log likelihood and derivatives for F distribution
Arguments
- x
variable that is distributed by f distribution
- df1, df2
degrees of freedom.
Infis allowed.- 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 dDf1 and dDf2
that has the derivatives with respect to the df1/df2 parameters at
the observation time-point
Details
In an rxode2() model, you can use llikF() but you have to
use the x and rate arguments. You can also get the derivative of df1 and df2 with
llikFDdf1() and llikFDdf2().
Examples
# \donttest{
x <- seq(0.001, 5, length.out = 100)
llikF(x^2, 1, 5)
#> fx dDf1 dDf2
#> 1 5.939135090 -5.769327755 0.0098138672
#> 2 1.996061339 -1.829698617 0.0098667834
#> 3 1.308027230 -1.151720596 0.0100203751
#> 4 0.898151814 -0.758467992 0.0102713542
#> 5 0.601410048 -0.484842238 0.0106143384
#> 6 0.365567397 -0.278507461 0.0110419510
#> 7 0.167275143 -0.115987118 0.0115449567
#> 8 -0.005928407 0.015333168 0.0121124287
#> 9 -0.161467803 0.123053577 0.0127319420
#> 10 -0.304110944 0.212138450 0.0133897879
#> 11 -0.437089645 0.286034532 0.0140712037
#> 12 -0.562684604 0.347253504 0.0147606108
#> 13 -0.682555520 0.397699568 0.0154418570
#> 14 -0.797939098 0.438864917 0.0160984557
#> 15 -0.909773848 0.471951996 0.0167138175
#> 16 -1.018782007 0.497952966 0.0172714700
#> 17 -1.125525217 0.517703019 0.0177552614
#> 18 -1.230443500 0.531917117 0.0181495454
#> 19 -1.333883243 0.541215913 0.0184393449
#> 20 -1.436117763 0.546144408 0.0186104926
#> 21 -1.537362702 0.547185650 0.0186497493
#> 22 -1.637787764 0.544770962 0.0185448973
#> 23 -1.737525805 0.539287723 0.0182848126
#> 24 -1.836679954 0.531085385 0.0178595139
#> 25 -1.935329266 0.520480216 0.0172601925
#> 26 -2.033533263 0.507759100 0.0164792220
#> 27 -2.131335592 0.493182655 0.0155101530
#> 28 -2.228767013 0.476987816 0.0143476919
#> 29 -2.325847849 0.459390036 0.0129876676
#> 30 -2.422589998 0.440585182 0.0114269877
#> 31 -2.518998603 0.420751193 0.0096635860
#> 32 -2.615073425 0.400049565 0.0076963639
#> 33 -2.710810000 0.378626673 0.0055251263
#> 34 -2.806200581 0.356614982 0.0031505147
#> 35 -2.901234940 0.334134152 0.0005739382
#> 36 -2.995901017 0.311292055 -0.0022024960
#> 37 -3.090185467 0.288185720 -0.0051760516
#> 38 -3.184074111 0.264902202 -0.0083434311
#> 39 -3.277552304 0.241519400 -0.0117008417
#> 40 -3.370605236 0.218106810 -0.0152440579
#> 41 -3.463218177 0.194726229 -0.0189684823
#> 42 -3.555376677 0.171432411 -0.0228692014
#> 43 -3.647066718 0.148273673 -0.0269410395
#> 44 -3.738274839 0.125292465 -0.0311786073
#> 45 -3.828988227 0.102525891 -0.0355763478
#> 46 -3.919194789 0.080006197 -0.0401285781
#> 47 -4.008883199 0.057761220 -0.0448295271
#> 48 -4.098042931 0.035814802 -0.0496733702
#> 49 -4.186664276 0.014187176 -0.0546542601
#> 50 -4.274738350 -0.007104684 -0.0597663547
#> 51 -4.362257091 -0.028046739 -0.0650038410
#> 52 -4.449213248 -0.048627585 -0.0703609577
#> 53 -4.535600366 -0.068838184 -0.0758320130
#> 54 -4.621412763 -0.088671614 -0.0814114015
#> 55 -4.706645505 -0.108122840 -0.0870936184
#> 56 -4.791294380 -0.127188508 -0.0928732707
#> 57 -4.875355868 -0.145866755 -0.0987450876
#> 58 -4.958827105 -0.164157039 -0.1047039284
#> 59 -5.041705859 -0.182059980 -0.1107447891
#> 60 -5.123990491 -0.199577223 -0.1168628074
#> 61 -5.205679923 -0.216711307 -0.1230532668
#> 62 -5.286773611 -0.233465550 -0.1293115988
#> 63 -5.367271506 -0.249843943 -0.1356333846
#> 64 -5.447174028 -0.265851061 -0.1420143563
#> 65 -5.526482033 -0.281491973 -0.1484503963
#> 66 -5.605196787 -0.296772169 -0.1549375368
#> 67 -5.683319932 -0.311697491 -0.1614719584
#> 68 -5.760853464 -0.326274073 -0.1680499885
#> 69 -5.837799706 -0.340508283 -0.1746680988
#> 70 -5.914161282 -0.354406680 -0.1813229026
#> 71 -5.989941093 -0.367975967 -0.1880111521
#> 72 -6.065142296 -0.381222952 -0.1947297352
#> 73 -6.139768282 -0.394154517 -0.2014756717
#> 74 -6.213822655 -0.406777586 -0.2082461105
#> 75 -6.287309215 -0.419099097 -0.2150383254
#> 76 -6.360231938 -0.431125983 -0.2218497115
#> 77 -6.432594959 -0.442865149 -0.2286777813
#> 78 -6.504402560 -0.454323453 -0.2355201612
#> 79 -6.575659147 -0.465507693 -0.2423745875
#> 80 -6.646369247 -0.476424593 -0.2492389023
#> 81 -6.716537483 -0.487080791 -0.2561110501
#> 82 -6.786168572 -0.497482830 -0.2629890742
#> 83 -6.855267306 -0.507637151 -0.2698711122
#> 84 -6.923838547 -0.517550083 -0.2767553934
#> 85 -6.991887212 -0.527227840 -0.2836402345
#> 86 -7.059418267 -0.536676516 -0.2905240366
#> 87 -7.126436719 -0.545902081 -0.2974052813
#> 88 -7.192947604 -0.554910380 -0.3042825282
#> 89 -7.258955983 -0.563707126 -0.3111544109
#> 90 -7.324466935 -0.572297907 -0.3180196342
#> 91 -7.389485548 -0.580688177 -0.3248769714
#> 92 -7.454016916 -0.588883261 -0.3317252608
#> 93 -7.518066132 -0.596888352 -0.3385634034
#> 94 -7.581638284 -0.604708517 -0.3453903600
#> 95 -7.644738447 -0.612348689 -0.3522051484
#> 96 -7.707371685 -0.619813679 -0.3590068413
#> 97 -7.769543041 -0.627108167 -0.3657945633
#> 98 -7.831257537 -0.634236713 -0.3725674892
#> 99 -7.892520171 -0.641203751 -0.3793248413
#> 100 -7.953335909 -0.648013598 -0.3860658874
model <- function(){
model({
fx <- llikF(time, df1, df2)
dMean <- llikFDdf1(time, df1, df2)
dSd <- llikFDdf2(time, df1, df2)
})
}
et <- et(x)
et$df1 <- 1
et$df2 <- 5
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: 100 × 6
#> time fx dMean dSd df1 df2
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 0.001 2.48 -2.32 0.00983 1 5
#> 2 0.0515 0.484 -0.380 0.0108 1 5
#> 3 0.102 0.112 -0.0731 0.0117 1 5
#> 4 0.152 -0.118 0.0943 0.0125 1 5
#> 5 0.203 -0.291 0.204 0.0133 1 5
#> 6 0.253 -0.431 0.283 0.0140 1 5
#> # ℹ 94 more rows
# }