使用 R 包 EMCluster 绘制单变量正态分布的混合图
Plotting mixture of univariate normal distributions using the R package EMCluster
我想可视化由 EMCluster R 包拟合的单变量正态分布的混合。我想为每个组分别绘制一组高斯曲线到我的数据的直方图上，如下所示：
但是，EMCluster 中似乎没有任何绘图功能可以做到这一点，而且 EMCluster 帮助文件也没有涵盖这个主题。我知道其他具有此功能的 R 软件包（例如 mixtools 或 mclust），但与 EMCluster 不同，这些软件包无法正确完成安装工作，而 EMCluster 是唯一能够正确安装发行版的软件包。
这是用于拟合模型的代码：
# input data
ratio <- c(2.3082202,2.2682008,2.3430013,2.3131582,2.3442648,2.2866254,2.4438874,2.4360583,2.4907970,2.4785809,2.4368449,2.4589041,2.2404580,2.2568378,2.2305135,2.2316156,2.1975250,2.2003426,2.3995671,2.2367229,2.2380535,2.2695250,2.2795190,2.2804133,2.2873157,2.3025447,2.2981834,2.2774566,2.1899404,2.2675393,2.2863328,2.2702749,2.2173223,2.1615549,2.3052489,1.4739972,1.4703164,1.8989637,1.6309663,1.4742799,1.6040551,1.5125876,2.3090968,2.4032732,2.2939723,2.4932422,2.4572377,2.2887470,2.2541456,2.3912709,2.3709839,2.2961881,2.3252021,2.4311603,2.4526981,2.2712559,2.4556190,2.4480402,2.2345277,2.2832188,2.3259353,2.3486292,2.3477749,2.3160682,2.3025502,2.3645101,2.2972784,2.3914385,2.4182051,2.3144094,2.3182206,2.3032635,2.3304741,2.4386540,2.4750668,1.5558920,1.5520053,1.5679544,1.5674089,1.5318896,1.5378909,1.5780276,1.5884973,1.5535807,2.4912484,1.5725149,1.6011670,1.5669198,1.5581934,1.5688439,1.5578162,1.5593121,1.5563160,1.5468341,1.5433628,1.5141012,1.5842708,1.5632946,1.5233117,1.5867471,1.5010637,1.5865281,1.5836973,1.6140125,1.6285195,1.5592994,1.5584742,1.6113194,1.6074361,1.5850861,1.5612799,1.5905453,2.3874244,2.4045643,2.3996815,2.3605345,2.3346210,2.3865179,2.4406780,2.3688209,2.3649233,2.3668617,2.4675781,2.4767129,2.4664701,2.3560843,2.5487013,2.4604951,2.5133258,2.4387729,1.4955564,1.5082731,1.5440476,1.5911176,2.4114691,2.4188795,2.4320730,2.4896641,2.4439351,2.4726592,2.4819837,2.4053318,2.4694447,2.3929463,2.3948703,2.3993741,2.4535933,2.4556870,2.3877090,2.4466891,2.4426443,2.3879938,2.3402072,2.3448416,2.4782167,2.5233350,1.5917363,1.6355997,1.5816622,1.6164543,1.5466306,1.5081628,1.4992875,1.6306420,1.6762845,1.6866838,2.4210023,2.4406259,2.3720587,2.4113856,2.3190864,2.4250728,2.4457677,2.4429783,2.4122941,2.4424428,2.4527037,2.4966437,2.4035152,2.4137089,2.3954934,2.4212645,2.4087689,2.4105695,2.5525013,1.5290941,1.5728092,1.5543364,1.5641066,1.6006943,1.5889370,1.5321614,1.5586370,1.5415335,1.5491241,1.5541842,1.5852345,1.5902462,1.5801461,1.5930383,1.5523744,1.5575027,1.5546879,1.5726514,1.5938686,1.6222843,1.5881920,1.5889394,1.6246987,1.5791531,1.6059873,1.5860296,1.5701796,1.5763713,1.6315066,1.6206847,1.5685662,1.5892450,1.6186198,1.6242586,1.5481500,2.5555498,2.5258320,1.6016010,1.6078024,1.7627993,2.5282046,2.5283876,1.6267890,1.6268478,1.6069182,1.5574029,1.5672845,1.6389830,1.5810995,1.5809019,1.5621111,1.6275267,1.5630592,1.5361265,1.5750796,1.5447555,1.5755329,1.5092036,1.5607702,1.5812295,1.6181003,1.6067561,1.6846355,1.6251237,1.7229672,1.6319477,2.0122061,1.6008821,1.4929003,1.5977780,1.6336924,1.7014357,1.7084902,1.5106016,1.6115451,1.5218875,1.5394796,1.5841880,1.6021178,1.6286143,1.6322306,1.6479547,1.6051730,1.6903781,1.5605062,1.6159015,1.5648148,1.6410461,1.5526851,1.5951099,1.6702494,1.6863064,1.5488679,1.5722265,1.5789145,2.3835058)
ratio <- c(ratio,2.4312322,2.4034768,2.4384596,2.4436314,2.4303576,2.4266296,2.3727400,2.3769620,1.4916100,2.0513010,2.0537072,1.6218816,1.6315519,1.6242272,1.5328026,2.4791800,2.4943584,1.5233619,1.5520066,1.5211411,1.5946195,1.5954327,1.5099963,1.6025225,1.4824897,1.5543129,1.6041963,1.9676651,1.8662227,1.9669943,1.5584472,1.5664382,1.5551137,1.5563330,1.5637281,1.6058321,2.3605461,1.4467948,2.4481076,2.2974519,2.4029441,2.4499736,2.4637541,2.4147364,2.4483680,2.4730025,2.4344831,2.4246536,2.3520329,2.3551388,2.4119589,2.4621961,2.3978363,2.4289587,2.4244460,2.3955454,2.4106017,2.4766059,2.5505131,2.5904964,2.4405065,2.5502677,2.5418027,2.5946520,2.3462233,2.3910095,2.3808582,2.4900000,2.4929675,2.5957481,2.6473263,2.6821399,2.5863157,2.5706163,2.5873251,2.3470114,2.3549401,2.4447632,2.3895783,2.4598023,1.9194875,1.9098258,1.5563858,1.9655190,1.9843544,1.5075750,1.9197088,1.8606831,1.5003864,1.5420225,1.5832182,1.4812740,1.5309472,1.5425323,1.6757806,1.6147225,1.5449271,1.6736108,1.6062912,1.5309035,1.5375653,1.5230470,1.4537051,1.5208274,1.6269986,1.6722362,1.5627355,1.5736269,1.5597532,1.6075006,1.5912113,1.4857339,1.4865164,1.5915908,1.5626763,1.6001816,1.5838017,1.6547792,1.6521739,1.5541260,1.5589220,1.6041114,1.6052877,1.6188839,1.5851005,1.5210468,1.5914289,1.5612923,1.5543678,1.6405511,1.5491183,1.5760101,1.5988843,1.5453074,1.5629486,2.3506363,2.3900338,2.3692994,2.3774440,2.3778159,1.4801504,1.5272571,1.5429716,1.5863007,1.5595683,1.5373692,1.5547804,1.6523496,1.6553747,2.4441022,2.3405286,2.4331678,2.4992773,2.4313793,2.3579883,2.4041657,2.3764722,2.3899039,2.4933925,2.4881635,2.3814493,2.4341179,2.5575816,2.4556496,2.5024020,2.4669698,2.4933790,2.5047439,2.4975195,2.4015712,2.4469022,2.4567287,2.5280128,2.4781728,2.5028472,2.5189290,2.5043568,2.4434804,2.4769850,2.4082988,2.4613414,2.3871942,2.4679938,2.4711610,2.3716282,2.4665808,2.4719631,2.4671665,2.3450332,2.3711461,2.3567956,2.4531954,2.4627118,2.4688380,2.4264698,2.4634535,2.4754286,2.4152280,2.4200143,2.4366610,2.4748473,2.3998817,2.4435630,2.4505969,2.4825692,2.4722832,2.3908582,2.5265103,2.4205017,2.4975109,1.8273926,1.8191600,1.7649152,1.8441525,1.8362518,1.7798777,1.7749614,1.8514624,1.8231416,1.7980675,1.8139444,1.7813007,1.8112133,1.8506497,1.7888465,1.7981612,1.7877846,1.8448715,1.8428863,1.7778798,1.8004113,1.8293173,1.8581288,0.7568285,0.7681167,0.7569872,0.7478473,0.7586729,0.7574590,0.7707119,0.7654296,0.7560802,0.7223322,0.7634792,0.7577954,0.7630233,0.7439842,0.7501500,0.7666750,0.7503895,0.7622286,0.7635520,0.7534987,0.7599475,0.7748956,0.7590139,0.7568013,0.7586510,0.7564873,0.7576587,0.7756744,0.7637029,0.7579558,0.7735586,0.7692345,0.7611547,0.7551704,0.7715118,0.7736083,0.7635049,0.7559560,0.7667778,0.7618454,0.7648308,0.7693512,0.7653699,0.7589299,2.3590999,2.3619440,2.3519471,2.3453709,2.3486040,2.4295357,2.4219361,2.4488210,2.4213269,2.3923218,1.5402144,0.7652187,0.7650076,0.7486516,0.7643569,0.7677992,0.7586368,0.7584026,0.7662775,0.7740569,0.7713377,0.7740677,0.7686109,0.7490695,0.7681402,0.7639513,0.7896797,0.7660664,0.7720809,2.4936417,2.3834268,0.7626155,0.7566950,0.7824697,0.7735270,2.4219853,2.5196019,0.7636966,0.7570312,2.4539218,2.4338622,2.4396830,0.7733773,0.7632390,0.7697633,0.7677199,0.7563686,0.7569366,0.7785563,2.3883388,2.4508850,2.5454545,2.4078138,2.4295884,2.5461211,2.3826057,2.4070722,2.4136287,2.4216196,2.3854115,2.4173648,2.4553045,2.4356992,2.3863270,2.4346182,2.3953523,2.4102911,2.4179386,2.4251441,2.4217263,2.4586260,2.4059818,2.4069762,2.4099267,2.4387039,2.4458400,2.4573490,2.4759171,2.4772782,2.4684424,2.4434910,2.4804417,2.4192554,2.4454277,2.3955812)
ratio <- c(ratio,2.4749573,2.4724740,2.4209932,2.4249042,0.7610100,2.3671184,2.3697960,2.4023920,2.4053188,2.4351452,2.4386339,2.4094596,2.3468609,2.3155974,2.3104149,2.3627904,2.2658038,2.3885135,2.3038569,2.3350929,2.3612206,2.2781386,2.2077955,2.2325030,2.2679324,2.2823724,2.4542063,2.1998876,2.3031394,2.2881462,2.3198411,2.1884115,2.2710756,2.1827032,2.3180018,2.2993929,2.2874717,2.2829849,2.3455578,2.2977960,2.3410225,2.4081727,2.3638018,2.2795117,2.3976837,2.3932511,2.4075917,2.4015616,2.3418264,2.3349013,2.4240838,2.4173924,2.3960085,2.4031925,2.3945173,2.3856273,2.4690719,2.4686576,2.6263546,2.4718199,2.3463103,2.3652738,2.4379702,2.4796148,2.4287476,2.2620077,2.3805959,2.3458551,2.3461876,2.3171412,2.3897433,2.3912464,2.3614724,2.5442086,1.7773526,1.7178727,2.3689272,2.3640495,2.2916104,2.3356112,2.3964407,2.4015147,1.7590361,2.3414859,2.2694388,2.3567392,2.2708003,2.2956377,2.3101355,2.3125120,2.3004763,2.2705803,2.2875544,2.2712565,2.3089819,2.2945688,2.3205069,2.2732516,1.7467849,1.7259182,1.7686619,1.7095978,2.2485174,2.4754472,2.4495703,2.4074395,2.4539152,2.3435356,2.3811995,2.4362843,2.4403479,2.5180754,0.7635700,0.7702974,0.7722231,0.7511177,0.7551106,0.7601832,0.7361963,0.7794874,0.7934396,0.7709755,0.7844490,0.7596845,0.7930613,0.7504008,0.7627609,0.7532478,0.7581377,0.7705301,0.7721196,0.7567074,0.7828257,0.7780374,0.7669904,0.7812995,0.7834886,0.7889141,0.7859603,0.7682853,0.7478378,0.7673373,0.7629394,0.7715725,0.7791851,0.7666474,0.7714516,0.7496962,0.7533639,0.7579321,0.7737278,0.7853168,0.7645964,0.7725103,0.7677113,1.6156064,1.5390375,1.5211357,1.5385035,1.4920242,1.6010156,1.5269279,1.5407954,1.4766077,1.5165483,2.4101888,2.4461818,2.4832620,2.4234102,2.3891139,2.4782895,2.4514298,2.4655178,1.5269570,1.5543206,1.5397302,1.5121552,1.5089835,1.5259734,1.5593889,1.5634023,1.5243902,1.5291230,1.5649990,2.3870746,2.4165985,2.4108952,2.5178706,2.4626444,2.4056250,2.4241015,2.2767663,2.1800944,2.2449665,2.2155462,2.2102232,2.1888782,2.1780130,2.1797660,2.2164432,2.1815838,2.2745605,2.2695021,2.1916002,2.1620086,2.1604276,2.1606576,2.1582508,2.1380764,2.1869745,2.1967953,2.1466257,2.1625341,2.2056076,2.1491951,2.2865496,2.2079291,2.1408957,2.1638916,2.5895003,2.1258483,2.1444175,2.2055520,2.1909330,2.2072956,2.2051386,2.4054279,2.4282109,2.4143596,2.4389768,2.4716971,2.4614070,2.4076957,2.4289880,2.4710598,2.4395144,2.4251923,2.4528039,2.4597420,2.4047160,2.4214961,2.4052775,2.4002135,2.3944374,2.4051049,2.4450801,1.5737999,1.5879028,1.4740943,1.5251975,1.5084994,1.5176669,1.5827066,1.8177106,2.4441547,2.4143742,2.4699203,2.3762657,2.3688625,2.4603598,2.4191691,2.4546725,2.4275861,2.4220888,2.4021738,2.4979091,2.4092485,2.4321795,2.4349427,2.4462136,2.4662561,2.3542403,2.4312644,2.4911342,2.4228929,2.4431390,2.4214492,2.4497284,2.4559866,2.4404771,2.4329174,2.4118930,2.4634206,2.4609880)
ratio <- c(ratio,2.4827362,2.3897923,2.4143036,2.4375662,2.4641043,2.4222062,2.4024445,2.4035411,2.4564304,2.4355113,2.3968869,2.4147049,2.4618251,2.4281002,2.3793209,2.4370193,2.3959920,2.3882394,2.4338975,2.4221606,2.4012736,2.4163148,2.4014352,2.3909576,2.4497283,2.3379209,2.2898380,2.3337816,2.2496425,2.3140063,2.2480368,2.3382981,2.4370101,2.3976064,1.5515221,1.6095634,1.5416116,1.5449938,1.5357950,1.6159637,2.5099319,2.4895688,2.5469330,2.4921635,2.4849558,2.5936576,2.4149410,2.3313097,2.3891210,2.3958461,2.4481496,2.3889537,2.3672844,2.3638062,2.3213211,2.2783695,2.3841916,2.3915916,2.4455549,2.3920387,2.3327502,2.3814912,2.3998684,2.5413619,2.4137805,2.4694112,2.2786062,2.3302104,2.3343673,2.3937296,2.3613661,2.4505636,2.4254633,2.5044136,2.4344560,2.3947676,2.3527630,2.3999480,2.3888254,2.4736389,2.4171134,2.4438647,2.2072640,2.4066542,2.4867753,2.4228284,2.4383648,2.4733934,2.3856568,2.3750662,2.2850762,2.3953039,2.4272293,2.4479172,2.4583161,2.4372287,2.4391820,2.4068650,2.3923539,2.4295108,2.4074787,2.4039005,2.4916317,2.4349603,2.4786877,2.4942217,2.2279876,2.4491045,2.2402399,2.3116072,2.3713333,2.3000641,2.2848940,2.4239510,2.4702209,2.4698362,2.4101398,2.3967287,2.4586776,2.4489123,2.4533943,2.4532398,2.4235131,2.4177043,2.4007880,2.4442298,2.4343659,2.4388599,2.3495992,2.4192377,2.3928401)
library(EMCluster)
ret <- init.EM(as.data.frame(ratio),nclass=6,method="Rnd.EM") # fitting model
# now how to plot the distribution curves?
预先感谢您的建议。
编辑：
结果对象的结构是这样的：
> str(ret,vec.len = 10)
List of 13
$ pi : num [1:6] 0.0537 0.234 0.299 0.1124 0.2225 0.0784
$ Mu : num [1:6, 1] 1.794 1.568 2.429 0.765 2.316 2.474
$ LTSigma : num [1:6, 1] 0.011002 0.001946 0.001355 0.000124 0.008215 0.006486
$ llhdval : num 435
$ nc : int [1:6] 52 252 406 119 195 35
$ class : num [1:1059] 5 5 5 5 5 5 3 3 3 3 3 3 5 5 5 5 5 5 3 5 5 5 5 5 5 ...
$ conv.iter: int 93
$ conv.eps : num 9.81e-07
$ flag : num 0
$ n : int 1059
$ p : int 1
$ nclass : num 6
$ method : chr "Rnd.EM"
- attr(*, "class")= chr "emret"
这很简单。使曲线的高度合理排列需要一些计算，但除此之外它是非常基本的。首先绘制直方图。如果你想要一个围绕它的盒子，就像你的例子一样，那就去做吧。然后你需要调用 lines() 6 次来绘制 6 条法线。在 R 中，线条只是一系列插值点——(x,y) 坐标——因此请制作一组足够细粒度的 x 坐标，然后使用 dnorm() 和拟合参数计算每个分量的法线密度。您需要将这些 y 值乘以适当的比例和高度调整因子才能使曲线的高度正确。事实证明，直方图中最高的 bin 是 82，这大约是第三个分量的峰值，但由于它仅代表 30%，因此您需要按此重新调整调整因子。您可能想要选择自己的颜色。考虑：
xs <- seq(min(ratio), max(ratio), length.out=1000)
windows()
h <- hist(ratio, breaks=seq(0, 3, by=0.02)); box()
# max(h$counts) # [1] 82
height <- 82/dnorm(ret$Mu[3,1], mean=ret$Mu[3,1], sd=sqrt(ret$LTSigma[3,1]))
height <- height/ret$pi[3]
for(i in 1:6){
lines(xs, dnorm(xs, mean=ret$Mu[i,1], sd=sqrt(ret$LTSigma[i,1]))*height*ret$pi[i],
lwd=2, col=i)
}
我想可视化由 EMCluster R 包拟合的单变量正态分布的混合。我想为每个组分别绘制一组高斯曲线到我的数据的直方图上，如下所示：
但是，EMCluster 中似乎没有任何绘图功能可以做到这一点，而且 EMCluster 帮助文件也没有涵盖这个主题。我知道其他具有此功能的 R 软件包（例如 mixtools 或 mclust），但与 EMCluster 不同，这些软件包无法正确完成安装工作，而 EMCluster 是唯一能够正确安装发行版的软件包。
这是用于拟合模型的代码：
# input data
ratio <- c(2.3082202,2.2682008,2.3430013,2.3131582,2.3442648,2.2866254,2.4438874,2.4360583,2.4907970,2.4785809,2.4368449,2.4589041,2.2404580,2.2568378,2.2305135,2.2316156,2.1975250,2.2003426,2.3995671,2.2367229,2.2380535,2.2695250,2.2795190,2.2804133,2.2873157,2.3025447,2.2981834,2.2774566,2.1899404,2.2675393,2.2863328,2.2702749,2.2173223,2.1615549,2.3052489,1.4739972,1.4703164,1.8989637,1.6309663,1.4742799,1.6040551,1.5125876,2.3090968,2.4032732,2.2939723,2.4932422,2.4572377,2.2887470,2.2541456,2.3912709,2.3709839,2.2961881,2.3252021,2.4311603,2.4526981,2.2712559,2.4556190,2.4480402,2.2345277,2.2832188,2.3259353,2.3486292,2.3477749,2.3160682,2.3025502,2.3645101,2.2972784,2.3914385,2.4182051,2.3144094,2.3182206,2.3032635,2.3304741,2.4386540,2.4750668,1.5558920,1.5520053,1.5679544,1.5674089,1.5318896,1.5378909,1.5780276,1.5884973,1.5535807,2.4912484,1.5725149,1.6011670,1.5669198,1.5581934,1.5688439,1.5578162,1.5593121,1.5563160,1.5468341,1.5433628,1.5141012,1.5842708,1.5632946,1.5233117,1.5867471,1.5010637,1.5865281,1.5836973,1.6140125,1.6285195,1.5592994,1.5584742,1.6113194,1.6074361,1.5850861,1.5612799,1.5905453,2.3874244,2.4045643,2.3996815,2.3605345,2.3346210,2.3865179,2.4406780,2.3688209,2.3649233,2.3668617,2.4675781,2.4767129,2.4664701,2.3560843,2.5487013,2.4604951,2.5133258,2.4387729,1.4955564,1.5082731,1.5440476,1.5911176,2.4114691,2.4188795,2.4320730,2.4896641,2.4439351,2.4726592,2.4819837,2.4053318,2.4694447,2.3929463,2.3948703,2.3993741,2.4535933,2.4556870,2.3877090,2.4466891,2.4426443,2.3879938,2.3402072,2.3448416,2.4782167,2.5233350,1.5917363,1.6355997,1.5816622,1.6164543,1.5466306,1.5081628,1.4992875,1.6306420,1.6762845,1.6866838,2.4210023,2.4406259,2.3720587,2.4113856,2.3190864,2.4250728,2.4457677,2.4429783,2.4122941,2.4424428,2.4527037,2.4966437,2.4035152,2.4137089,2.3954934,2.4212645,2.4087689,2.4105695,2.5525013,1.5290941,1.5728092,1.5543364,1.5641066,1.6006943,1.5889370,1.5321614,1.5586370,1.5415335,1.5491241,1.5541842,1.5852345,1.5902462,1.5801461,1.5930383,1.5523744,1.5575027,1.5546879,1.5726514,1.5938686,1.6222843,1.5881920,1.5889394,1.6246987,1.5791531,1.6059873,1.5860296,1.5701796,1.5763713,1.6315066,1.6206847,1.5685662,1.5892450,1.6186198,1.6242586,1.5481500,2.5555498,2.5258320,1.6016010,1.6078024,1.7627993,2.5282046,2.5283876,1.6267890,1.6268478,1.6069182,1.5574029,1.5672845,1.6389830,1.5810995,1.5809019,1.5621111,1.6275267,1.5630592,1.5361265,1.5750796,1.5447555,1.5755329,1.5092036,1.5607702,1.5812295,1.6181003,1.6067561,1.6846355,1.6251237,1.7229672,1.6319477,2.0122061,1.6008821,1.4929003,1.5977780,1.6336924,1.7014357,1.7084902,1.5106016,1.6115451,1.5218875,1.5394796,1.5841880,1.6021178,1.6286143,1.6322306,1.6479547,1.6051730,1.6903781,1.5605062,1.6159015,1.5648148,1.6410461,1.5526851,1.5951099,1.6702494,1.6863064,1.5488679,1.5722265,1.5789145,2.3835058)
ratio <- c(ratio,2.4312322,2.4034768,2.4384596,2.4436314,2.4303576,2.4266296,2.3727400,2.3769620,1.4916100,2.0513010,2.0537072,1.6218816,1.6315519,1.6242272,1.5328026,2.4791800,2.4943584,1.5233619,1.5520066,1.5211411,1.5946195,1.5954327,1.5099963,1.6025225,1.4824897,1.5543129,1.6041963,1.9676651,1.8662227,1.9669943,1.5584472,1.5664382,1.5551137,1.5563330,1.5637281,1.6058321,2.3605461,1.4467948,2.4481076,2.2974519,2.4029441,2.4499736,2.4637541,2.4147364,2.4483680,2.4730025,2.4344831,2.4246536,2.3520329,2.3551388,2.4119589,2.4621961,2.3978363,2.4289587,2.4244460,2.3955454,2.4106017,2.4766059,2.5505131,2.5904964,2.4405065,2.5502677,2.5418027,2.5946520,2.3462233,2.3910095,2.3808582,2.4900000,2.4929675,2.5957481,2.6473263,2.6821399,2.5863157,2.5706163,2.5873251,2.3470114,2.3549401,2.4447632,2.3895783,2.4598023,1.9194875,1.9098258,1.5563858,1.9655190,1.9843544,1.5075750,1.9197088,1.8606831,1.5003864,1.5420225,1.5832182,1.4812740,1.5309472,1.5425323,1.6757806,1.6147225,1.5449271,1.6736108,1.6062912,1.5309035,1.5375653,1.5230470,1.4537051,1.5208274,1.6269986,1.6722362,1.5627355,1.5736269,1.5597532,1.6075006,1.5912113,1.4857339,1.4865164,1.5915908,1.5626763,1.6001816,1.5838017,1.6547792,1.6521739,1.5541260,1.5589220,1.6041114,1.6052877,1.6188839,1.5851005,1.5210468,1.5914289,1.5612923,1.5543678,1.6405511,1.5491183,1.5760101,1.5988843,1.5453074,1.5629486,2.3506363,2.3900338,2.3692994,2.3774440,2.3778159,1.4801504,1.5272571,1.5429716,1.5863007,1.5595683,1.5373692,1.5547804,1.6523496,1.6553747,2.4441022,2.3405286,2.4331678,2.4992773,2.4313793,2.3579883,2.4041657,2.3764722,2.3899039,2.4933925,2.4881635,2.3814493,2.4341179,2.5575816,2.4556496,2.5024020,2.4669698,2.4933790,2.5047439,2.4975195,2.4015712,2.4469022,2.4567287,2.5280128,2.4781728,2.5028472,2.5189290,2.5043568,2.4434804,2.4769850,2.4082988,2.4613414,2.3871942,2.4679938,2.4711610,2.3716282,2.4665808,2.4719631,2.4671665,2.3450332,2.3711461,2.3567956,2.4531954,2.4627118,2.4688380,2.4264698,2.4634535,2.4754286,2.4152280,2.4200143,2.4366610,2.4748473,2.3998817,2.4435630,2.4505969,2.4825692,2.4722832,2.3908582,2.5265103,2.4205017,2.4975109,1.8273926,1.8191600,1.7649152,1.8441525,1.8362518,1.7798777,1.7749614,1.8514624,1.8231416,1.7980675,1.8139444,1.7813007,1.8112133,1.8506497,1.7888465,1.7981612,1.7877846,1.8448715,1.8428863,1.7778798,1.8004113,1.8293173,1.8581288,0.7568285,0.7681167,0.7569872,0.7478473,0.7586729,0.7574590,0.7707119,0.7654296,0.7560802,0.7223322,0.7634792,0.7577954,0.7630233,0.7439842,0.7501500,0.7666750,0.7503895,0.7622286,0.7635520,0.7534987,0.7599475,0.7748956,0.7590139,0.7568013,0.7586510,0.7564873,0.7576587,0.7756744,0.7637029,0.7579558,0.7735586,0.7692345,0.7611547,0.7551704,0.7715118,0.7736083,0.7635049,0.7559560,0.7667778,0.7618454,0.7648308,0.7693512,0.7653699,0.7589299,2.3590999,2.3619440,2.3519471,2.3453709,2.3486040,2.4295357,2.4219361,2.4488210,2.4213269,2.3923218,1.5402144,0.7652187,0.7650076,0.7486516,0.7643569,0.7677992,0.7586368,0.7584026,0.7662775,0.7740569,0.7713377,0.7740677,0.7686109,0.7490695,0.7681402,0.7639513,0.7896797,0.7660664,0.7720809,2.4936417,2.3834268,0.7626155,0.7566950,0.7824697,0.7735270,2.4219853,2.5196019,0.7636966,0.7570312,2.4539218,2.4338622,2.4396830,0.7733773,0.7632390,0.7697633,0.7677199,0.7563686,0.7569366,0.7785563,2.3883388,2.4508850,2.5454545,2.4078138,2.4295884,2.5461211,2.3826057,2.4070722,2.4136287,2.4216196,2.3854115,2.4173648,2.4553045,2.4356992,2.3863270,2.4346182,2.3953523,2.4102911,2.4179386,2.4251441,2.4217263,2.4586260,2.4059818,2.4069762,2.4099267,2.4387039,2.4458400,2.4573490,2.4759171,2.4772782,2.4684424,2.4434910,2.4804417,2.4192554,2.4454277,2.3955812)
ratio <- c(ratio,2.4749573,2.4724740,2.4209932,2.4249042,0.7610100,2.3671184,2.3697960,2.4023920,2.4053188,2.4351452,2.4386339,2.4094596,2.3468609,2.3155974,2.3104149,2.3627904,2.2658038,2.3885135,2.3038569,2.3350929,2.3612206,2.2781386,2.2077955,2.2325030,2.2679324,2.2823724,2.4542063,2.1998876,2.3031394,2.2881462,2.3198411,2.1884115,2.2710756,2.1827032,2.3180018,2.2993929,2.2874717,2.2829849,2.3455578,2.2977960,2.3410225,2.4081727,2.3638018,2.2795117,2.3976837,2.3932511,2.4075917,2.4015616,2.3418264,2.3349013,2.4240838,2.4173924,2.3960085,2.4031925,2.3945173,2.3856273,2.4690719,2.4686576,2.6263546,2.4718199,2.3463103,2.3652738,2.4379702,2.4796148,2.4287476,2.2620077,2.3805959,2.3458551,2.3461876,2.3171412,2.3897433,2.3912464,2.3614724,2.5442086,1.7773526,1.7178727,2.3689272,2.3640495,2.2916104,2.3356112,2.3964407,2.4015147,1.7590361,2.3414859,2.2694388,2.3567392,2.2708003,2.2956377,2.3101355,2.3125120,2.3004763,2.2705803,2.2875544,2.2712565,2.3089819,2.2945688,2.3205069,2.2732516,1.7467849,1.7259182,1.7686619,1.7095978,2.2485174,2.4754472,2.4495703,2.4074395,2.4539152,2.3435356,2.3811995,2.4362843,2.4403479,2.5180754,0.7635700,0.7702974,0.7722231,0.7511177,0.7551106,0.7601832,0.7361963,0.7794874,0.7934396,0.7709755,0.7844490,0.7596845,0.7930613,0.7504008,0.7627609,0.7532478,0.7581377,0.7705301,0.7721196,0.7567074,0.7828257,0.7780374,0.7669904,0.7812995,0.7834886,0.7889141,0.7859603,0.7682853,0.7478378,0.7673373,0.7629394,0.7715725,0.7791851,0.7666474,0.7714516,0.7496962,0.7533639,0.7579321,0.7737278,0.7853168,0.7645964,0.7725103,0.7677113,1.6156064,1.5390375,1.5211357,1.5385035,1.4920242,1.6010156,1.5269279,1.5407954,1.4766077,1.5165483,2.4101888,2.4461818,2.4832620,2.4234102,2.3891139,2.4782895,2.4514298,2.4655178,1.5269570,1.5543206,1.5397302,1.5121552,1.5089835,1.5259734,1.5593889,1.5634023,1.5243902,1.5291230,1.5649990,2.3870746,2.4165985,2.4108952,2.5178706,2.4626444,2.4056250,2.4241015,2.2767663,2.1800944,2.2449665,2.2155462,2.2102232,2.1888782,2.1780130,2.1797660,2.2164432,2.1815838,2.2745605,2.2695021,2.1916002,2.1620086,2.1604276,2.1606576,2.1582508,2.1380764,2.1869745,2.1967953,2.1466257,2.1625341,2.2056076,2.1491951,2.2865496,2.2079291,2.1408957,2.1638916,2.5895003,2.1258483,2.1444175,2.2055520,2.1909330,2.2072956,2.2051386,2.4054279,2.4282109,2.4143596,2.4389768,2.4716971,2.4614070,2.4076957,2.4289880,2.4710598,2.4395144,2.4251923,2.4528039,2.4597420,2.4047160,2.4214961,2.4052775,2.4002135,2.3944374,2.4051049,2.4450801,1.5737999,1.5879028,1.4740943,1.5251975,1.5084994,1.5176669,1.5827066,1.8177106,2.4441547,2.4143742,2.4699203,2.3762657,2.3688625,2.4603598,2.4191691,2.4546725,2.4275861,2.4220888,2.4021738,2.4979091,2.4092485,2.4321795,2.4349427,2.4462136,2.4662561,2.3542403,2.4312644,2.4911342,2.4228929,2.4431390,2.4214492,2.4497284,2.4559866,2.4404771,2.4329174,2.4118930,2.4634206,2.4609880)
ratio <- c(ratio,2.4827362,2.3897923,2.4143036,2.4375662,2.4641043,2.4222062,2.4024445,2.4035411,2.4564304,2.4355113,2.3968869,2.4147049,2.4618251,2.4281002,2.3793209,2.4370193,2.3959920,2.3882394,2.4338975,2.4221606,2.4012736,2.4163148,2.4014352,2.3909576,2.4497283,2.3379209,2.2898380,2.3337816,2.2496425,2.3140063,2.2480368,2.3382981,2.4370101,2.3976064,1.5515221,1.6095634,1.5416116,1.5449938,1.5357950,1.6159637,2.5099319,2.4895688,2.5469330,2.4921635,2.4849558,2.5936576,2.4149410,2.3313097,2.3891210,2.3958461,2.4481496,2.3889537,2.3672844,2.3638062,2.3213211,2.2783695,2.3841916,2.3915916,2.4455549,2.3920387,2.3327502,2.3814912,2.3998684,2.5413619,2.4137805,2.4694112,2.2786062,2.3302104,2.3343673,2.3937296,2.3613661,2.4505636,2.4254633,2.5044136,2.4344560,2.3947676,2.3527630,2.3999480,2.3888254,2.4736389,2.4171134,2.4438647,2.2072640,2.4066542,2.4867753,2.4228284,2.4383648,2.4733934,2.3856568,2.3750662,2.2850762,2.3953039,2.4272293,2.4479172,2.4583161,2.4372287,2.4391820,2.4068650,2.3923539,2.4295108,2.4074787,2.4039005,2.4916317,2.4349603,2.4786877,2.4942217,2.2279876,2.4491045,2.2402399,2.3116072,2.3713333,2.3000641,2.2848940,2.4239510,2.4702209,2.4698362,2.4101398,2.3967287,2.4586776,2.4489123,2.4533943,2.4532398,2.4235131,2.4177043,2.4007880,2.4442298,2.4343659,2.4388599,2.3495992,2.4192377,2.3928401)
library(EMCluster)
ret <- init.EM(as.data.frame(ratio),nclass=6,method="Rnd.EM") # fitting model
# now how to plot the distribution curves?
预先感谢您的建议。
编辑： 结果对象的结构是这样的：
> str(ret,vec.len = 10)
List of 13
$ pi : num [1:6] 0.0537 0.234 0.299 0.1124 0.2225 0.0784
$ Mu : num [1:6, 1] 1.794 1.568 2.429 0.765 2.316 2.474
$ LTSigma : num [1:6, 1] 0.011002 0.001946 0.001355 0.000124 0.008215 0.006486
$ llhdval : num 435
$ nc : int [1:6] 52 252 406 119 195 35
$ class : num [1:1059] 5 5 5 5 5 5 3 3 3 3 3 3 5 5 5 5 5 5 3 5 5 5 5 5 5 ...
$ conv.iter: int 93
$ conv.eps : num 9.81e-07
$ flag : num 0
$ n : int 1059
$ p : int 1
$ nclass : num 6
$ method : chr "Rnd.EM"
- attr(*, "class")= chr "emret"
这很简单。使曲线的高度合理排列需要一些计算，但除此之外它是非常基本的。首先绘制直方图。如果你想要一个围绕它的盒子，就像你的例子一样，那就去做吧。然后你需要调用 lines() 6 次来绘制 6 条法线。在 R 中，线条只是一系列插值点——(x,y) 坐标——因此请制作一组足够细粒度的 x 坐标，然后使用 dnorm() 和拟合参数计算每个分量的法线密度。您需要将这些 y 值乘以适当的比例和高度调整因子才能使曲线的高度正确。事实证明，直方图中最高的 bin 是 82，这大约是第三个分量的峰值，但由于它仅代表 30%，因此您需要按此重新调整调整因子。您可能想要选择自己的颜色。考虑：
xs <- seq(min(ratio), max(ratio), length.out=1000)
windows()
h <- hist(ratio, breaks=seq(0, 3, by=0.02)); box()
# max(h$counts) # [1] 82
height <- 82/dnorm(ret$Mu[3,1], mean=ret$Mu[3,1], sd=sqrt(ret$LTSigma[3,1]))
height <- height/ret$pi[3]
for(i in 1:6){
lines(xs, dnorm(xs, mean=ret$Mu[i,1], sd=sqrt(ret$LTSigma[i,1]))*height*ret$pi[i],
lwd=2, col=i)
}