varlog <- function(x){
### D.vec <- seq(0.1,15,length=300);
### n <- 10^5;
###
### v <- 0*D.vec;
### m <- 0*D.vec;
###
### for (i in 1:length(D.vec)){
### print(i);
### D <- D.vec[i];
### psample <- rpois(n,D);
### lnsample <- log(psample + a);
### v[i] <- var(lnsample);
### m[i] <- mean(lnsample);
### }
###
### v <- c(0,v);
### D.vec <- c(0,D.vec);
v <- c(0, 0.110045205147111, 0.155674302499040,
0.199240283140136, 0.242189047882198, 0.274830813611156,
0.30678253149971, 0.336376960225776, 0.36276580819325,
0.385654336904667, 0.404089446791022, 0.424333614612062,
0.437129858162966, 0.452943660446181, 0.466434893326834,
0.476488197083339, 0.484486487973629, 0.49249522841152,
0.501087237376189, 0.504282875285597, 0.509923189883806,
0.512543583522428, 0.516145773969493, 0.517377526505327,
0.516160210949451, 0.514249381591851, 0.515095766797131,
0.512427733792008, 0.515117600490143, 0.509917348559294,
0.507838070157467, 0.505295798702281, 0.504929502636041,
0.500265191435747, 0.497015315029826, 0.487320048031361,
0.487777758974984, 0.485618508316968, 0.476952624245141,
0.475303845688937, 0.474006216097499, 0.461848434437896,
0.458332447053067, 0.453446492173319, 0.449843396834474,
0.441924663807357, 0.43838647075641, 0.429512142424767,
0.428074776646514, 0.422959937779594, 0.417528249217847,
0.410848959103104, 0.408669676593975, 0.401633566673017,
0.401134906526841, 0.390649687094264, 0.38747992343559,
0.382243413467166, 0.378522848674293, 0.374564896691806,
0.367458951184484, 0.362988549853204, 0.359544379099291,
0.353591368503773, 0.347167348783288, 0.34532934013547,
0.343491754076066, 0.334715970021219, 0.328658320850336,
0.327302967322452, 0.325237744264657, 0.317196459879728,
0.314765696718547, 0.307332293377655, 0.309124724513742,
0.301419471275718, 0.299942126585102, 0.294086480682256,
0.29451286892268, 0.286642099560306, 0.284687076424098,
0.278509088913386, 0.279246898930461, 0.272296945853559,
0.275854357665941, 0.266234682115901, 0.264232235767492,
0.260743675639475, 0.255895230554581, 0.253129574082959,
0.253298405429449, 0.248730389085991, 0.244982024541409,
0.243653272630269, 0.242542398779603, 0.240009571527733,
0.235318245743064, 0.230953677868414, 0.233100068287879,
0.227364492975657, 0.227413577565514, 0.223276423252749,
0.220469116366241, 0.217005874041464, 0.218544785776868,
0.214799027675302, 0.214018994678519, 0.209908302955636,
0.209051702471355, 0.208269790368667, 0.204259169294716,
0.203328013924332, 0.20139968939544, 0.196635030214222,
0.197297827567890, 0.192382446324047, 0.190582509801817,
0.189428806176448, 0.189018477853706, 0.186473265172133,
0.185725521054363, 0.183336063547263, 0.179873235505833,
0.181615456173920, 0.178567664485195, 0.180557785189292,
0.176737837993348, 0.174040551678814, 0.171824187553651,
0.171777723418986, 0.168380946262357, 0.167631607118801,
0.166919135507693, 0.164922649827378, 0.162995673372005,
0.162041121757856, 0.160429501411519, 0.158707612157130,
0.158642112150017, 0.157617876132955, 0.155840318142859,
0.155284818162058, 0.154345535308525, 0.152630388942585,
0.150400283124370, 0.150179674628796, 0.148869143035009,
0.147554042030182, 0.147637243060954, 0.146194131788119,
0.145835948812554, 0.143900378918811, 0.142903437859195,
0.140917152296187, 0.139117847089593, 0.139003657513961,
0.137598972361976, 0.136898074042553, 0.137154473844298,
0.138277493211632, 0.136153278722467, 0.133522299804145,
0.133384294590176, 0.132111294310897, 0.131449376323826,
0.129586583208922, 0.129584131533865, 0.128605107720163,
0.128189826312729, 0.126278134313609, 0.126045116482753,
0.125363001954594, 0.125224617388382, 0.126668143826167,
0.123422245086036, 0.122700642899329, 0.120987094238997,
0.120618983640502, 0.120998211699260, 0.119009954803664,
0.119072562187199, 0.116957337765395, 0.116680737862498,
0.117294560721681, 0.116695492579975, 0.114830982812096,
0.114452052183997, 0.114245211769627, 0.114315514762654,
0.112282326346754, 0.111852441235201, 0.110154831749858,
0.110949143154516, 0.111595448779907, 0.110139507919548,
0.109619808328594, 0.107627781123346, 0.106292421187722,
0.107528857315614, 0.107070062504316, 0.104962719477169,
0.105885465593304, 0.105345175432258, 0.104004548692924,
0.104007877693652, 0.103411120226547, 0.101789057880723,
0.101536467048211, 0.101502818722149, 0.101222738630674,
0.100589257283155, 0.100600012398812, 0.0994090515882939,
0.098141116855587, 0.0983345183753183, 0.0983475058437739,
0.0978642331067521, 0.0967356239827741, 0.0976418040766334,
0.0962194080615377, 0.0944875846858419, 0.0952789448608961,
0.0944033012813256, 0.0937156161305736, 0.0950085227687757,
0.0938882650397986, 0.0922415298468536, 0.0925269942322057,
0.0922305335446072, 0.092350127862761, 0.0908886172472816,
0.0906072445847259, 0.0897827360739802, 0.0907187777163641,
0.0894486510392851, 0.0893203696074944, 0.0885045853082157,
0.088157737706543, 0.0888194346308406, 0.0886673668526806,
0.0872805761693292, 0.0866006855426778, 0.0873018174147107,
0.0864056772925893, 0.085843020560773, 0.085786798274907,
0.084957644963066, 0.08442702492386, 0.0838130981202873,
0.0838018083043259, 0.0844442109155162, 0.0836936371055533,
0.083441746455094, 0.0824912376277994, 0.0831439339542078,
0.0826213771814651, 0.0817736620904201, 0.081650093627315,
0.0814936959202959, 0.0804695057361529, 0.079961385522678,
0.0805956075603186, 0.0798579970053057, 0.0790915589787416,
0.0795055152002543, 0.0794399668442776, 0.0787265600649642,
0.0773199836971551, 0.0782699753415416, 0.0775746639743982,
0.0771684649725518, 0.0768586185492326, 0.0768449587685232,
0.0768041986132872, 0.07564320206542, 0.0759214939671308,
0.075275584293215, 0.0759191546693133, 0.0744105683163762,
0.0749816614371138, 0.0746608077961628, 0.0741655284219431,
0.0739561819308535, 0.0734252353479796, 0.0735356772211536,
0.0727903233661427, 0.0730900291306994, 0.0721686067912985,
0.071879392007249, 0.0721158795158988, 0.0719603110339099,
0.0710458334842105, 0.0706505701035134, 0.0714675497242161,
0.0708831343963561, 0.0704377484045542, 0.0704691611990377,
0.070369020316722, 0.0700854770164202, 0.0701091716474867,
0.0696031176289019)
D.vec <- c(0, 0.1, 0.149832775919732,
0.199665551839465, 0.249498327759197, 0.29933110367893,
0.349163879598662, 0.398996655518395, 0.448829431438127,
0.49866220735786, 0.548494983277592, 0.598327759197325,
0.648160535117057, 0.697993311036789, 0.747826086956522,
0.797658862876254, 0.847491638795987, 0.89732441471572,
0.947157190635452, 0.996989966555184, 1.04682274247492,
1.09665551839465, 1.14648829431438, 1.19632107023411,
1.24615384615385, 1.29598662207358, 1.34581939799331,
1.39565217391304, 1.44548494983278, 1.49531772575251,
1.54515050167224, 1.59498327759197, 1.64481605351171,
1.69464882943144, 1.74448160535117, 1.79431438127090,
1.84414715719064, 1.89397993311037, 1.9438127090301,
1.99364548494983, 2.04347826086957, 2.09331103678930,
2.14314381270903, 2.19297658862876, 2.24280936454850,
2.29264214046823, 2.34247491638796, 2.39230769230769,
2.44214046822743, 2.49197324414716, 2.54180602006689,
2.59163879598662, 2.64147157190635, 2.69130434782609,
2.74113712374582, 2.79096989966555, 2.84080267558528,
2.89063545150502, 2.94046822742475, 2.99030100334448,
3.04013377926421, 3.08996655518395, 3.13979933110368,
3.18963210702341, 3.23946488294314, 3.28929765886288,
3.33913043478261, 3.38896321070234, 3.43879598662207,
3.48862876254181, 3.53846153846154, 3.58829431438127,
3.63812709030100, 3.68795986622074, 3.73779264214047,
3.7876254180602, 3.83745819397993, 3.88729096989967,
3.9371237458194, 3.98695652173913, 4.03678929765886,
4.08662207357860, 4.13645484949833, 4.18628762541806,
4.23612040133779, 4.28595317725753, 4.33578595317726,
4.38561872909699, 4.43545150501672, 4.48528428093645,
4.53511705685619, 4.58494983277592, 4.63478260869565,
4.68461538461538, 4.73444816053512, 4.78428093645485,
4.83411371237458, 4.88394648829431, 4.93377926421405,
4.98361204013378, 5.03344481605351, 5.08327759197324,
5.13311036789298, 5.18294314381271, 5.23277591973244,
5.28260869565217, 5.33244147157191, 5.38227424749164,
5.43210702341137, 5.4819397993311, 5.53177257525084,
5.58160535117057, 5.6314381270903, 5.68127090301003,
5.73110367892977, 5.7809364548495, 5.83076923076923,
5.88060200668896, 5.9304347826087, 5.98026755852843,
6.03010033444816, 6.07993311036789, 6.12976588628763,
6.17959866220736, 6.22943143812709, 6.27926421404682,
6.32909698996656, 6.37892976588629, 6.42876254180602,
6.47859531772575, 6.52842809364549, 6.57826086956522,
6.62809364548495, 6.67792642140468, 6.72775919732442,
6.77759197324415, 6.82742474916388, 6.87725752508361,
6.92709030100334, 6.97692307692308, 7.02675585284281,
7.07658862876254, 7.12642140468227, 7.17625418060201,
7.22608695652174, 7.27591973244147, 7.3257525083612,
7.37558528428094, 7.42541806020067, 7.4752508361204,
7.52508361204013, 7.57491638795987, 7.6247491638796,
7.67458193979933, 7.72441471571906, 7.7742474916388,
7.82408026755853, 7.87391304347826, 7.923745819398,
7.97357859531773, 8.02341137123746, 8.0732441471572,
8.12307692307692, 8.17290969899665, 8.22274247491639,
8.27257525083612, 8.32240802675585, 8.37224080267559,
8.42207357859532, 8.47190635451505, 8.52173913043478,
8.57157190635452, 8.62140468227425, 8.67123745819398,
8.72107023411371, 8.77090301003344, 8.82073578595318,
8.87056856187291, 8.92040133779264, 8.97023411371237,
9.0200668896321, 9.06989966555184, 9.11973244147157,
9.1695652173913, 9.21939799331104, 9.26923076923077,
9.3190635451505, 9.36889632107023, 9.41872909698997,
9.4685618729097, 9.51839464882943, 9.56822742474916,
9.6180602006689, 9.66789297658863, 9.71772575250836,
9.7675585284281, 9.81739130434783, 9.86722408026756,
9.9170568561873, 9.96688963210702, 10.0167224080268,
10.0665551839465, 10.1163879598662, 10.1662207357860,
10.2160535117057, 10.2658862876254, 10.3157190635452,
10.3655518394649, 10.4153846153846, 10.4652173913043,
10.5150501672241, 10.5648829431438, 10.6147157190635,
10.6645484949833, 10.714381270903, 10.7642140468227,
10.8140468227425, 10.8638795986622, 10.9137123745819,
10.9635451505017, 11.0133779264214, 11.0632107023411,
11.1130434782609, 11.1628762541806, 11.2127090301003,
11.2625418060201, 11.3123745819398, 11.3622073578595,
11.4120401337793, 11.461872909699, 11.5117056856187,
11.5615384615385, 11.6113712374582, 11.6612040133779,
11.7110367892977, 11.7608695652174, 11.8107023411371,
11.8605351170569, 11.9103678929766, 11.9602006688963,
12.0100334448161, 12.0598662207358, 12.1096989966555,
12.1595317725753, 12.2093645484950, 12.2591973244147,
12.3090301003344, 12.3588628762542, 12.4086956521739,
12.4585284280936, 12.5083612040134, 12.5581939799331,
12.6080267558528, 12.6578595317726, 12.7076923076923,
12.7575250836120, 12.8073578595318, 12.8571906354515,
12.9070234113712, 12.9568561872910, 13.0066889632107,
13.0565217391304, 13.1063545150502, 13.1561872909699,
13.2060200668896, 13.2558528428094, 13.3056856187291,
13.3555183946488, 13.4053511705686, 13.4551839464883,
13.5050167224080, 13.5548494983278, 13.6046822742475,
13.6545150501672, 13.7043478260870, 13.7541806020067,
13.8040133779264, 13.8538461538462, 13.9036789297659,
13.9535117056856, 14.0033444816054, 14.0531772575251,
14.1030100334448, 14.1528428093646, 14.2026755852843,
14.2525083612040, 14.3023411371237, 14.3521739130435,
14.4020066889632, 14.4518394648829, 14.5016722408027,
14.5515050167224, 14.6013377926421, 14.6511705685619,
14.7010033444816, 14.7508361204013, 14.8006688963211,
14.8505016722408, 14.9003344481605, 14.9501672240803,
15)
if (is.na(x)) return(NA);
if (x > 15) {y <- 1/x
} else {
ind <- which.min(abs(x-D.vec));
y <- v[ind]}
return(y);
}
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