Log likelihood of T and it's derivatives (from stan)
llikT(x, df, mean = 0, sd = 1, full = FALSE)Observation
degrees of freedom (\(> 0\), maybe non-integer). df
= Inf is allowed.
Mean for the likelihood
Standard deviation for the likelihood
Add the data frame showing x, mean, sd as well as the fx and derivatives
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
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