- 0
et$sd <- 1 model <- function() { model({ fx <- llikT(time, nu, mean, sd) dDf <- llikTDdf(time, nu, mean, sd) dMean <- llikTDmean(time, nu, mean, sd) dSd <- llikTDsd(time, nu, mean, sd) }) } rxSolve(model, et) #> #> #> #> #> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’ #> ── Solved rxode2 object ── #> ── Parameters ($params): ──
#> # A tibble: 1 × 0
#> ── Initial Conditions (\$inits): ──
#> named numeric(0)
#> ── First part of data (object): ──
#> # A tibble: 10 × 8
#>     time    fx       dDf  dMean    dSd    nu  mean    sd
#>    <dbl> <dbl>     <dbl>  <dbl>  <dbl> <dbl> <dbl> <dbl>
#> 1 -3     -4.26 -0.0869   -1.5    3.5       7     0     1
#> 2 -2.33  -3.26 -0.0326   -1.5    2.5       7     0     1
#> 3 -1.67  -2.29  0.000289 -1.36   1.27      7     0     1
#> 4 -1     -1.49  0.00971  -1      0         7     0     1
#> 5 -0.333 -1.02  0.00611  -0.375 -0.875     7     0     1
#> 6  0.333 -1.02  0.00611   0.375 -0.875     7     0     1
#> # ℹ 4 more rows
# }