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

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

Author

Matthew L. Fidler

Examples


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)
#>       x df mean sd         fx           dDf      dMean        dSd
#> 1  -3.0 15    0  1 -4.6956220 -0.0338931511 -2.0000000  5.0000000
#> 2  -2.7 15    0  1 -4.1042965 -0.0225073150 -1.9380888  4.2328398
#> 3  -2.4 15    0  1 -3.5354158 -0.0134033865 -1.8497110  3.4393064
#> 4  -2.1 15    0  1 -2.9974985 -0.0065857823 -1.7310665  2.6352396
#> 5  -1.8 15    0  1 -2.5001272 -0.0019378861 -1.5789474  1.8421053
#> 6  -1.5 15    0  1 -2.0536885  0.0007929097 -1.3913043  1.0869565
#> 7  -1.2 15    0  1 -1.6689304  0.0019903977 -1.1678832  0.4014599
#> 8  -0.9 15    0  1 -1.3563325  0.0021369166 -0.9108159 -0.1802657
#> 9  -0.6 15    0  1 -1.1253251  0.0017504002 -0.6250000 -0.6250000
#> 10 -0.3 15    0  1 -0.9834495  0.0012985422 -0.3180915 -0.9045726
#> 11  0.0 15    0  1 -0.9355929  0.0011086635  0.0000000 -1.0000000
#> 12  0.3 15    0  1 -0.9834495  0.0012985422  0.3180915 -0.9045726
#> 13  0.6 15    0  1 -1.1253251  0.0017504002  0.6250000 -0.6250000
#> 14  0.9 15    0  1 -1.3563325  0.0021369166  0.9108159 -0.1802657
#> 15  1.2 15    0  1 -1.6689304  0.0019903977  1.1678832  0.4014599
#> 16  1.5 15    0  1 -2.0536885  0.0007929097  1.3913043  1.0869565
#> 17  1.8 15    0  1 -2.5001272 -0.0019378861  1.5789474  1.8421053
#> 18  2.1 15    0  1 -2.9974985 -0.0065857823  1.7310665  2.6352396
#> 19  2.4 15    0  1 -3.5354158 -0.0134033865  1.8497110  3.4393064
#> 20  2.7 15    0  1 -4.1042965 -0.0225073150  1.9380888  4.2328398
#> 21  3.0 15    0  1 -4.6956220 -0.0338931511  2.0000000  5.0000000