用R拟合分布

如何解决用R拟合分布

下午好。我有一个包含16000个值的向量“ a”。我借助以下内容获得描述性统计数据：

library(pastecs)
library(timeDate)
 stat.desc(a)
 skewness(a)
 kurtosis(a)

特别是偏度= -0.5012，峰度= 420.8073 （1）

然后我建立经验数据的直方图：

 hist(a,col="lightblue",breaks = 140,border="white",main="",xlab="Value",xlim=c(-0.001,0.001))

此后，我尝试将理论分布拟合到我的经验数据。我选择Variance-Gamma分布，并尝试在我的数据上获取其参数估算值：

library(VarianceGammma)
 a_VG<-vgFit(a)

参数估计如下： vgC = -11.7485，sigma = 0.4446，theta = 11.7193，nu = 0.1186 （2）

此外，我使用（2）中的参数从Variance-Gamma分布中创建了一个样本 并建立创建的理论值的直方图：

VG<-rvg(length(a),vgC=-11.7485,sigma=0.4446,theta=11.7193,nu=0.1186)
 hist(VG,breaks=140,col="orange",xlab="Value")

第二直方图与第一（经验）直方图完全不同。而且，它是基于我根据经验数据得到的参数（2）建立的。

我的代码有什么问题？我该如何解决？

P.S。当我输入dput(a[abs(a) > 5e-4])时，我得到：

c(0.000801110480004752,0.000588162271316861,0.000555169128569233,0.000502563410256229,0.000854633994686438,0.00593622112246628,-0.000506168123513007,-0.000502909585836875,0.000720924373137422,0.00119141739181039,0.000548159382141478,-0.000516511318695123,-0.000744590777740584,0.000595213912401249,0.000514055190913965,-0.000589061375421807,-0.00175392114572581,0.000745548313668465,-0.00075910234096277,-0.00059987613053103,0.000583568488865538,0.00426484136013094,0.000610760059768012,0.000575522836335551,0.000823785810599276,0.00181936036509178,-0.00073316272551871,-0.00184238143420679,-0.000519146793923397,-0.00120324664043103,-0.000882469414168696,-0.00148118339830283,0.000929612782487155,0.000565364610238817,0.000578158613453894,0.00060479145432879,-0.00520576206828594,0.000708404040882016,0.00105224485893451,0.000636486872540587,-0.00359655507585543,0.000769164650506582,0.000635701125126786,0.000570489501935612,-0.000641260260277221,0.000735092947873994,0.000757195823062773,0.000556002742616357,-0.00207489740356159,-0.000553386431560554,0.000511326871983186,0.000504591469525195,-0.000749886905655472,-0.0013939718643865,-0.000513742626250036,-0.00105021597423516,-0.00156667292147716,0.000864563166150134,0.00433724128055069,0.00053855648931922,-0.00150732363190365,0.00052621785349416,0.000987781100809215,0.000560725818171903,0.00176012436713435,-0.000594895431092368,-0.000686229580335151,0.00138682284509528,-0.000531964338888358,-0.00179959148771403,0.000574543871314503,-0.000686996216439084,-0.000559043343629995,0.00055881173674166,-0.000636332688477736,-0.000623778186703561,-0.00173834148094443,-0.000567224129968125,-0.00122578683434504,0.00130960156515414,-0.000548203197176633,-0.000522749285863711,-0.000820371086264871,0.000756014225812507,-0.000714081490558627,-0.000617600335221624,0.000523639760748651,-0.000578502663833191,0.00107478825239227,0.000612725356974764,-0.00065509337422931,0.000505887803587513,-0.000566716376848575,0.000511727090058756,0.000572807738912218,-0.000756026937699161,0.000547948751494332,0.000628323894238392,-0.000541350489317693,-0.00133529454372372,-0.000590618859845904,-0.000700581963648972,0.000735987224462775,0.000528958898682319,0.000838250041022448,-0.000519084424130511,-0.00052258402856431,-0.000538130765869838,-0.000631819887885854,0.00054800880764283,0.00266115500510899,-0.000839092093771754,0.000559253571783103,-0.000801028189803432,-0.000608879021022801,-0.000538018076854385,-0.000689859734395171,0.00329650346269972,0.000765494493951024,-0.000689450477848297,-0.000560199139975737,0.00159082699266122,-0.00208548663121455,-0.000598493596793759,0.000563544422691464,0.000626996183768824,-0.000653166846808162,-0.000851350174739807,-0.00140687473245116,-0.000887003220306326,-0.000765614651347946,-0.00100676206277761,0.000724714394852555,0.00108872127644233,-0.000678558537305918,-0.000705087556212902,0.000544828152248655,-0.000791700964308362,0.000606125736727137,-0.00119335967326073,0.00075413211796338,0.000526038939010931,0.00086543737231537,-0.000817788712950573,-0.000584070926663571,0.000619657281937691,0.000680783312420274,-0.000513831718574664,-0.00050972403875349,-0.00114542220685365,-0.00070564389723593,-0.01057964950882,-0.000610357922434801,0.000818264221596365,0.000940825400308043,-0.000726555639413817,-0.000591089505560305,0.000564738888193972,-0.00068515060569041,0.000668920238348747,-0.00110103375121717,-0.0015480433031172,0.000663030855223568,0.000500097431997304,-0.000600730311271391,-0.000672397772962796,-0.000607852365856587,0.000536711920570809,0.000595055206488837,0.000523123873687581,0.000977280737528119,0.000616410821629998,0.000788593666889881,-0.000671642905915704,0.000717328711735021,-0.000551853104219902,-0.000565153434708421,-0.000802585212152707,0.000536342062561701,0.000682048510343591,-0.000541902545439399,0.000779676683974273,0.000698841439971787,0.000559313965908359,-0.00064986819016255,0.000795421518319017,0.00364973919549527,0.000669658692276087,0.00109045476974678,0.000514411572742901,0.000503832507211754,-0.000507376233564116,0.001232871590787,0.000561820312542594,-0.000501190337518054,-0.000769036505996468,-0.000695537959007453,-0.000572065848166048,-0.00167929926328192,0.000597078186826749,0.00710238430870014,0.000745192112519888,-0.00116091022028009,-0.000791139281769659,-0.00148898466632552,0.000565144038962018,-0.000514019821833855,-0.00148427996685285,-0.000822717245339888,-0.00062922111212238,-0.000636011367371125,0.00119640327632808,0.000548455410294579,0.000652678152560426,0.000509244387833618,0.000961872348987924,0.000662064072514568,-0.00068116858054168,-0.000569930302445343,0.00188358126928101,0.00130560555273895,0.000593470885775105,0.00160093110088155,0.000785262438315115,-0.000912313442922752,0.000609996052359563,0.000720137994393966,0.000568163899000496,0.00128685533068307,-0.000756787473447318,0.000765932134255465,0.00064884753100003,0.000687571386270847,-0.000582094290400903,-0.000693177295971736,-0.000601776208094762,0.0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)

拟合数据后，如下所示（经验直方图为蓝色，理论直方图为橙色）：

在freq=FALSE

中包含hist时是相同的

解决方法

这都是由于a中的异常值未由您显示的直方图表示。这可能是导致峰度极高的原因，也可能是vgFit()算法无法找到合适的结果的原因。

在控制台中输入dput(a[abs(a) > 5e-4])，然后将输出复制到您的问题中。这样一来，人们便可以像向量a一样重新创建事物，而不必获取所有16000值并调试vgFit问题。

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感谢额外的数据。那里有一些极限值，但是我不认为这些是导致vgFit问题的原因。拟合几乎可以是任何值的4个参数都很困难，但是您可以通过将数据重新缩放为典型值来帮助实现这一点。试试这个：

b <- (a-mean(a))/sd(a)
vgf <- vgFit(b)
vgf$param
VG <- rvg(16000,param = vgf$param)
VG_rescaled <- VG*sd(a)+mean(a)
hist(VG_rescaled,breaks=140,col="orange",main="",xlab="Value")

看看两个直方图现在是否足够接近。