log likelihood and derivatives for F distribution
llikF(x, df1, df2, full = FALSE)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
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