# [R] Fitting an Inverse Gamma Distribution

emorway emorway at engr.colostate.edu
Thu Jan 13 23:46:33 CET 2011

```http://r.789695.n4.nabble.com/file/n3216865/Inverse_Gamma.png

Hello,

I am seeking help in estimating the parameters of an inverse gamma
distribution (from the 'actuar' package) using a function like 'fitdistr'.
Unfortunately I haven't found such a package using findFn('fit Inverse
Gamma') from the 'sos' package and was therefore hoping someone might be
aware of such a function?

Secondly, is there a way to shift the pdf (code below) to the right (rather
than the data to the left)?  I tried:

par(new=T)
shift<-1
hist(iniSal_US_forHist,breaks=seq(1.1,21,by=0.625),col="grey",freq=F,xlim=c(0-shift,21-shift),plot=F)

but this failed in shifting the curve.  More broadly, the data plotted in
the histogram represents a calibration target for output generated by a
finite difference solute transport model.  The values that will be generated
by the finite difference model would ideally fit the shifted (if that can be
figured out) inverse gamma pdf.  To the extent that fit is deemed poor, the
parameter estimation software associated with the finite difference model
will adjust parameters until a better fit is found.  I will try to use a
goodness of fit test to determine if one set of parameter values in the
finite difference model produce output that fits the inv. gamma curve herein
better than another.  But first I need to establish the curve the finite
difference model output should target and would greatly appreciate any leads
on how it might be shifted and/or fit more precisely by a fitdistr-like
function.

library(MASS)
library(actuar)

iniSal_US_forHist<-c(2.368000,3.532614,3.064330,3.347069,3.066333,4.233636,3.465650,2.858553,
2.946731,2.945417,2.415000,2.873019,5.521000,5.788148,5.314630,5.509672,6.032840,6.009310,
4.110833,6.073182,5.652833,4.425733,6.481852,4.076857,3.289310,4.524000,3.985811,5.399714,
4.490606,6.956729,5.270933,8.099107,5.058250,6.394500,5.644000,5.202459,5.666667,3.152680,
3.220952,2.777381,3.115467,3.642759,3.488333,3.022439,2.610290,2.618571,3.218000,3.417634,
10.327317,7.344270,6.886154,4.015800,3.063103,6.832292,4.600238,2.939000,5.999027,7.894878,
4.411538,2.384762,6.816154,2.782500,2.475333,2.799138,2.739063,2.619917,2.892545,2.468167,
2.577079,2.821875,2.502500,2.969032,2.046023,3.073077,4.408000,3.411774,3.500000,4.283607,
4.284000,4.276714,3.228103,2.639875,3.453194,2.821200,3.838723,1.714253,2.273750,2.611882,
2.321781,2.567500,2.557045,1.288875,2.175211,1.736000,2.250781,7.433366,7.033553,5.474444,
7.132727,8.505937,9.174545,6.554487,7.060286,6.617160,8.210986,4.404045,6.062381,5.149625,
2.972105,5.358889,3.910968,3.715873,1.728966,2.843667,4.413906,3.016346,7.168636,3.839394,
3.930141,7.019882,3.459429,5.050250,3.492714,3.226667,3.987667,2.770227,3.661167,1.553000,
2.867391,2.897193,2.611707,2.577167,2.904697,2.733077,2.507241,11.044865,6.425484,8.567222,
8.552344,7.493396,4.807381,9.697869,9.471333,6.783175,4.563571,8.059649,9.448679,5.803778,
4.769423,4.424634,7.586042,4.451556,3.622373,6.390152,4.424375,4.135806,5.025400,5.410635,
7.012292,2.961071,3.192188,2.989643,3.471429,2.867966,1.980541,3.172344,2.574783,2.958983,
1.708140,3.604853,3.479000,2.845000,2.742603,2.923968,3.620308,2.452500,2.721375,3.166333,
2.742162,2.793000,3.337000,5.192025,5.365875,3.079000,8.415970,6.612277,6.734706,4.856857,
5.164783,7.743667,6.894151,4.666538,9.227167,8.077581,6.109833,6.621724,18.098182,12.705600,
15.490784,17.394750,12.422364,14.832727,8.326000,11.352400,3.431429,2.658261,3.219773,3.605185,
4.030299,3.262241,3.503250,3.522763,2.847312,2.996618,3.075769,3.387731,3.066923,3.078200,
2.466957,3.214167,2.707778,3.384839,2.283556,2.912258,3.378000,2.726750,2.950000,2.195000,
4.819063,3.604578,3.694906,5.068000,4.676582,3.028831,4.261042,3.593235,4.501224,2.880317,
5.750333,3.257833,3.967458,2.522292,2.725738,2.549231,2.591389,2.990488,2.681222,2.685854,
2.284750,2.585938,2.432824,3.108875,2.611340,3.916667,2.418095,2.476406,2.801235,3.278000,
2.434921,2.617826,3.133939,2.774321,4.196173,3.764286,3.555833,5.317361,3.970800,4.136400,
4.487013,3.746393,4.754000,3.854316,3.742353,3.044079,2.817821,3.995179,3.643134,3.642593,
3.604533,2.935902,4.088310,5.344407,3.076883,3.287105,3.720870,2.032258,2.872593,5.787313,
6.017838,5.425205,4.880600,3.582295,4.903333,3.489016,4.603030,5.344407,6.184286,4.047083,
4.788304,4.661325,4.815938,4.056790,3.765595,5.348772,5.200222,4.906311,3.900147,3.782897,
3.767313,3.417732,3.725455,2.888750,2.552333,2.521613,2.531522,2.510833,2.710208,2.445273,
2.619750,2.094737,2.399355,2.758000,2.317077,2.247755,3.594333,4.607805,2.693333,3.084706,
3.529000,2.326200,3.309851,2.647805,2.802250,2.778667,3.231235,2.418065,3.134545,3.807843,
2.988372,2.709792,3.084035,3.633279,2.958750,2.170081,2.674444,2.640706,2.841600,3.399219,
2.561373,2.574824,3.046447,2.647500,3.554875,1.865000,2.858333,2.355000,2.508082,2.376833,
2.728710,1.752833,1.571967,1.800333,2.265455,2.353226,2.568028,2.359500,2.472639,1.675385,
2.667386,2.490000,2.482632,2.593452,2.695510,2.466941,2.624211,3.835645,3.519667,2.661940,
3.516167,3.146585,3.420462,4.809833,3.028500,3.192297,4.256333,2.516897,3.033846,2.793359,
6.700714,5.441250,6.872500,4.528333,7.490328,4.673788,6.376885,3.023167,4.429167,4.317625,
16.729231,8.372500,6.279828,10.805098,8.359452,8.277576,8.008846,8.742308,12.155942,5.975063,
3.317333,2.883021,3.310822,3.119219,3.921190,3.552986,3.647162,4.017667,3.895342,3.381096,
2.769412,3.225294,4.169333,3.733919,2.859492,3.674875,3.401017,3.160267,4.109545,4.347867,
3.867000,3.672763,4.364844,3.804250,2.613000,4.289909,4.212059,4.785797,4.149687,6.299444,
5.640135,5.713448,4.766438,7.032027,5.610533,3.126111,6.322029,4.417692,6.392532,2.753175,
2.549655,3.456533,3.199000,3.852338,3.387549,3.098033,3.271733,3.679180,2.655484,6.858167,
5.808033,7.551111,8.388387,5.108732,7.895152,5.223580,5.741714,8.026250,4.928421,2.797292,
3.052500,2.934615,2.842051,2.869259,2.702400,2.666977,2.935385,2.546471,2.617755,3.020250,
2.922955,3.133500,3.353750,3.101000,2.581235,3.624715,2.376164,3.597467,3.011519,2.885250,
2.642716,2.843788,3.125000,2.394034,3.126125,2.960125,3.553800,3.045733,2.823375,2.953951,
3.170694,3.746500,3.421519,2.876707,3.162206,2.976852,2.912917,3.510784,2.822763,3.245244,
3.322738,3.168776,2.822700,2.898500,4.311667,3.517195,4.239014,3.615676,3.625652,4.693542,
3.426379,3.446250,4.204375,4.061000,2.864167,3.498772,3.817303,2.649300,2.913529,2.773400,
3.844833,3.312581,4.072025,3.578395,3.856429,3.666889,2.554505,2.615469,2.686667,4.848387,
3.182667,3.172364,2.829063,2.998182,2.224000,3.238167,4.072407,5.915490,5.872632,4.942597,
6.163684,5.003750,1.592295,2.398679,2.360000,1.930200,2.341746,2.352031,2.577647,2.286604,
2.172000,2.430889,2.647231,2.748500,2.837692,2.764884,2.511774,3.047451,2.744737,2.733871,
2.666818,3.047800,6.127000,3.212807,7.100615,5.016842,5.404091,4.586324,4.815738,2.667867,
2.583625,3.023099,2.364154,3.033077,2.712821,3.104861,2.451831,10.244054,9.028333,6.488088,
11.350333,10.805227,2.796250,3.901455,8.846500,5.692500,4.502549,9.645833,12.323077,11.690702,
9.757213,10.140000,6.435873,8.559375,12.581639,9.658000,7.910395,10.317167,14.744098,3.019400,
3.196154,2.924583,2.926393,3.435926,2.940968,2.729048,2.419625,3.257031,2.246915,2.405352,
4.807167,3.329661,3.300256,2.626364,2.588714,2.516825,3.369804,2.802381,2.703889,1.899500,
2.624286,3.370244,3.224510,2.587368,3.243881,3.209474,2.644154,3.591132,3.179851,3.118125,
3.428333,3.078033,2.639219,2.392979,3.035208,8.924667,7.126420,4.412626,7.663580,9.798000,
7.091940,6.561806,10.351000,7.816000,5.686581,7.486833,5.878148,5.549032,1.775849,3.393235,
3.730208,3.131846,2.988404,3.922286,3.835077,1.918780,2.614118,2.564207,3.160625,2.085614,
2.498033,1.107183,2.408000,2.226296,3.063281,2.647500,3.149726,1.929091,2.297000,4.035500,
7.813846,18.976765,10.127547,12.294455,5.909020,7.263115,13.789367,6.608750,3.110926,4.948333,
7.655873,5.366154,2.468889,3.215000,3.329375,2.722821,3.115902,2.538235,3.233171,3.060541,
3.377647,2.837049,3.071290,2.293400,3.034937,2.943846,2.987534,2.947222,3.286522,2.794600,
2.950822,1.542667,2.318085,3.049583,2.384250,2.554146,1.761333,2.028356,2.434590,3.128333,
2.838437,3.331000,2.645116,3.038667,2.646000,3.082857,4.406301,4.136000,2.161429,1.832424,
3.027742,3.908958,3.479608,3.566562,2.101875,2.960122,2.804752,2.334105,3.993836,2.878116,
2.828197,2.674353,3.231500,2.468000,2.152400,3.290274,5.412121,2.775909,9.023833,6.593125,
3.417558,4.213469,2.771452,7.874776,2.453871,3.166833,2.657000,2.526111,3.105400,2.973265,
4.900667,3.042551,2.861647,3.745125,3.244643,2.177500,2.119167,2.798000,3.005577,2.837347,
3.211167,3.381358,3.200306,4.640167,5.564706,3.043121,6.172000,2.490000,4.449667,5.433918,
4.652576,3.197619,2.675631,2.547407,3.462195,2.657468,3.016087,2.814262,2.966383,3.288033,
2.278676,2.609537,2.633667,2.815000,3.465000,2.231538,3.161538,3.412667,3.516800,3.249452,
2.418734,3.245455,2.650800,3.634038,3.255484,1.992093,3.184429,3.155200,2.997500,3.887931,
2.597500,3.316406,3.684091,3.707107,4.479692,3.292833,2.806935,2.833143,2.962857,2.229474,
3.786700,4.029756,3.174118,6.493770,4.611944,6.103279,5.899687,2.946711,6.338660,5.237273,
3.413553,3.226667,4.193143,6.192375,9.437436,1.863548,3.185567)

#plot it
hist(iniSal_US_forHist,breaks=seq(1.1,21,by=0.625),col="grey",freq=F,xlim=c(0,21))

#try fitting it