draw.gamma.alpha.less.than.one: Generates variation from Gamma distribution with alpha<1

Description Usage Arguments Value References Examples

View source: R/draw.gamma.alpha.less.than.one.R

Description

This function implements pseudo-random number generation for a gamma distribution for α<1 with pdf

f(x|α,β)=\frac{1}{Γ(α)β^{α}}x^{α-1}e^{-x/β}

for 0 ≤q x < ∞ and \min(α,β)>0 where α and β are the shape and scale parameters, respectively.

Usage

1

Arguments

nrep

Number of data points to generate.

alpha

Shape parameter for desired gamma distribution. Must be less than 1.

beta

Scale parameter for desired gamma distribution.

Value

A list of length five containing generated data, the theoretical mean, the empirical mean, the theoretical variance, and the empirical variance with names y, theo.mean, emp.mean, theo.var, and emp.var, respectively.

References

Ahrens, J. H., & Dieter, U. (1974). Computer methods for sampling from gamma, beta, poisson and binomial distributions. Computing, 1, 223-246.

Examples

1
draw.gamma.alpha.less.than.one(nrep=100000,alpha=0.5,beta=2)

Example output

$y
     [1] 6.130583e-01 1.696769e+00 6.933895e-01 7.039627e-01 2.988526e+00
     [6] 5.789858e+00 3.212172e-01 5.027064e-01 8.897131e-03 9.445264e-01
    [11] 9.264500e-02 7.715085e-01 7.115674e-04 7.146609e-01 1.623273e-01
    [16] 3.490255e-01 2.188843e+00 2.372095e-01 2.542133e+00 6.444552e-02
    [21] 3.548279e-04 1.557100e+00 9.005480e-02 8.047754e-01 2.047535e-02
    [26] 2.030995e-01 1.108691e+00 1.586625e-02 6.927904e-01 1.271387e+00
    [31] 2.113272e+00 9.597596e-02 7.353214e-01 1.426952e-01 1.844752e-01
    [36] 2.817109e+00 7.651664e-01 3.410285e-01 6.728693e-01 3.074337e-01
    [41] 1.126608e-02 6.080656e+00 7.891524e-01 1.611880e+00 6.576221e+00
    [46] 9.765002e-01 2.448569e-01 1.142199e+00 1.614277e+00 1.626012e-01
    [51] 3.762691e-01 6.399777e-01 6.483639e-02 4.253842e+00 3.067456e-01
    [56] 2.988910e-01 2.742050e+00 5.171203e+00 1.727592e-01 8.540185e-03
    [61] 2.080410e-01 3.366008e-01 1.507825e+00 4.781764e-03 6.643731e-05
    [66] 1.867265e-01 4.859034e-05 1.582754e-01 3.703866e-03 1.435922e-01
    [71] 3.425153e-03 3.402427e-01 1.293424e+00 2.824088e+00 2.498270e-01
    [76] 4.703256e+00 2.976439e+00 1.952527e-03 1.678771e+00 9.350011e-01
    [81] 2.587454e+00 1.803809e-02 3.120106e-01 8.172241e-01 9.559946e-01
    [86] 5.532192e-02 1.245623e+00 6.784352e+00 5.632233e-02 4.437427e-02
    [91] 2.619454e+00 1.822655e-01 1.762296e+00 3.923278e-01 5.217634e-01
    [96] 3.483501e-02 1.239734e-02 8.878193e-02 3.161582e-01 3.577951e-03
   [101] 2.391586e-03 5.797689e-02 1.805039e-02 4.202834e-01 4.469650e+00
   [106] 1.060234e+00 5.691360e-02 2.425992e-02 8.051760e-06 1.347401e+00
   [111] 1.168639e+00 1.838730e-01 2.347392e+00 3.476103e-01 3.001266e-01
   [116] 1.051101e-04 6.698055e-01 8.210690e-01 5.343946e-04 1.028016e+00
   [121] 2.507425e+00 1.356966e+00 1.076133e+00 1.213981e+00 5.601073e-01
   [126] 2.726938e+00 1.273434e+00 5.359121e-01 6.630600e+00 3.516373e-03
   [131] 5.278893e-04 5.191882e-03 3.697571e-02 8.001067e-02 5.973061e-01
   [136] 6.510369e-01 7.687366e-03 3.181551e-01 4.690877e+00 1.621916e-01
   [141] 3.131179e-02 1.399394e-01 2.600333e-02 4.193598e-01 2.009305e+00
   [146] 8.840627e-01 1.535246e+00 2.851059e-01 8.319050e-01 3.733827e-01
   [151] 3.378571e+00 1.022121e+00 1.244225e-02 2.486744e+00 7.397490e+00
   [156] 4.449272e-02 1.277165e+00 4.007521e-01 4.133292e-02 3.255867e-01
   [161] 1.104349e-01 4.669339e-02 8.367290e-02 5.336294e-01 4.468841e+00
   [166] 3.737837e+00 2.664590e-01 5.462028e-02 1.252593e+00 3.462831e-02
   [171] 8.764492e-02 2.352657e-01 3.281276e+00 9.591186e-02 1.184731e-01
   [176] 4.611838e-01 4.876899e+00 1.847615e+00 7.167957e-01 1.905223e-02
   [181] 9.426186e-01 2.751496e-02 4.839447e-01 4.356289e-02 2.563022e-01
   [186] 3.195353e+00 1.573656e-01 3.698190e+00 2.203673e-01 6.819124e-01
   [191] 1.017016e-02 4.292109e-01 7.996505e+00 1.196225e-01 4.102282e-02
   [196] 1.237325e-01 3.101235e+00 8.776529e-01 7.105577e-01 5.222478e-03
   [201] 4.956525e-02 1.486274e+00 1.722970e-01 6.857240e-01 9.969026e+00
   [206] 4.574989e-01 1.449134e+00 4.251950e+00 2.707977e-01 2.430605e-01
   [211] 7.775656e-02 3.793328e-01 3.334940e-01 9.992998e-02 8.791022e-01
   [216] 1.762322e+00 1.074132e-01 4.337399e-06 1.374250e-01 3.915824e+00
   [221] 6.286975e+00 9.455372e-01 7.879726e-02 3.590046e-02 4.459231e+00
   [226] 9.212899e-03 7.517219e-01 9.725189e-03 1.474878e-01 7.891550e-02
   [231] 9.313935e-01 1.137874e-01 3.436412e-02 1.064807e-01 3.204822e+00
   [236] 2.045643e+00 2.252134e-02 1.084881e-02 3.465602e-01 1.756610e-02
   [241] 7.646395e-01 1.360751e+00 3.120432e+00 4.456303e-01 1.600437e+00
   [246] 2.220617e-01 4.323171e-02 2.303235e+00 1.896411e+00 1.117197e+00
   [251] 1.426593e+00 4.972283e-02 5.936215e-01 2.269140e+00 4.023011e+00
   [256] 3.882834e-01 2.609192e-03 8.154509e-01 4.777380e-01 3.121877e+00
   [261] 5.329296e-01 1.264929e+00 2.669511e-03 5.732262e-04 4.801240e-02
   [266] 4.464543e-03 6.444291e-02 2.986973e-01 1.040821e-01 1.532911e+00
   [271] 6.127924e-01 3.386853e-02 2.295498e-04 1.210007e+00 4.920062e-01
   [276] 2.574700e+00 1.821613e+00 2.842726e-03 4.039463e-01 1.385612e+00
   [281] 4.031240e-01 7.968307e-01 3.177765e-03 4.658503e+00 1.780878e-02
   [286] 4.705637e-01 4.043354e-02 1.193931e+00 3.711464e-01 1.914879e-01
   [291] 6.081037e-03 7.445157e-01 6.040322e-01 4.195086e+00 2.901530e+00
   [296] 3.267273e+00 4.410659e-01 1.654856e-01 1.344058e-01 6.479054e-03
   [301] 1.135972e+01 2.149446e-01 1.325013e-01 3.113161e-02 5.099681e-01
   [306] 2.905061e+00 1.664434e+00 9.291465e-02 7.559883e-02 7.804175e-01
   [311] 8.337137e-02 9.558843e-01 1.450352e+00 6.490264e-01 1.321587e+00
   [316] 1.865839e+00 4.173029e-01 3.945533e-01 8.193754e-01 1.610311e+00
   [321] 1.277491e-01 2.687819e+00 5.988372e-01 9.845745e-01 1.667674e+00
   [326] 2.439681e+00 5.226920e-02 5.171651e-03 1.022123e-01 7.571349e-03
   [331] 1.320868e-01 1.471022e-01 9.416976e-02 4.212927e-01 2.148808e+00
   [336] 1.523765e+00 5.424293e-02 6.944656e-01 3.459601e-01 2.106567e+00
   [341] 1.527384e-02 1.393185e-02 9.163092e-04 1.778503e+00 1.234489e+00
   [346] 1.512949e-01 2.022161e+00 7.192221e-01 6.888277e-01 1.492573e+00
   [351] 1.332758e+00 2.534908e+00 3.184958e+00 7.339563e-03 2.961829e+00
   [356] 1.503740e+00 5.971957e-01 1.577181e-05 9.377012e-01 9.952207e-01
   [361] 1.467886e-02 1.372669e-01 7.600630e-01 3.491387e-01 1.111876e-01
   [366] 5.390891e-02 3.254202e+00 1.320829e-01 2.191014e+00 4.933692e-01
   [371] 1.937015e+00 2.074398e+00 1.253816e+00 5.821476e-01 2.698186e+00
   [376] 2.689844e-01 2.097414e-01 2.203377e-01 8.414939e-02 2.267739e-01
   [381] 4.524809e-01 1.507474e+01 2.547382e+00 1.928067e-01 9.985938e-01
   [386] 9.528084e-01 3.048861e-01 8.006249e-02 4.232178e-02 1.843860e+00
   [391] 3.216570e-02 8.410819e-01 8.632553e-03 3.229549e-01 4.609919e+00
   [396] 2.570867e-01 5.974690e-02 1.903407e-01 1.062420e+00 1.579993e-02
   [401] 1.424079e+00 2.211131e-01 2.429409e-04 1.272815e-01 7.364882e-01
   [406] 6.218140e-01 1.554445e+00 5.170564e-02 8.711056e-01 3.125210e+00
   [411] 3.095733e+00 2.043963e+00 1.025860e+00 2.458827e-01 8.878706e-02
   [416] 3.356715e-01 6.054363e-02 1.251496e+00 1.980794e-01 1.242938e+00
   [421] 5.252332e-02 2.577810e-02 3.376992e-01 4.148862e-01 5.292795e-01
   [426] 6.796297e-01 4.047284e-03 3.646902e-02 9.791984e-01 3.981675e-04
   [431] 6.739136e-01 5.839122e-01 1.524046e-04 2.209115e-03 4.218884e-02
   [436] 5.978526e-02 1.166682e-01 3.316321e+00 8.658384e-03 1.751783e-01
   [441] 1.919014e-01 1.066891e+00 2.152360e+00 2.747672e-01 2.465064e-01
   [446] 4.920644e-01 5.810646e-02 3.931938e-01 4.410547e-01 9.599448e-01
   [451] 5.115361e-02 4.283397e-03 5.345720e-01 1.054643e-02 1.321449e+00
   [456] 2.399601e+00 3.468598e+00 2.868024e-01 1.162929e+00 9.670164e-02
   [461] 1.560736e+00 3.854071e-01 4.583155e-01 5.584209e-01 1.409141e+00
   [466] 2.690790e-01 1.458717e-01 3.141797e-04 1.034282e+00 2.045742e-02
   [471] 1.950510e-04 2.413617e+00 9.077125e-01 7.884766e-04 7.429347e-01
   [476] 7.641644e-02 1.229344e-01 1.250790e-02 4.143956e-01 1.307785e+00
   [481] 8.428626e-01 2.137495e-03 2.665658e-02 4.379244e-01 8.184827e-01
   [486] 6.248986e-02 2.850218e+00 8.222205e-01 1.299094e-01 2.969843e-01
   [491] 7.208000e-02 3.661173e-01 1.786016e+00 1.864556e-01 3.781719e+00
   [496] 3.179961e+00 3.094121e-03 3.591044e-01 9.587068e-01 4.105257e-01
   [501] 8.958812e-01 4.417513e-02 6.975279e-01 2.703533e-02 5.608625e-02
   [506] 5.781546e-01 1.372812e+00 5.985370e-01 3.901808e-02 1.034811e-05
   [511] 3.988263e-01 2.022880e+00 5.328616e-03 1.435419e+00 2.463382e-01
   [516] 2.439408e-01 5.628910e-01 2.175528e+00 8.494858e-02 2.010352e-01
   [521] 1.527212e-01 1.598553e-01 2.623171e-01 4.102920e-02 7.154443e-01
   [526] 2.080984e+00 1.104711e+00 2.579207e+00 2.491470e+00 2.419899e-01
   [531] 2.262743e-01 3.133785e-02 4.156624e-01 5.288244e-02 4.746322e-01
   [536] 1.824146e-02 2.763468e-01 7.741578e-01 1.479222e+00 4.020460e-01
   [541] 1.841414e-03 8.732341e-05 1.266709e+00 1.275717e-01 2.752953e-05
   [546] 8.719835e-01 1.023486e-01 1.477418e+00 1.920677e+00 2.559876e-01
   [551] 3.074941e+00 4.068897e-04 1.872139e-01 2.482942e-01 2.235202e-03
   [556] 1.020219e-01 6.312322e-02 1.060419e-01 2.852537e-01 6.892143e-01
   [561] 1.123880e+00 2.363775e-02 9.478864e-01 1.147294e-02 4.726215e-03
   [566] 8.744781e-02 1.032352e+00 1.439300e+00 2.466659e-02 1.253263e+00
   [571] 3.199332e+00 2.324714e-02 3.500485e-02 2.679978e+00 2.090681e-01
   [576] 1.087100e-01 3.454965e-02 1.903538e-01 3.004072e+00 4.134752e-01
   [581] 2.372549e-01 7.011009e-01 5.121848e+00 5.742119e+00 8.347856e-02
   [586] 1.184881e-01 1.799094e+00 8.411309e-01 1.939359e+00 8.418344e-01
   [591] 1.204333e+00 9.624224e-01 1.109352e-01 3.899574e-01 1.858671e-01
   [596] 9.569776e-02 8.368929e-01 5.073608e-02 1.932517e-01 9.275884e-02
   [601] 5.577769e-01 5.571816e-01 1.468137e-01 9.552464e-02 1.452746e+00
   [606] 2.470873e+00 1.816899e-02 1.889182e+00 9.817924e-01 9.200946e-02
   [611] 1.085497e+00 1.582587e-01 4.050376e-02 5.528339e-01 3.906304e-02
   [616] 5.159405e-02 3.477253e-01 4.162757e-01 1.322192e-02 7.972116e-01
   [621] 1.894310e-03 1.861877e-02 2.204991e-01 5.287976e-03 3.017064e-01
   [626] 5.011168e-01 1.408178e+00 2.101321e-01 2.875009e-02 7.091089e-01
   [631] 2.172100e-01 1.817588e-01 3.033944e+00 1.461374e+00 4.207642e-02
   [636] 7.423329e-01 3.051180e+00 4.195183e+00 6.613219e-01 1.761205e+00
   [641] 1.191312e-01 1.305339e-01 6.144317e-01 4.247293e-01 1.833493e+00
   [646] 2.215024e+00 2.435294e+00 6.491331e-01 5.286689e-01 5.513301e-02
   [651] 2.336943e-01 4.246377e-01 2.198352e+00 7.647241e-02 6.147454e-01
   [656] 4.651463e-01 2.672913e+00 2.443087e+00 8.469278e-01 3.009592e+00
   [661] 6.849589e-02 1.005436e+00 2.317564e+00 1.576950e-05 9.250179e-01
   [666] 1.748250e-01 3.910230e+00 7.146965e+00 3.808007e+00 3.572260e-02
   [671] 4.749308e-01 5.624676e-03 4.132737e-01 1.319368e-01 1.085396e+00
   [676] 3.628867e+00 3.362121e-03 4.278651e-01 3.939884e-03 1.200320e-01
   [681] 2.309283e-01 1.015092e+00 1.169719e-01 3.944571e-01 3.114509e-01
   [686] 1.446412e+00 1.166980e-01 1.798585e-02 5.124669e-01 1.623094e-01
   [691] 2.285083e-01 5.116478e-02 1.005418e-01 8.970238e-01 4.431758e-01
   [696] 3.217744e-01 6.647790e-03 6.810744e-02 2.939456e-02 3.338231e+00
   [701] 2.626297e+00 2.443769e+00 2.114458e+00 4.480505e+00 2.666511e-01
   [706] 2.507782e+00 1.374029e-01 7.590010e-01 2.493547e-01 4.791165e-02
   [711] 5.866783e+00 2.639586e-01 1.412471e+00 1.223673e-01 2.447169e+00
   [716] 6.236552e-01 1.002961e+00 1.183536e-02 4.661975e+00 3.389255e-02
   [721] 1.679162e-01 3.787591e+00 2.054529e+00 5.493415e-01 2.025963e+00
   [726] 1.369162e+00 4.566254e-01 1.848792e-01 2.343143e+00 2.000889e-02
   [731] 3.723943e+00 8.491366e-01 2.328544e+00 1.643330e+00 4.913598e-03
   [736] 1.872188e-03 2.610128e-01 2.888567e-01 5.040699e-03 2.925201e-01
   [741] 3.139168e+00 8.711500e-01 6.038024e-01 1.569592e-01 1.344548e-01
   [746] 1.306590e-01 3.963381e-05 1.910402e-02 2.243370e+00 1.083560e+00
   [751] 3.629204e-01 1.264795e+00 3.026336e-02 1.478970e-02 1.370177e+00
   [756] 1.109379e-01 3.965501e+00 3.083718e-01 2.224135e+00 5.170654e-01
   [761] 1.503939e+00 8.865205e-02 8.527740e-01 5.489324e-01 1.415618e+00
   [766] 3.629058e-01 1.525764e-03 5.954229e-02 6.153638e-01 5.791608e-04
   [771] 1.189472e-01 2.594983e-01 1.108468e+00 4.270796e-01 1.363844e-01
   [776] 7.290386e-02 6.718217e-01 2.128679e-01 5.101425e+00 9.060073e-01
   [781] 4.654265e-02 3.558106e-03 1.307472e+00 2.669315e-01 2.021378e-01
   [786] 1.509308e+00 1.194347e-01 4.842638e-02 5.892557e-02 1.063111e-01
   [791] 2.136181e-02 1.859123e+00 3.850501e-01 1.954702e+00 1.130708e+00
   [796] 7.090010e+00 4.870910e+00 3.628391e-01 7.813847e-02 1.290948e+01
   [801] 3.192132e-01 9.726223e-01 7.104782e-02 1.498059e-04 2.988838e+00
   [806] 7.163035e-01 2.813718e+00 1.204715e+00 3.161168e-01 7.415100e-01
   [811] 1.183270e+00 4.051835e-01 1.094698e-02 1.689912e+00 2.304875e-02
   [816] 2.605473e-01 2.233327e+00 1.275496e-01 1.526905e+00 6.147764e-02
   [821] 1.452486e+00 9.587191e-03 1.605430e+00 2.015181e-04 9.001258e-01
   [826] 4.216894e-01 3.373450e+00 3.651738e-01 5.524966e+00 1.094909e+00
   [831] 5.386145e+00 1.434822e+00 2.130145e-01 2.235000e-02 1.316378e-01
   [836] 2.575917e+00 2.309674e+00 4.815625e-02 2.839118e-02 5.934349e-01
   [841] 2.897221e+00 9.549176e-01 3.831344e-02 3.996555e-04 7.458975e-01
   [846] 2.277539e-01 6.397139e-01 1.101890e+00 1.256268e+00 6.833462e-01
   [851] 8.264356e-03 3.409026e-01 1.192552e-02 8.983549e-03 4.867372e+00
   [856] 7.776104e-01 7.398516e-03 7.350560e-04 1.533786e+00 1.701679e-01
   [861] 5.977318e-02 1.347416e+00 4.732253e-01 1.696840e-02 1.523504e+00
   [866] 1.907373e-04 3.368878e+00 5.251917e-01 2.927679e+00 1.339947e-01
   [871] 1.346707e-02 2.501201e-04 3.289190e-01 1.018889e+00 6.783694e-01
   [876] 4.880073e-01 1.977420e-01 1.390965e-01 2.677321e+00 7.812279e-01
   [881] 5.926304e-02 1.031333e-01 7.186645e-01 4.354138e-01 2.646345e-01
   [886] 1.407906e+00 1.009623e-01 7.979043e-02 4.299301e-02 6.244070e-02
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  [1786] 9.645195e+00 8.934395e-02 5.083398e+00 1.346591e+00 8.013518e-01
  [1791] 1.993242e-03 1.293333e+00 3.569777e-03 1.006777e-01 2.658475e-02
  [1796] 6.333295e-02 1.286543e-01 6.991264e-01 8.711908e-04 2.325000e-01
  [1801] 2.046810e-03 3.853799e-01 1.964386e-04 2.984773e-03 3.373224e-01
  [1806] 5.173325e-02 4.135027e-02 2.114241e-02 8.755683e-01 1.301723e-02
  [1811] 1.095197e-01 1.875639e-02 2.011503e-02 2.071991e+00 1.533710e+00
  [1816] 4.076388e-03 7.289784e-01 7.572823e-02 2.429396e+00 6.873785e-01
  [1821] 1.626976e-01 4.691429e-02 4.290893e-03 1.376988e-01 5.798181e-01
  [1826] 4.946908e-01 4.025730e-01 8.794054e-01 2.953372e+00 1.639486e+00
  [1831] 1.122120e+00 5.970686e-01 1.593026e-01 5.384147e-04 1.070100e+00
  [1836] 3.708044e-02 8.776289e-01 5.910143e-02 1.238020e+00 4.767990e-02
  [1841] 2.277682e+00 3.828134e-01 5.991097e-04 5.293417e-04 1.097752e+00
  [1846] 5.919569e-02 8.130464e-01 1.785863e-01 9.293737e-03 1.771717e-01
  [1851] 9.278914e-02 1.384672e+00 2.134704e+00 1.338623e-02 2.810787e-01
  [1856] 2.546600e-02 7.406243e-02 5.451185e-03 2.466673e+00 1.941694e+00
  [1861] 3.085868e-01 7.747265e+00 1.363504e-01 7.713802e-01 8.325817e-01
  [1866] 1.099033e-01 7.786191e-01 4.841406e-01 6.205810e-02 2.358702e+00
  [1871] 4.934200e-01 1.001154e-02 4.735353e+00 8.762294e-01 2.133243e+00
  [1876] 1.060135e+01 1.347789e+01 7.792921e-01 5.674034e-01 2.376279e+00
  [1881] 6.426926e-04 4.848572e+00 7.603048e-02 6.427661e-01 2.402633e+00
  [1886] 4.953254e+00 1.671369e+00 9.346923e-01 6.979242e-01 6.218542e+00
  [1891] 1.100878e+00 5.439614e-02 8.789911e-01 2.438582e-01 2.165951e+00
  [1896] 5.069807e-01 8.665818e-01 1.121235e+00 2.359183e-02 3.497196e-01
  [1901] 1.877465e-01 1.198759e+00 9.408928e-01 4.406898e+00 1.204167e+00
  [1906] 7.670409e-02 1.339551e+00 4.178251e+00 2.737307e+00 4.455622e-01
  [1911] 9.596661e-02 3.898846e-01 1.866805e-01 3.430547e-01 6.358155e-01
  [1916] 2.713207e-01 4.658102e-02 9.215578e-01 5.949042e-02 3.879328e-02
  [1921] 1.526238e+00 1.834686e-01 1.022236e+00 2.167709e+00 1.451764e-01
  [1926] 1.568316e-01 1.355744e+00 4.456192e-01 7.421570e-01 1.221822e+00
  [1931] 2.511517e+00 5.621147e-01 1.205945e+00 6.363055e-01 2.773350e-01
  [1936] 4.042311e+00 2.045796e-01 1.677295e-01 2.967083e-01 2.321157e+00
  [1941] 8.996463e-01 1.886073e-01 6.673477e-01 5.791268e-02 1.101518e-01
  [1946] 1.205295e+00 2.134480e+00 1.432193e+00 1.479380e+00 4.107727e-04
  [1951] 7.060608e-01 6.103855e-02 4.049372e-01 2.672897e+00 1.659004e+00
  [1956] 1.048172e-01 1.739028e+00 4.108578e-02 9.489618e-01 2.974824e-02
  [1961] 4.145889e+00 6.285174e-01 9.056083e-01 9.948943e-01 1.427675e-01
  [1966] 1.405519e-01 7.129971e-01 2.090858e+00 4.454561e-02 1.005229e+00
  [1971] 7.750132e-01 3.014897e-01 1.612244e+00 1.714917e-04 5.415615e-03
  [1976] 1.172751e+00 3.411584e-02 1.977697e-01 3.965750e-03 1.113226e-02
  [1981] 5.590742e+00 7.827394e-03 4.426241e-01 2.401517e+00 4.344365e+00
  [1986] 5.574260e-01 4.594135e-01 3.005442e-01 3.496017e-03 2.443972e-01
  [1991] 2.435252e-01 2.794059e+00 2.986804e-01 9.529673e-01 9.891182e-02
  [1996] 7.615991e-01 8.079746e-01 1.178748e+00 2.130552e-02 1.232908e-03
  [2001] 1.297235e+00 5.588140e-01 4.909921e-02 7.923190e-01 1.159842e-01
  [2006] 3.220738e-01 1.379317e-01 4.911599e-02 4.830037e-01 3.646474e+00
  [2011] 3.990397e-01 8.873718e-02 1.769602e+00 6.644567e-02 4.401337e-01
  [2016] 2.110254e-01 1.156886e+00 2.686985e-01 7.759482e-01 3.229367e-01
  [2021] 2.533767e+00 5.217431e+00 4.183944e-02 8.816534e-01 3.274197e+00
  [2026] 1.007556e-02 2.162411e+00 1.491094e+00 3.494666e-02 1.514647e-02
  [2031] 2.660388e-01 4.668068e+00 3.640930e-02 2.759999e-02 2.169075e+00
  [2036] 6.932106e+00 5.470843e-02 4.240300e-01 7.271873e-05 7.693463e-01
  [2041] 4.855736e+00 4.503375e-01 5.003296e-01 6.837772e-01 6.340924e-01
  [2046] 8.482247e-01 4.750164e-01 4.062524e+00 5.103563e-03 2.247078e-01
  [2051] 5.564076e-03 1.006726e-01 3.856105e-01 3.930259e-01 5.695077e+00
  [2056] 1.960281e-02 1.594867e-01 5.161573e-02 6.848581e-01 3.286920e-01
  [2061] 8.494640e-01 1.156818e-03 2.190594e-01 2.075366e-01 6.607311e-02
  [2066] 2.928076e-01 1.564381e-01 1.264633e+00 1.240023e+00 5.146094e-01
  [2071] 1.649582e+00 1.966041e+00 1.335112e+00 1.072660e+00 1.755739e+00
  [2076] 1.095271e-01 3.417038e-01 1.054685e-01 6.347847e-02 1.253139e+00
  [2081] 2.919185e-01 2.056808e+00 2.865175e-01 1.752708e-03 9.793198e-02
  [2086] 2.367786e-01 1.220724e+00 2.893212e-03 3.946678e-02 2.493920e+00
  [2091] 1.382318e+00 1.265041e+00 1.026162e-01 1.065699e-02 1.601334e+00
  [2096] 7.684612e-01 2.233332e-03 6.308267e-01 4.161087e+00 1.714537e+00
  [2101] 2.411973e-01 1.356308e-01 7.928762e-01 2.388061e+00 9.794264e-01
  [2106] 5.555549e-01 1.004137e-01 5.326088e-01 2.325949e-02 1.404921e+00
  [2111] 2.823014e-01 2.239283e-02 4.496059e-01 1.342959e-03 2.042030e-01
  [2116] 1.638822e-01 1.832018e-01 5.310398e-02 5.063243e-02 5.177211e-01
  [2121] 7.957688e-03 9.783031e-01 1.208789e+00 9.928974e-02 1.766206e-01
  [2126] 6.283894e-01 2.296112e+00 3.969601e-02 9.848984e-01 9.703895e-01
  [2131] 4.507554e-01 2.623789e+00 1.559055e+00 5.727594e-01 3.333512e-01
  [2136] 3.859932e-01 8.268232e-01 3.418449e-03 4.781801e-01 5.308818e-01
  [2141] 2.937437e-01 1.031695e+00 1.435211e+00 6.785984e-05 4.267246e-01
  [2146] 2.624802e-02 1.192715e+00 1.404703e-01 6.332644e-01 1.582535e+00
  [2151] 8.668796e-01 1.474926e-01 2.227151e-01 6.209333e-02 1.432788e-01
  [2156] 6.789859e-01 4.142643e-01 3.991040e-01 2.235869e-01 2.172078e-01
  [2161] 1.649223e+00 9.238186e-01 1.114717e+00 1.133663e+00 1.227823e+00
  [2166] 3.513450e-01 1.168571e-02 5.822699e-01 1.636894e+00 9.289710e-02
  [2171] 1.354977e+00 8.312718e-03 4.123120e-01 6.301824e-01 2.095790e-01
  [2176] 5.877312e+00 8.825686e-02 1.755763e-01 8.679475e-01 8.809618e-01
  [2181] 6.581734e-01 2.993296e+00 1.429814e-01 1.730336e+00 1.742437e-03
  [2186] 2.467155e+00 3.732394e-02 9.365755e-02 3.106862e+00 9.204523e-01
  [2191] 1.825776e-01 5.131421e-01 1.984603e-01 5.213888e-02 1.343623e+00
  [2196] 6.124677e+00 2.672794e-01 1.421467e+00 4.349753e-05 4.055047e-03
  [2201] 7.734633e-01 1.246647e+00 8.259969e-02 1.521567e-01 3.950951e-01
  [2206] 1.812631e+00 2.658161e+00 4.292986e-02 9.361113e-01 1.224173e-02
  [2211] 3.275062e+00 4.728514e-01 1.450620e+00 3.120613e+00 2.928858e-01
  [2216] 9.349309e-01 1.560202e+00 4.461217e-01 3.126611e+00 2.514740e-02
  [2221] 6.897668e-01 8.896848e-01 1.185955e-03 7.706631e-01 1.811378e+00
  [2226] 8.449345e-01 2.599389e-02 1.037901e+00 1.634770e-01 1.082969e-02
  [2231] 4.231330e-02 1.324859e+00 8.599139e-01 5.187343e+00 2.984186e-01
  [2236] 1.733312e-01 1.195963e+00 1.338950e+00 4.154453e-02 1.631930e-02
  [2241] 4.412533e-01 1.328863e-02 2.792514e-02 1.702868e+00 3.207440e-01
  [2246] 7.012549e-01 1.945985e-01 1.273971e+00 2.658255e-01 4.122813e+00
  [2251] 6.870818e-05 2.638614e+00 3.590070e+00 1.873894e-01 3.049361e-03
  [2256] 4.301479e-02 1.342069e+00 2.956481e-02 2.012414e+00 6.901295e-01
  [2261] 1.033846e+00 1.766699e-01 1.413304e+00 1.078122e-01 9.951184e-01
  [2266] 4.868973e-01 7.592753e-02 5.858332e-01 1.597909e+00 1.085761e+00
  [2271] 4.438997e+00 1.618166e+00 1.031269e-01 8.127740e-01 3.416780e-01
  [2276] 1.436352e+00 6.634368e-01 2.822765e+00 1.197108e+00 6.726046e-01
  [2281] 3.029557e+00 1.878900e-01 6.884445e-05 3.163200e-02 1.232043e+00
  [2286] 7.591564e+00 2.053490e-01 1.436445e+00 8.978955e-02 4.170160e-01
  [2291] 1.052500e-01 1.189426e-02 4.124218e-01 5.604380e-02 8.383480e-01
  [2296] 1.794139e-03 4.700483e-01 1.059309e-01 1.321601e-01 5.312353e-03
  [2301] 1.934159e-01 1.251156e-03 1.700962e-01 7.848130e-02 1.231268e+00
  [2306] 1.272213e+00 4.719561e+00 3.931067e-02 9.581898e-01 4.801879e-01
  [2311] 7.110597e-01 2.437178e-02 1.067943e+00 1.372919e-01 1.309734e-02
  [2316] 3.826404e-01 2.099859e-02 6.130865e-01 3.633957e-02 2.458888e-01
  [2321] 2.421787e+00 6.045075e-03 7.988298e-02 6.296577e-02 6.801454e-02
  [2326] 3.474988e+00 5.471584e-01 5.783355e+00 1.648960e+00 4.618780e-01
  [2331] 1.135245e-01 6.161983e+00 5.808524e+00 1.046128e+00 5.436359e-02
  [2336] 1.689665e+00 4.988254e-01 2.591085e-01 1.843546e-01 8.673128e-03
  [2341] 1.522957e-01 2.929293e-01 3.071860e-01 3.235088e-03 3.901929e-01
  [2346] 1.042974e+00 3.590154e+00 2.919934e+00 3.415686e-01 7.631328e-01
  [2351] 7.327258e-01 2.539725e+00 1.821344e-01 2.395399e-01 1.985864e-02
  [2356] 5.277885e+00 1.651865e-01 2.564984e+00 2.858040e-01 4.705025e+00
  [2361] 3.288893e+00 1.787056e-03 2.858071e-02 5.385914e-04 2.371249e+00
  [2366] 1.436529e+00 1.503597e+00 8.784272e-01 1.495258e+00 8.110697e-01
  [2371] 8.782883e-01 1.357591e-01 3.202316e+00 6.788438e-01 1.453591e+00
  [2376] 4.777917e-02 1.498612e+00 1.605356e+00 8.969292e-02 3.149287e+00
  [2381] 2.899471e+00 1.069441e+00 1.539401e+00 7.931634e-01 4.802389e-01
  [2386] 2.467407e+00 1.036617e+00 3.911919e-02 1.181000e-02 2.370116e-03
  [2391] 8.808562e-01 1.437106e+00 5.749559e-01 6.794424e-01 4.296617e-01
  [2396] 4.842122e-03 2.602695e-02 2.633574e+00 2.965417e-01 1.443363e+00
  [2401] 5.496616e+00 3.357749e-01 7.823575e-02 1.483433e+00 3.726532e-01
  [2406] 5.119593e-01 1.055647e-01 6.945919e-03 2.200881e-01 1.178460e+00
  [2411] 3.927888e-01 2.971793e+00 2.705339e+00 5.999453e-01 3.348982e-02
  [2416] 4.660656e+00 1.504041e-04 4.589243e-01 6.866738e-01 6.349160e-01
  [2421] 6.325643e-01 3.272579e-03 3.027489e-02 5.056707e-02 9.886245e-01
  [2426] 4.260026e-02 2.462053e-02 4.234884e-02 7.135951e-02 8.969310e-02
  [2431] 2.011785e-03 8.465343e-01 3.829236e+00 2.767436e-01 4.340567e+00
  [2436] 2.270934e-03 1.034385e+00 5.975637e-01 6.768735e+00 3.532765e-01
  [2441] 1.034129e+00 2.150450e+00 3.155598e+00 2.845370e-03 2.148502e+00
  [2446] 1.382309e-01 5.174065e-01 2.041141e-01 1.031396e-01 1.439862e+00
  [2451] 1.785332e+00 6.351647e-01 6.001911e+00 2.025051e+00 5.063079e+00
  [2456] 1.858344e+00 9.562566e-03 1.055874e-02 1.436627e+00 8.071195e-01
  [2461] 1.545530e-01 2.382146e+00 7.972861e+00 1.478541e-01 6.932611e+00
  [2466] 7.139722e-01 4.553117e-01 1.982816e-02 5.636596e-01 2.266187e-02
  [2471] 1.039297e+00 3.468510e-02 5.174426e-02 8.563884e-02 8.370991e-02
  [2476] 8.709546e-01 2.975693e-02 5.512649e-01 3.052475e-01 4.281514e-01
  [2481] 1.910221e+00 5.170573e-01 9.720196e-01 5.115077e-04 7.665621e-01
  [2486] 7.062959e-02 5.871185e-02 6.101515e+00 3.248670e+00 7.438094e-01
  [2491] 3.250077e+00 7.530416e-01 3.183473e+00 7.578543e-01 6.046704e-01
  [2496] 7.181235e-03 1.848111e-01 4.059736e-02 3.193290e-01 9.802021e-03
  [2501] 1.997062e+00 2.777384e+00 2.213634e-02 3.846648e+00 2.662297e-02
  [2506] 2.848342e+00 2.624470e-01 1.110306e-02 3.587797e-01 4.622105e-01
  [2511] 4.727208e-01 8.023405e-01 6.467041e-01 2.942820e-01 3.473620e-01
  [2516] 8.801963e-02 1.954036e-02 8.808914e-01 2.800496e-01 2.170285e-01
  [2521] 5.246555e+00 4.238533e+00 2.475354e+00 8.508896e-03 1.243059e+00
  [2526] 5.801937e+00 1.225963e-01 7.303205e-01 3.295770e-02 1.434035e+00
  [2531] 5.411647e-01 2.310652e-03 1.007059e+00 6.146318e-01 4.062924e-01
  [2536] 3.362994e-02 1.615112e+00 8.551596e-03 1.574923e-01 8.565407e-01
  [2541] 5.259598e-02 2.575856e+00 1.917233e-02 3.042994e-02 2.120062e-01
  [2546] 4.393767e+00 4.828173e-01 1.144319e-01 1.841381e+00 7.843433e-01
  [2551] 2.870938e-01 1.455962e+00 1.537585e+00 5.215546e-01 5.474481e-01
  [2556] 1.085200e-01 1.396962e+00 2.316663e+00 1.732317e-01 2.287839e+00
  [2561] 3.419973e-02 3.968414e-06 3.253433e-01 6.169757e-01 1.762350e-01
  [2566] 8.429806e-01 4.107095e-01 3.169096e-02 7.492303e-01 3.610013e-01
  [2571] 7.122161e-01 1.158055e-01 2.774769e-01 6.182193e-01 1.106043e-01
  [2576] 4.790448e-01 1.788075e+00 1.606625e+00 4.404014e+00 2.677026e-03
  [2581] 1.108031e+00 4.090578e-01 9.906253e-02 2.315980e-01 7.060539e-01
  [2586] 3.324902e-01 1.171605e-01 6.464358e+00 2.703146e-02 1.705132e-01
  [2591] 3.559056e+00 1.734568e-01 2.446675e+00 1.058446e-04 5.015887e-02
  [2596] 5.689518e-01 8.332041e-02 4.415802e-02 7.990090e-01 1.217267e+00
  [2601] 3.101902e-02 5.078615e-01 2.686185e+00 7.985942e-01 5.543002e-01
  [2606] 2.227159e-03 2.135053e+00 9.692815e-01 4.302588e-01 4.685574e-02
  [2611] 3.958047e+00 5.535794e-03 2.535388e+00 1.626690e-01 6.541637e-01
  [2616] 5.661999e-01 4.615672e-01 1.014135e+00 1.119129e+00 9.082442e-02
  [2621] 3.591052e-03 7.258711e-02 1.980918e-02 2.110564e+00 8.599575e-01
  [2626] 3.947458e-01 2.053949e-02 3.202539e+00 1.100894e-02 2.227814e+00
  [2631] 4.788871e-01 2.487845e-01 2.337372e+00 9.212995e-02 5.946917e-02
  [2636] 1.168213e+00 3.545180e-01 9.428533e-03 2.475056e-03 1.196088e-01
  [2641] 5.493949e-01 1.456005e+00 2.616359e-02 1.331940e+00 4.410692e-01
  [2646] 2.941820e+00 1.932407e+00 3.321505e-01 1.046830e+00 2.317466e-01
  [2651] 8.134004e-01 1.627084e-01 1.329998e-01 1.259800e-01 1.441060e-01
  [2656] 9.069972e-01 4.191969e-01 2.257863e-03 7.512404e+00 7.082235e-02
  [2661] 4.558605e-01 1.490294e-02 5.463082e-02 8.482232e-02 2.390776e-02
  [2666] 1.490972e+00 1.197363e+00 1.870367e-01 1.944398e+00 1.641695e+00
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