log likelihood and derivatives for F distribution

## Usage

llikF(x, df1, df2, full = FALSE)

## Arguments

x

variable that is distributed by f distribution

df1, df2

degrees of freedom. Inf is 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().

## Author

Matthew L. Fidler

## 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
# }