Last data update: 2014.03.03
R: Poisson sampling with a discrete prior
Poisson sampling with a discrete prior
Description
Evaluates and plots the posterior density for mu , the mean rate
of occurance in a Poisson process and a discrete prior on mu
Usage
poisdp(y.obs, mu, mu.prior, plot = TRUE)
Arguments
y.obs
a random sample from a Poisson distribution.
mu
a vector of possibilities for the mean rate of occurance of an
event over a finite period of space or time.
mu.prior
the associated prior probability mass.
plot
if TRUE then a plot showing the prior and the posterior
will be produced.
Value
A list will be returned with the following components:
likelihood
the scaled likelihood function for mu given
y.obs
posterior
the posterior probability of
mu given y.obs
mu
the vector of possible
mu values used in the prior
mu.prior
the associated
probability mass for the values in mu
See Also
poisgamp poisgcp
Examples
## simplest call with an observation of 4 and a uniform prior on the
## values mu = 1,2,3
poisdp(4,1:3,c(1,1,1)/3)
## Same as the previous example but a non-uniform discrete prior
mu = 1:3
mu.prior = c(0.3,0.4,0.3)
poisdp(4,mu=mu,mu.prior=mu.prior)
## Same as the previous example but a non-uniform discrete prior
mu = seq(0.5,9.5,by=0.05)
mu.prior = runif(length(mu))
mu.prior = sort(mu.prior/sum(mu.prior))
poisdp(4,mu=mu,mu.prior=mu.prior)
## A random sample of 50 observations from a Poisson distribution with
## parameter mu = 3 and non-uniform prior
y.obs = rpois(50,3)
mu = c(1:5)
mu.prior = c(0.1,0.1,0.05,0.25,0.5)
results = poisdp(y.obs, mu, mu.prior)
## Same as the previous example but a non-uniform discrete prior
mu = seq(0.5,5.5,by=0.05)
mu.prior = runif(length(mu))
mu.prior = sort(mu.prior/sum(mu.prior))
y.obs = rpois(50,3)
poisdp(y.obs,mu=mu,mu.prior=mu.prior)
Results
R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> library(Bolstad)
Attaching package: 'Bolstad'
The following objects are masked from 'package:stats':
IQR, sd, var
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/Bolstad/poisdp.Rd_%03d_medium.png", width=480, height=480)
> ### Name: poisdp
> ### Title: Poisson sampling with a discrete prior
> ### Aliases: poisdp
> ### Keywords: misc
>
> ### ** Examples
>
>
> ## simplest call with an observation of 4 and a uniform prior on the
> ## values mu = 1,2,3
> poisdp(4,1:3,c(1,1,1)/3)
Prior
-----
mu Pr(mu)
[1,] 1 0.3333333
[2,] 2 0.3333333
[3,] 3 0.3333333
k1: 0.9995
k2: 3
Conditional probability of y1 given mu
-------------------------------------
0 1 2 3 4 5 6
1 0.36787944 0.3678794 0.1839397 0.06131324 0.01532831 0.003065662 0.0005109437
2 0.13533528 0.2706706 0.2706706 0.18044704 0.09022352 0.036089409 0.0120298030
3 0.04978707 0.1493612 0.2240418 0.22404181 0.16803136 0.100818813 0.0504094067
7 8 9 10
1 7.299195e-05 9.123994e-06 1.013777e-06 1.013777e-07
2 3.437087e-03 8.592716e-04 1.909493e-04 3.818985e-05
3 2.160403e-02 8.101512e-03 2.700504e-03 8.101512e-04
Joint probability of y1 and mu
-------------------------------
0 1 2 3 4 5
[1,] 0.12262648 0.12262648 0.06131324 0.02043775 0.005109437 0.001021887
[2,] 0.04511176 0.09022352 0.09022352 0.06014901 0.030074507 0.012029803
[3,] 0.01659569 0.04978707 0.07468060 0.07468060 0.056010452 0.033606271
6 7 8 9 10
[1,] 0.0001703146 2.433065e-05 3.041331e-06 3.379257e-07 3.379257e-08
[2,] 0.0040099343 1.145696e-03 2.864239e-04 6.364975e-05 1.272995e-05
[3,] 0.0168031356 7.201344e-03 2.700504e-03 9.001680e-04 2.700504e-04
Marginal probability of y1
-------------------------
0 1 2 3 4 5
0.1843339309 0.2626370709 0.2262173649 0.1552673641 0.0911943960 0.0466579614
6 7 8 9 10
0.0209833844 0.0083713700 0.0029899691 0.0009641557 0.0002828141
Mu Prior Likelihood Posterior
1 1 0.3333333 0.01532831 0.05602797
2 2 0.3333333 0.09022352 0.32978460
3 3 0.3333333 0.16803136 0.61418743
>
> ## Same as the previous example but a non-uniform discrete prior
> mu = 1:3
> mu.prior = c(0.3,0.4,0.3)
> poisdp(4,mu=mu,mu.prior=mu.prior)
Prior
-----
mu Pr(mu)
[1,] 1 0.3
[2,] 2 0.4
[3,] 3 0.3
k1: 0.9995
k2: 3
Conditional probability of y1 given mu
-------------------------------------
0 1 2 3 4 5 6
1 0.36787944 0.3678794 0.1839397 0.06131324 0.01532831 0.003065662 0.0005109437
2 0.13533528 0.2706706 0.2706706 0.18044704 0.09022352 0.036089409 0.0120298030
3 0.04978707 0.1493612 0.2240418 0.22404181 0.16803136 0.100818813 0.0504094067
7 8 9 10
1 7.299195e-05 9.123994e-06 1.013777e-06 1.013777e-07
2 3.437087e-03 8.592716e-04 1.909493e-04 3.818985e-05
3 2.160403e-02 8.101512e-03 2.700504e-03 8.101512e-04
Joint probability of y1 and mu
-------------------------------
0 1 2 3 4 5
[1,] 0.11036383 0.11036383 0.05518192 0.01839397 0.004598493 0.0009196986
[2,] 0.05413411 0.10826823 0.10826823 0.07217882 0.036089409 0.0144357635
[3,] 0.01493612 0.04480836 0.06721254 0.06721254 0.050409407 0.0302456440
6 7 8 9 10
[1,] 0.0001532831 2.189759e-05 2.737198e-06 3.041331e-07 3.041331e-08
[2,] 0.0048119212 1.374835e-03 3.437087e-04 7.637970e-05 1.527594e-05
[3,] 0.0151228220 6.481209e-03 2.430454e-03 8.101512e-04 2.430454e-04
Marginal probability of y1
-------------------------
0 1 2 3 4 5
0.1794340662 0.2634404205 0.2306626851 0.1577853321 0.0910973086 0.0456011062
6 7 8 9 10
0.0200880263 0.0078779416 0.0027768994 0.0008868350 0.0002583517
Mu Prior Likelihood Posterior
1 1 0.3 0.01532831 0.05047891
2 2 0.4 0.09022352 0.39616328
3 3 0.3 0.16803136 0.55335780
>
> ## Same as the previous example but a non-uniform discrete prior
> mu = seq(0.5,9.5,by=0.05)
> mu.prior = runif(length(mu))
> mu.prior = sort(mu.prior/sum(mu.prior))
> poisdp(4,mu=mu,mu.prior=mu.prior)
Prior
-----
mu Pr(mu)
[1,] 0.50 5.986956e-05
[2,] 0.55 1.187011e-04
[3,] 0.60 1.403208e-04
[4,] 0.65 1.475793e-04
[5,] 0.70 2.101066e-04
[6,] 0.75 2.315652e-04
[7,] 0.80 2.906881e-04
[8,] 0.85 3.785063e-04
[9,] 0.90 4.717971e-04
[10,] 0.95 4.842567e-04
[11,] 1.00 4.897606e-04
[12,] 1.05 5.048671e-04
[13,] 1.10 5.937611e-04
[14,] 1.15 6.374555e-04
[15,] 1.20 6.867924e-04
[16,] 1.25 8.198570e-04
[17,] 1.30 8.241057e-04
[18,] 1.35 9.966328e-04
[19,] 1.40 1.153649e-03
[20,] 1.45 1.248920e-03
[21,] 1.50 1.281130e-03
[22,] 1.55 1.297436e-03
[23,] 1.60 1.367652e-03
[24,] 1.65 1.481028e-03
[25,] 1.70 1.536817e-03
[26,] 1.75 1.638525e-03
[27,] 1.80 1.668740e-03
[28,] 1.85 1.706234e-03
[29,] 1.90 1.827724e-03
[30,] 1.95 1.968139e-03
[31,] 2.00 2.018513e-03
[32,] 2.05 2.166667e-03
[33,] 2.10 2.206932e-03
[34,] 2.15 2.226827e-03
[35,] 2.20 2.242243e-03
[36,] 2.25 2.287424e-03
[37,] 2.30 2.349047e-03
[38,] 2.35 2.358263e-03
[39,] 2.40 2.430005e-03
[40,] 2.45 2.477198e-03
[41,] 2.50 2.582001e-03
[42,] 2.55 2.603139e-03
[43,] 2.60 2.657922e-03
[44,] 2.65 2.754622e-03
[45,] 2.70 2.779528e-03
[46,] 2.75 2.841847e-03
[47,] 2.80 2.891311e-03
[48,] 2.85 2.907313e-03
[49,] 2.90 3.076586e-03
[50,] 2.95 3.115674e-03
[51,] 3.00 3.194865e-03
[52,] 3.05 3.215182e-03
[53,] 3.10 3.380846e-03
[54,] 3.15 3.388764e-03
[55,] 3.20 3.414471e-03
[56,] 3.25 3.456337e-03
[57,] 3.30 3.673883e-03
[58,] 3.35 3.772186e-03
[59,] 3.40 3.799181e-03
[60,] 3.45 3.803770e-03
[61,] 3.50 3.840417e-03
[62,] 3.55 3.950429e-03
[63,] 3.60 3.962562e-03
[64,] 3.65 4.110264e-03
[65,] 3.70 4.142728e-03
[66,] 3.75 4.144188e-03
[67,] 3.80 4.233056e-03
[68,] 3.85 4.430202e-03
[69,] 3.90 4.493981e-03
[70,] 3.95 4.530885e-03
[71,] 4.00 4.532313e-03
[72,] 4.05 4.563983e-03
[73,] 4.10 4.566035e-03
[74,] 4.15 4.629178e-03
[75,] 4.20 4.695777e-03
[76,] 4.25 4.753561e-03
[77,] 4.30 4.778764e-03
[78,] 4.35 4.840611e-03
[79,] 4.40 4.861580e-03
[80,] 4.45 4.889429e-03
[81,] 4.50 4.910063e-03
[82,] 4.55 5.034331e-03
[83,] 4.60 5.079136e-03
[84,] 4.65 5.132282e-03
[85,] 4.70 5.151779e-03
[86,] 4.75 5.225650e-03
[87,] 4.80 5.282954e-03
[88,] 4.85 5.438927e-03
[89,] 4.90 5.464852e-03
[90,] 4.95 5.468096e-03
[91,] 5.00 5.530356e-03
[92,] 5.05 5.531041e-03
[93,] 5.10 5.583586e-03
[94,] 5.15 5.625971e-03
[95,] 5.20 5.664565e-03
[96,] 5.25 5.770314e-03
[97,] 5.30 5.808555e-03
[98,] 5.35 5.837258e-03
[99,] 5.40 5.885121e-03
[100,] 5.45 5.930632e-03
[101,] 5.50 5.963026e-03
[102,] 5.55 5.996797e-03
[103,] 5.60 6.009386e-03
[104,] 5.65 6.023571e-03
[105,] 5.70 6.115469e-03
[106,] 5.75 6.208854e-03
[107,] 5.80 6.222356e-03
[108,] 5.85 6.224529e-03
[109,] 5.90 6.266665e-03
[110,] 5.95 6.339701e-03
[111,] 6.00 6.397103e-03
[112,] 6.05 6.434804e-03
[113,] 6.10 6.452420e-03
[114,] 6.15 6.513992e-03
[115,] 6.20 6.620730e-03
[116,] 6.25 6.710868e-03
[117,] 6.30 6.742486e-03
[118,] 6.35 6.745570e-03
[119,] 6.40 6.766296e-03
[120,] 6.45 6.958640e-03
[121,] 6.50 7.057951e-03
[122,] 6.55 7.066850e-03
[123,] 6.60 7.070143e-03
[124,] 6.65 7.315979e-03
[125,] 6.70 7.324343e-03
[126,] 6.75 7.456511e-03
[127,] 6.80 7.731341e-03
[128,] 6.85 7.748995e-03
[129,] 6.90 7.944457e-03
[130,] 6.95 7.970188e-03
[131,] 7.00 8.160190e-03
[132,] 7.05 8.203450e-03
[133,] 7.10 8.249453e-03
[134,] 7.15 8.282918e-03
[135,] 7.20 8.303515e-03
[136,] 7.25 8.444092e-03
[137,] 7.30 8.445565e-03
[138,] 7.35 8.489851e-03
[139,] 7.40 8.532391e-03
[140,] 7.45 8.569456e-03
[141,] 7.50 8.626334e-03
[142,] 7.55 8.695048e-03
[143,] 7.60 8.719981e-03
[144,] 7.65 8.833614e-03
[145,] 7.70 9.021507e-03
[146,] 7.75 9.029013e-03
[147,] 7.80 9.058163e-03
[148,] 7.85 9.096221e-03
[149,] 7.90 9.149269e-03
[150,] 7.95 9.153749e-03
[151,] 8.00 9.223826e-03
[152,] 8.05 9.234910e-03
[153,] 8.10 9.344412e-03
[154,] 8.15 9.361524e-03
[155,] 8.20 9.399783e-03
[156,] 8.25 9.539269e-03
[157,] 8.30 9.563010e-03
[158,] 8.35 9.596891e-03
[159,] 8.40 9.671588e-03
[160,] 8.45 9.793054e-03
[161,] 8.50 9.817912e-03
[162,] 8.55 9.818783e-03
[163,] 8.60 9.918147e-03
[164,] 8.65 9.952852e-03
[165,] 8.70 9.997749e-03
[166,] 8.75 1.012553e-02
[167,] 8.80 1.014288e-02
[168,] 8.85 1.015512e-02
[169,] 8.90 1.023069e-02
[170,] 8.95 1.030069e-02
[171,] 9.00 1.031828e-02
[172,] 9.05 1.037516e-02
[173,] 9.10 1.049449e-02
[174,] 9.15 1.049549e-02
[175,] 9.20 1.071025e-02
[176,] 9.25 1.076960e-02
[177,] 9.30 1.100021e-02
[178,] 9.35 1.109427e-02
[179,] 9.40 1.110745e-02
[180,] 9.45 1.115599e-02
[181,] 9.50 1.118581e-02
k1: 0.9995
k2: 9.5
Conditional probability of y1 given mu
-------------------------------------
0 1 2 3 4 5
0.5 6.065307e-01 0.3032653299 0.075816332 0.01263606 0.001579507 0.0001579507
0.55 5.769498e-01 0.3173223957 0.087263659 0.01599834 0.002199771 0.0002419749
0.6 5.488116e-01 0.3292869817 0.098786094 0.01975722 0.002963583 0.0003556299
0.65 5.220458e-01 0.3393297549 0.110282170 0.02389447 0.003882851 0.0005047707
0.7 4.965853e-01 0.3476097127 0.121663399 0.02838813 0.004967922 0.0006955091
0.75 4.723666e-01 0.3542749146 0.132853093 0.03321327 0.006227489 0.0009341233
0.8 4.493290e-01 0.3594631713 0.143785269 0.03834274 0.007668548 0.0012269676
0.85 4.274149e-01 0.3633026922 0.154403644 0.04374770 0.009296386 0.0015803856
0.9 4.065697e-01 0.3659126938 0.164660712 0.04939821 0.011114598 0.0020006277
0.95 3.867410e-01 0.3674039723 0.174516887 0.05526368 0.013125124 0.0024937736
1 3.678794e-01 0.3678794412 0.183939721 0.06131324 0.015328310 0.0030656620
1.05 3.499377e-01 0.3674346366 0.192903184 0.06751611 0.017722980 0.0037218258
1.1 3.328711e-01 0.3661581921 0.201387006 0.07384190 0.020306523 0.0044674351
1.15 3.166368e-01 0.3641322848 0.209376064 0.08026082 0.023074987 0.0053072470
1.2 3.011942e-01 0.3614330543 0.216859833 0.08674393 0.026023180 0.0062455632
1.25 2.865048e-01 0.3581309961 0.223831873 0.09326328 0.029144775 0.0072861938
1.3 2.725318e-01 0.3542913309 0.230289365 0.09979206 0.032432419 0.0084324289
1.35 2.592403e-01 0.3499743519 0.236232688 0.10630471 0.035877839 0.0096870166
1.4 2.465970e-01 0.3452357495 0.241665025 0.11277701 0.039471954 0.0110521471
1.45 2.345703e-01 0.3401269177 0.246592015 0.11918614 0.043204976 0.0125294430
1.5 2.231302e-01 0.3346952402 0.251021430 0.12551072 0.047066518 0.0141199554
1.55 2.122480e-01 0.3289843594 0.254962879 0.13173082 0.051045693 0.0158241648
1.6 2.018965e-01 0.3230344288 0.258427543 0.13782802 0.055131209 0.0176419869
1.65 1.920499e-01 0.3168823492 0.261427938 0.14378537 0.059311463 0.0195727829
1.7 1.826835e-01 0.3105619909 0.263977692 0.14958736 0.063574628 0.0216153734
1.75 1.737739e-01 0.3041044010 0.266091351 0.15521995 0.067908730 0.0237680556
1.8 1.652989e-01 0.2975379988 0.267784199 0.16067052 0.072301734 0.0260286241
1.85 1.572372e-01 0.2908887577 0.269072101 0.16592780 0.076741605 0.0283943940
1.9 1.495686e-01 0.2841803765 0.269971358 0.17098186 0.081216383 0.0308622257
1.95 1.422741e-01 0.2774344396 0.270498579 0.17582408 0.085714237 0.0334285525
2 1.353353e-01 0.2706705665 0.270670566 0.18044704 0.090223522 0.0360894089
2.05 1.287349e-01 0.2639065524 0.270504216 0.18484455 0.094732831 0.0388404606
2.1 1.224564e-01 0.2571584993 0.270016424 0.18901150 0.099231036 0.0416770351
2.15 1.164842e-01 0.2504409392 0.269224010 0.19294387 0.103707332 0.0445941528
2.2 1.108032e-01 0.2437669484 0.268143643 0.19663867 0.108151269 0.0475865586
2.25 1.053992e-01 0.2371482553 0.266791787 0.20009384 0.112552785 0.0506487533
2.3 1.002588e-01 0.2305953406 0.265184642 0.20330823 0.116902230 0.0537750256
2.35 9.536916e-02 0.2241175312 0.263338099 0.20628151 0.121190388 0.0569594822
2.4 9.071795e-02 0.2177230879 0.261267705 0.20901416 0.125408499 0.0601960793
2.45 8.629359e-02 0.2114192869 0.258988626 0.21150738 0.129548269 0.0634786519
2.5 8.208500e-02 0.2052124966 0.256515621 0.21376302 0.133601886 0.0668009429
2.55 7.808167e-02 0.1991082483 0.253863017 0.21578356 0.137562022 0.0701566313
2.6 7.427358e-02 0.1931113034 0.251044694 0.21757207 0.141421844 0.0735393591
2.65 7.065121e-02 0.1872257146 0.248074072 0.21913210 0.145175014 0.0769427575
2.7 6.720551e-02 0.1814548844 0.244964094 0.22046768 0.148815687 0.0803604710
2.75 6.392786e-02 0.1758016183 0.241727225 0.22158329 0.152338512 0.0837861814
2.8 6.081006e-02 0.1702681754 0.238375445 0.22248375 0.155738624 0.0872136297
2.85 5.784432e-02 0.1648563145 0.234920248 0.22317424 0.159011643 0.0906366365
2.9 5.502322e-02 0.1595673382 0.231372640 0.22366022 0.162153659 0.0940491221
2.95 5.233971e-02 0.1544021325 0.227743146 0.22394743 0.165161227 0.0974451239
3 4.978707e-02 0.1493612051 0.224041808 0.22404181 0.168031356 0.1008188134
3.05 4.735892e-02 0.1444447194 0.220278197 0.22394950 0.170761494 0.1041645114
3.1 4.504920e-02 0.1396525274 0.216461418 0.22367680 0.173349519 0.1074767015
3.15 4.285213e-02 0.1349841996 0.212600114 0.22323012 0.175793720 0.1107500434
3.2 4.076220e-02 0.1304390527 0.208702484 0.22261598 0.178092787 0.1139793835
3.25 3.877421e-02 0.1260161755 0.204776285 0.22184098 0.180245793 0.1171597652
3.3 3.688317e-02 0.1217144524 0.200828846 0.22091173 0.182252178 0.1202864376
3.35 3.508435e-02 0.1175325862 0.196867082 0.21983491 0.184111736 0.1233548629
3.4 3.337327e-02 0.1134691179 0.192897500 0.21861717 0.185824592 0.1263607226
3.45 3.174564e-02 0.1095224455 0.188926218 0.21726515 0.187391193 0.1292999231
3.5 3.019738e-02 0.1056908420 0.184958973 0.21578547 0.188812285 0.1321685998
3.55 2.872464e-02 0.1019724708 0.181001136 0.21418468 0.190088901 0.1349631197
3.6 2.732372e-02 0.0983654008 0.177057721 0.21246927 0.191222339 0.1376800842
3.65 2.599113e-02 0.0948676200 0.173133407 0.21064564 0.192214151 0.1403163301
3.7 2.472353e-02 0.0914770479 0.169232539 0.20872013 0.193066121 0.1428689297
3.75 2.351775e-02 0.0881915470 0.165359151 0.20669894 0.193780255 0.1453351909
3.8 2.237077e-02 0.0850089331 0.161516973 0.20458817 0.194358757 0.1477126555
3.85 2.127974e-02 0.0819269853 0.157709447 0.20239379 0.194804023 0.1499990975
3.9 2.024191e-02 0.0789434546 0.153939737 0.20012166 0.195118616 0.1521925205
3.95 1.925470e-02 0.0760560720 0.150210742 0.19777748 0.195305259 0.1542911544
4 1.831564e-02 0.0732625556 0.146525111 0.19536681 0.195366815 0.1562934519
4.05 1.742237e-02 0.0705606173 0.142885250 0.19289509 0.195306276 0.1581980836
4.1 1.657268e-02 0.0679479691 0.139293337 0.19036756 0.195126749 0.1600039344
4.15 1.576442e-02 0.0654223284 0.135751331 0.18778934 0.194831442 0.1617100970
4.2 1.499558e-02 0.0629814226 0.132260988 0.18516538 0.194423652 0.1633158674
4.25 1.426423e-02 0.0606229941 0.128823862 0.18250047 0.193906751 0.1648207387
4.3 1.356856e-02 0.0583448038 0.125441328 0.17979924 0.193284180 0.1662243945
4.35 1.290681e-02 0.0561446347 0.122114581 0.17706614 0.192559429 0.1675267034
4.4 1.227734e-02 0.0540202956 0.118844650 0.17430549 0.191736036 0.1687277115
4.45 1.167857e-02 0.0519696230 0.115632411 0.17152141 0.190817569 0.1698276360
4.5 1.110900e-02 0.0499904844 0.112478590 0.16871788 0.189807621 0.1708268585
4.55 1.056720e-02 0.0480807799 0.109383774 0.16589872 0.188709799 0.1717259172
4.6 1.005184e-02 0.0462384444 0.106348422 0.16306758 0.187527718 0.1725255004
4.65 9.561602e-03 0.0444614490 0.103372869 0.16022795 0.186264988 0.1732264389
4.7 9.095277e-03 0.0427478024 0.100457336 0.15738316 0.184925212 0.1738296992
4.75 8.651695e-03 0.0410955522 0.097601937 0.15453640 0.183511974 0.1743363757
4.8 8.229747e-03 0.0395027858 0.094806686 0.15169070 0.182028837 0.1747476836
4.85 7.828378e-03 0.0379676311 0.092071505 0.14884893 0.180479332 0.1750649523
4.9 7.446583e-03 0.0364882570 0.089396230 0.14601384 0.178866956 0.1752896173
4.95 7.083409e-03 0.0350628742 0.086780614 0.14318801 0.177195165 0.1754232138
5 6.737947e-03 0.0336897350 0.084224337 0.14037390 0.175467370 0.1754673698
5.05 6.409333e-03 0.0323671339 0.081727013 0.13757381 0.173686929 0.1754237986
5.1 6.096747e-03 0.0310934075 0.079288189 0.13478992 0.171857150 0.1752942928
5.15 5.799405e-03 0.0298669343 0.076907356 0.13202429 0.169981279 0.1750807173
5.2 5.516564e-03 0.0286861350 0.074583951 0.12927885 0.168062503 0.1747850030
5.25 5.247518e-03 0.0275494716 0.072317363 0.12655539 0.166103943 0.1744091401
5.3 4.991594e-03 0.0264554477 0.070106936 0.12385559 0.164108654 0.1739551729
5.35 4.748151e-03 0.0254026078 0.067951976 0.12118102 0.162079619 0.1734251928
5.4 4.516581e-03 0.0243895371 0.065851750 0.11853315 0.160019753 0.1728213331
5.45 4.296305e-03 0.0234148606 0.063805495 0.11591332 0.157931893 0.1721457634
5.5 4.086771e-03 0.0224772429 0.061812418 0.11332277 0.155818804 0.1714006841
5.55 3.887457e-03 0.0215753877 0.059871701 0.11076265 0.153683172 0.1705883211
5.6 3.697864e-03 0.0207080368 0.057982503 0.10823401 0.151527608 0.1697109210
5.65 3.517517e-03 0.0198739698 0.056143965 0.10573780 0.149354643 0.1687707461
5.7 3.345965e-03 0.0190720031 0.054355209 0.10327490 0.147166728 0.1677700699
5.75 3.182781e-03 0.0183009896 0.052615345 0.10084608 0.144966237 0.1667111727
5.8 3.027555e-03 0.0175598175 0.050923471 0.09845204 0.142755463 0.1655963373
5.85 2.879899e-03 0.0168474101 0.049278674 0.09609342 0.140536620 0.1644278451
5.9 2.739445e-03 0.0161627244 0.047680037 0.09377074 0.138311841 0.1632079722
5.95 2.605841e-03 0.0155047511 0.046126634 0.09148449 0.136083181 0.1619389859
6 2.478752e-03 0.0148725131 0.044617539 0.08923508 0.133852618 0.1606231410
6.05 2.357862e-03 0.0142650651 0.043151822 0.08702284 0.131622047 0.1592626771
6.1 2.242868e-03 0.0136814931 0.041728554 0.08484806 0.129393291 0.1578598150
6.15 2.133482e-03 0.0131209129 0.040346807 0.08271095 0.127168093 0.1564167540
6.2 2.029431e-03 0.0125824699 0.039005657 0.08061169 0.124948121 0.1549356697
6.25 1.930454e-03 0.0120653384 0.037704182 0.07855038 0.122734969 0.1534187107
6.3 1.836305e-03 0.0115687201 0.036441468 0.07652708 0.120530156 0.1518679971
6.35 1.746747e-03 0.0110918443 0.035216606 0.07454182 0.118335132 0.1502856176
6.4 1.661557e-03 0.0106339665 0.034028693 0.07259454 0.116151272 0.1486736281
6.45 1.580522e-03 0.0101943680 0.032876837 0.07068520 0.113979883 0.1470340497
6.5 1.503439e-03 0.0097723548 0.031760153 0.06881366 0.111822205 0.1453688667
6.55 1.430116e-03 0.0093672572 0.030677767 0.06697979 0.109679409 0.1436800258
6.6 1.360368e-03 0.0089784290 0.029628816 0.06518339 0.107552602 0.1419694341
6.65 1.294022e-03 0.0086052470 0.028612446 0.06342426 0.105442825 0.1402389579
6.7 1.230912e-03 0.0082471097 0.027627818 0.06170213 0.103351061 0.1384904220
6.75 1.170880e-03 0.0079034374 0.026674101 0.06001673 0.101278229 0.1367256086
6.8 1.113775e-03 0.0075736710 0.025750481 0.05836776 0.099225188 0.1349462562
6.85 1.059456e-03 0.0072572715 0.024856155 0.05675489 0.097192744 0.1331540592
6.9 1.007785e-03 0.0069537195 0.023990332 0.05517776 0.095181643 0.1313506670
6.95 9.586352e-04 0.0066625143 0.023152237 0.05363602 0.093192578 0.1295376839
7 9.118820e-04 0.0063831738 0.022341108 0.05212925 0.091226192 0.1277166683
7.05 8.674090e-04 0.0061152331 0.021556197 0.05065706 0.089283073 0.1258891327
7.1 8.251049e-04 0.0058582450 0.020796770 0.04921902 0.087363763 0.1240565434
7.15 7.848641e-04 0.0056117782 0.020062107 0.04781469 0.085468755 0.1222203202
7.2 7.465858e-04 0.0053754178 0.019351504 0.04644361 0.083598498 0.1203818370
7.25 7.101744e-04 0.0051487643 0.018664271 0.04510532 0.081753394 0.1185424211
7.3 6.755388e-04 0.0049314331 0.017999731 0.04379934 0.079933804 0.1167033537
7.35 6.425924e-04 0.0047230538 0.017357223 0.04252520 0.078140048 0.1148658703
7.4 6.112528e-04 0.0045232704 0.016736101 0.04128238 0.076372406 0.1130311605
7.45 5.814416e-04 0.0043317400 0.016135732 0.04007040 0.074631120 0.1112003688
7.5 5.530844e-04 0.0041481328 0.015555498 0.03888874 0.072916396 0.1093745947
7.55 5.261101e-04 0.0039721315 0.014994796 0.03773690 0.071228406 0.1075548933
7.6 5.004514e-04 0.0038034309 0.014453037 0.03661436 0.069567287 0.1057422757
7.65 4.760441e-04 0.0036417376 0.013929646 0.03552060 0.067933144 0.1039377098
7.7 4.528272e-04 0.0034867693 0.013424062 0.03445509 0.066326052 0.1021421204
7.75 4.307425e-04 0.0033382547 0.012935737 0.03341732 0.064746058 0.1003563903
7.8 4.097350e-04 0.0031959328 0.012464138 0.03240676 0.063193180 0.0985813607
7.85 3.897520e-04 0.0030595530 0.012008745 0.03142288 0.061667409 0.0968178323
7.9 3.707435e-04 0.0029288740 0.011569052 0.03046517 0.060168712 0.0950665653
7.95 3.526622e-04 0.0028036642 0.011144565 0.02953310 0.058697032 0.0933282809
8 3.354626e-04 0.0026837010 0.010734804 0.02862614 0.057252288 0.0916036616
8.05 3.191019e-04 0.0025687705 0.010339301 0.02774379 0.055834380 0.0898933523
8.1 3.035391e-04 0.0024586670 0.009957601 0.02688552 0.054443186 0.0881979610
8.15 2.887354e-04 0.0023531932 0.009589262 0.02605083 0.053078564 0.0865180595
8.2 2.746536e-04 0.0022521593 0.009233853 0.02523920 0.051740356 0.0848541846
8.25 2.612586e-04 0.0021553831 0.008890955 0.02445013 0.050428387 0.0832068385
8.3 2.485168e-04 0.0020626897 0.008560162 0.02368312 0.049142464 0.0815764902
8.35 2.363965e-04 0.0019739109 0.008241078 0.02293767 0.047882381 0.0799635760
8.4 2.248673e-04 0.0018888855 0.007933319 0.02221329 0.046647917 0.0783685004
8.45 2.139004e-04 0.0018074585 0.007636512 0.02150951 0.045438839 0.0767916372
8.5 2.034684e-04 0.0017294811 0.007350295 0.02082584 0.044254900 0.0752333302
8.55 1.935451e-04 0.0016548106 0.007074315 0.02016180 0.043095845 0.0736938943
8.6 1.841058e-04 0.0015833098 0.006808232 0.01951693 0.041961405 0.0721736162
8.65 1.751268e-04 0.0015148472 0.006551714 0.01889078 0.040851304 0.0706727552
8.7 1.665858e-04 0.0014492966 0.006304440 0.01828288 0.039765255 0.0691915444
8.75 1.584613e-04 0.0013865366 0.006066098 0.01769278 0.038702966 0.0677301913
8.8 1.507331e-04 0.0013264511 0.005836385 0.01712006 0.037664136 0.0662888789
8.85 1.433817e-04 0.0012689284 0.005615008 0.01656427 0.036648455 0.0648677662
8.9 1.363889e-04 0.0012138614 0.005401683 0.01602499 0.035655612 0.0634669895
8.95 1.297372e-04 0.0011611476 0.005196135 0.01550180 0.034685287 0.0620866629
9 1.234098e-04 0.0011106882 0.004998097 0.01499429 0.033737155 0.0607268793
9.05 1.173910e-04 0.0010623889 0.004807310 0.01450205 0.032810890 0.0593877113
9.1 1.116658e-04 0.0010161589 0.004623523 0.01402469 0.031906160 0.0580692117
9.15 1.062198e-04 0.0009719112 0.004446494 0.01356181 0.031022631 0.0567714145
9.2 1.010394e-04 0.0009295625 0.004275987 0.01311303 0.030159965 0.0554943357
9.25 9.611165e-05 0.0008890328 0.004111777 0.01267798 0.029317824 0.0542379742
9.3 9.142423e-05 0.0008502454 0.003953641 0.01225629 0.028495867 0.0530023121
9.35 8.696542e-05 0.0008131267 0.003801367 0.01184759 0.027693752 0.0517873159
9.4 8.272407e-05 0.0007776062 0.003654749 0.01145155 0.026911137 0.0505929371
9.45 7.868957e-05 0.0007436164 0.003513587 0.01106780 0.026147679 0.0494191126
9.5 7.485183e-05 0.0007110924 0.003377689 0.01069601 0.025403035 0.0482657659
6 7 8 9 10
0.5 1.316256e-05 9.401827e-07 5.876142e-08 3.264523e-09 1.632262e-10
0.55 2.218103e-05 1.742795e-06 1.198172e-07 7.322160e-09 4.027188e-10
0.6 3.556299e-05 3.048257e-06 2.286192e-07 1.524128e-08 9.144770e-10
0.65 5.468349e-05 5.077753e-06 4.125674e-07 2.979654e-08 1.936775e-09
0.7 8.114273e-05 8.114273e-06 7.099989e-07 5.522213e-08 3.865549e-09
0.75 1.167654e-04 1.251058e-05 1.172867e-06 9.773891e-08 7.330418e-09
0.8 1.635957e-04 1.869665e-05 1.869665e-06 1.661924e-07 1.329540e-08
0.85 2.238880e-04 2.718640e-05 2.888555e-06 2.728079e-07 2.318867e-08
0.9 3.000941e-04 3.858353e-05 4.340647e-06 4.340647e-07 3.906583e-08
0.95 3.948475e-04 5.358644e-05 6.363390e-06 6.716912e-07 6.381066e-08
1 5.109437e-04 7.299195e-05 9.123994e-06 1.013777e-06 1.013777e-07
1.05 6.513195e-04 9.769793e-05 1.282285e-05 1.496000e-06 1.570799e-07
1.1 8.190298e-04 1.287047e-04 1.769689e-05 2.162954e-06 2.379249e-07
1.15 1.017222e-03 1.671151e-04 2.402280e-05 3.069579e-06 3.530016e-07
1.2 1.249113e-03 2.141336e-04 3.212004e-05 4.282672e-06 5.139206e-07
1.25 1.517957e-03 2.710638e-04 4.235371e-05 5.882460e-06 7.353075e-07
1.3 1.827026e-03 3.393049e-04 5.513704e-05 7.964239e-06 1.035351e-06
1.35 2.179579e-03 4.203473e-04 7.093361e-05 1.064004e-05 1.436406e-06
1.4 2.578834e-03 5.157669e-04 9.025920e-05 1.404032e-05 1.965645e-06
1.45 3.027949e-03 6.272180e-04 1.136833e-04 1.831564e-05 2.655767e-06
1.5 3.529989e-03 7.564262e-04 1.418299e-04 2.363832e-05 3.545748e-06
1.55 4.087909e-03 9.051799e-04 1.753786e-04 3.020409e-05 4.681634e-06
1.6 4.704530e-03 1.075321e-03 2.150642e-04 3.823364e-05 6.117382e-06
1.65 5.382515e-03 1.268736e-03 2.616767e-04 4.797407e-05 7.915722e-06
1.7 6.124356e-03 1.487344e-03 3.160605e-04 5.970032e-05 1.014905e-05
1.75 6.932350e-03 1.733087e-03 3.791129e-04 7.371639e-05 1.290037e-05
1.8 7.808587e-03 2.007922e-03 4.517825e-04 9.035651e-05 1.626417e-05
1.85 8.754938e-03 2.313805e-03 5.350674e-04 1.099861e-04 2.034743e-05
1.9 9.773038e-03 2.652682e-03 6.300119e-04 1.330025e-04 2.527048e-05
1.95 1.086428e-02 3.026478e-03 7.377040e-04 1.598359e-04 3.116799e-05
2 1.202980e-02 3.437087e-03 8.592716e-04 1.909493e-04 3.818985e-05
2.05 1.327049e-02 3.886358e-03 9.958792e-04 2.268392e-04 4.650203e-05
2.1 1.458696e-02 4.376089e-03 1.148723e-03 2.680354e-04 5.628744e-05
2.15 1.597957e-02 4.908011e-03 1.319028e-03 3.151011e-04 6.774674e-05
2.2 1.744840e-02 5.483784e-03 1.508041e-03 3.686322e-04 8.109908e-05
2.25 1.899328e-02 6.104984e-03 1.717027e-03 4.292567e-04 9.658275e-05
2.3 2.061376e-02 6.773093e-03 1.947264e-03 4.976342e-04 1.144559e-04
2.35 2.230913e-02 7.489494e-03 2.200039e-03 5.744546e-04 1.349968e-04
2.4 2.407843e-02 8.255462e-03 2.476639e-03 6.604370e-04 1.585049e-04
2.45 2.592045e-02 9.072157e-03 2.778348e-03 7.563281e-04 1.853004e-04
2.5 2.783373e-02 9.940617e-03 3.106443e-03 8.629007e-04 2.157252e-04
2.55 2.981657e-02 1.086175e-02 3.462183e-03 9.809518e-04 2.501427e-04
2.6 3.186706e-02 1.183633e-02 3.846809e-03 1.111300e-03 2.889381e-04
2.65 3.398305e-02 1.286501e-02 4.261535e-03 1.254785e-03 3.325181e-04
2.7 3.616221e-02 1.394828e-02 4.707545e-03 1.412264e-03 3.813112e-04
2.75 3.840200e-02 1.508650e-02 5.185984e-03 1.584606e-03 4.357667e-04
2.8 4.069969e-02 1.627988e-02 5.697957e-03 1.772698e-03 4.963554e-04
2.85 4.305240e-02 1.752848e-02 6.244520e-03 1.977431e-03 5.635680e-04
2.9 4.545708e-02 1.883222e-02 6.826679e-03 2.199708e-03 6.379152e-04
2.95 4.791052e-02 2.019086e-02 7.445380e-03 2.440430e-03 7.199269e-04
3 5.040941e-02 2.160403e-02 8.101512e-03 2.700504e-03 8.101512e-04
3.05 5.295029e-02 2.307120e-02 8.795895e-03 2.980831e-03 9.091534e-04
3.1 5.552963e-02 2.459169e-02 9.529281e-03 3.282308e-03 1.017515e-03
3.15 5.814377e-02 2.616470e-02 1.030235e-02 3.605822e-03 1.135834e-03
3.2 6.078900e-02 2.778926e-02 1.111570e-02 3.952250e-03 1.264720e-03
3.25 6.346154e-02 2.946429e-02 1.196987e-02 4.322452e-03 1.404797e-03
3.3 6.615754e-02 3.118855e-02 1.286528e-02 4.717269e-03 1.556699e-03
3.35 6.887313e-02 3.296071e-02 1.380230e-02 5.137522e-03 1.721070e-03
3.4 7.160441e-02 3.477928e-02 1.478120e-02 5.584007e-03 1.898563e-03
3.45 7.434746e-02 3.664267e-02 1.580215e-02 6.057492e-03 2.089835e-03
3.5 7.709835e-02 3.854917e-02 1.686526e-02 6.558714e-03 2.295550e-03
3.55 7.985318e-02 4.049697e-02 1.797053e-02 7.088376e-03 2.516373e-03
3.6 8.260805e-02 4.248414e-02 1.911786e-02 7.647145e-03 2.752972e-03
3.65 8.535910e-02 4.450867e-02 2.030708e-02 8.235650e-03 3.006012e-03
3.7 8.810251e-02 4.656847e-02 2.153792e-02 8.854477e-03 3.276156e-03
3.75 9.083449e-02 4.866134e-02 2.281000e-02 9.504167e-03 3.564063e-03
3.8 9.355135e-02 5.078502e-02 2.412288e-02 1.018522e-02 3.870383e-03
3.85 9.624942e-02 5.293718e-02 2.547602e-02 1.089807e-02 4.195759e-03
3.9 9.892514e-02 5.511543e-02 2.686877e-02 1.164314e-02 4.540823e-03
3.95 1.015750e-01 5.731733e-02 2.830043e-02 1.242074e-02 4.906194e-03
4 1.041956e-01 5.954036e-02 2.977018e-02 1.323119e-02 5.292477e-03
4.05 1.067837e-01 6.178200e-02 3.127714e-02 1.407471e-02 5.700258e-03
4.1 1.093360e-01 6.403967e-02 3.282033e-02 1.495148e-02 6.130108e-03
4.15 1.118495e-01 6.631077e-02 3.439871e-02 1.586163e-02 6.582575e-03
4.2 1.143211e-01 6.859266e-02 3.601115e-02 1.680520e-02 7.058185e-03
4.25 1.167480e-01 7.088273e-02 3.765645e-02 1.778221e-02 7.557440e-03
4.3 1.191275e-01 7.317831e-02 3.933334e-02 1.879260e-02 8.080817e-03
4.35 1.214569e-01 7.547676e-02 4.104049e-02 1.983624e-02 8.628763e-03
4.4 1.237337e-01 7.777544e-02 4.277649e-02 2.091295e-02 9.201699e-03
4.45 1.259555e-01 8.007171e-02 4.453989e-02 2.202250e-02 9.800013e-03
4.5 1.281201e-01 8.236295e-02 4.632916e-02 2.316458e-02 1.042406e-02
4.55 1.302255e-01 8.464657e-02 4.814273e-02 2.433883e-0
providing 
.
