log likelihood of Cauchy distribution and it's derivatives (from stan)

llikCauchy(x, location = 0, scale = 1, full = FALSE)

Arguments

x: Observation
location, scale: location and scale parameters.
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 dLocation and dScale 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)

llikCauchy(x, 0, 1)
#>           fx  dLocation     dScale
#> 1  -3.447315 -0.6000000  0.8000000
#> 2  -3.259780 -0.6513872  0.7587455
#> 3  -3.055753 -0.7100592  0.7041420
#> 4  -2.832979 -0.7763401  0.6303142
#> 5  -2.589293 -0.8490566  0.5283019
#> 6  -2.323385 -0.9230769  0.3846154
#> 7  -2.036728 -0.9836066  0.1803279
#> 8  -1.738057 -0.9944751 -0.1049724
#> 9  -1.452215 -0.8823529 -0.4705882
#> 10 -1.230908 -0.5504587 -0.8348624
#> 11 -1.144730  0.0000000 -1.0000000
#> 12 -1.230908  0.5504587 -0.8348624
#> 13 -1.452215  0.8823529 -0.4705882
#> 14 -1.738057  0.9944751 -0.1049724
#> 15 -2.036728  0.9836066  0.1803279
#> 16 -2.323385  0.9230769  0.3846154
#> 17 -2.589293  0.8490566  0.5283019
#> 18 -2.832979  0.7763401  0.6303142
#> 19 -3.055753  0.7100592  0.7041420
#> 20 -3.259780  0.6513872  0.7587455
#> 21 -3.447315  0.6000000  0.8000000

llikCauchy(x, 3, 1, full=TRUE)
#>       x location scale        fx  dLocation     dScale
#> 1  -3.0        3     1 -4.755648 -0.3243243  0.9459459
#> 2  -2.7        3     1 -4.655977 -0.3404001  0.9402807
#> 3  -2.4        3     1 -4.551246 -0.3580902  0.9336870
#> 4  -2.1        3     1 -4.440937 -0.3776379  0.9259534
#> 5  -1.8        3     1 -4.324449 -0.3993344  0.9168053
#> 6  -1.5        3     1 -4.201087 -0.4235294  0.9058824
#> 7  -1.2        3     1 -4.070040 -0.4506438  0.8927039
#> 8  -0.9        3     1 -3.930358 -0.4811845  0.8766194
#> 9  -0.6        3     1 -3.780926 -0.5157593  0.8567335
#> 10 -0.3        3     1 -3.620428 -0.5550883  0.8317914
#> 11  0.0        3     1 -3.447315 -0.6000000  0.8000000
#> 12  0.3        3     1 -3.259780 -0.6513872  0.7587455
#> 13  0.6        3     1 -3.055753 -0.7100592  0.7041420
#> 14  0.9        3     1 -2.832979 -0.7763401  0.6303142
#> 15  1.2        3     1 -2.589293 -0.8490566  0.5283019
#> 16  1.5        3     1 -2.323385 -0.9230769  0.3846154
#> 17  1.8        3     1 -2.036728 -0.9836066  0.1803279
#> 18  2.1        3     1 -1.738057 -0.9944751 -0.1049724
#> 19  2.4        3     1 -1.452215 -0.8823529 -0.4705882
#> 20  2.7        3     1 -1.230908 -0.5504587 -0.8348624
#> 21  3.0        3     1 -1.144730  0.0000000 -1.0000000