R/sdfFGN.R

In FGN: Fractional Gaussian Noise and power law decay time series model fitting

sdfFGN <- function(H, n){
hs<-c(0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
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0.5,
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0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
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0.9,
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0.05,
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0.15000000000000002,
0.2,
0.25,
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0.05,
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0.2,
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0.4,
0.45,
0.5,
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0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
0.35000000000000003,
0.4,
0.45,
0.5,
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0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
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0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
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0.30000000000000004,
0.35000000000000003,
0.4,
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0.75,
0.8,
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0.9,
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0.2,
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0.6000000000000001,
0.65,
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0.75,
0.8,
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0.9,
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0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
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0.35000000000000003,
0.4,
0.45,
0.5,
0.55,
0.6000000000000001,
0.65,
0.7000000000000001,
0.75,
0.8,
0.8500000000000001,
0.9,
0.9500000000000001,
0.05,
0.1,
0.15000000000000002,
0.2,
0.25,
0.30000000000000004,
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0.4,
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0.1760038744016896,
0.15915494309189532,
0.1422640633872097,
0.12539160240184324,
0.10860311195429198,
0.09196932977067568,
0.07556612107288356,
0.05947435175108323,
0.04377968348224836,
0.02857228130698079,
0.013946422873553835,
0.3037439258895553,
0.2888063043601276,
0.27351704312820935,
0.257899826942864,
0.24198223927932014,
0.22579599153878835,
0.20937714223486362,
0.19276630196079475,
0.17600881940424523,
0.15915494309189535,
0.14225995300584748,
0.12538425556809468,
0.10859343491536459,
0.09195825284821926,
0.0755545888954427,
0.05946331212746812,
0.043770074798009165,
0.028565018575793494,
0.01394238149221338)
xo <- 2*pi*(1:floor(n/2))/n
ind <- xo < 0.1
xoLow <- xo[!ind]
xoHi <- xo[ind]
zLow <- as.vector(interp(x=lams, y=hs, z=sdfs, xo=xoLow, yo=H, linear=TRUE)$z)
zHi <- (sin(pi*H)*gamma(2*H+1)*xoHi^(1-2*H))/(2*pi)
if (H<0.05 || H>0.95)
    zLow <- (sin(pi*H)*gamma(2*H+1)*xoLow^(1-2*H))/(2*pi)
c(zHi, zLow)
}