之前一直在关注中欧医疗健康这支基金，收益还不错，于是想通过数学的方法分析，基金涨幅服从什么分布。
首先是一坨涨幅数据，
2016-11-07到2021-07-29 这期间的涨幅. 单位都是百分比
[0,0,-0.7071,0.5086,-0.3036,-0.1015,0.1016,-0.203,-0.1017,-0.4073,0.3067,0.7136,-0.3036,0.5076,0.404,0.1006,-0.7035,-1.0121,0.2045,-1.4286,-0.4141,-0.2079,0.8333,-0.3099,0.3109,-2.2727,-0.3171,-0.4242,-1.1715,0,0.2155,0,0.2151,0,-0.4292,0.1078,-0.1076,-0.5388,-0.5417,0.9804,-0.1079,0.6472,0.4287,0.2134,-0.852,0.4296,-0.3209,-0.5365,-0.863,-0.6529,-0.2191,0.6586,0.2181,-0.5441,0.9847,0.4334,-0.3236,0.7576,0.4296,-0.107,0.2141,0.4274,0,-0.3191,0,0.9605,-0.4228,-1.2739,0.9677,-0.9585,1.2903,1.38,0.3141,1.9833,-0.5118,-0.5144,0.3102,-0.1031,-0.2064,-0.1034,0.5176,0.103,-0.1029,-0.7209,0.6224,1.0309,-0.2041,0.7157,0.203,-0.7092,0.4082,1.0163,1.2072,-0.0994,-0.2985,-0.8982,0.2014,-0.7035,-0.4049,1.626,1.7,0,-0.4916,-1.6798,-0.7035,0.4049,1.3105,-0.995,0.1005,1.004,-0.2982,2.1934,-1.1707,-2.0731,0.3024,0.5025,1.1,-1.1869,0.2002,-0.2997,-0.501,-0.4028,-1.1122,0.1022,0.3064,0.9165,0.7064,2.004,1.8664,-1.2536,-0.0977,0.5865,0.3887,0.5808,-0.385,-0.2899,-0.8721,0.1955,0.7805,-1.0649,-0.7828,1.3807,2.0428,1.4299,0.6579,0.747,0.278,-1.8484,-0.6591,-0.3791,1.2369,-0.7519,1.9886,-1.4856,1.3195,1.8605,0.274,-1.5483,0.555,0.552,-1.3724,-1.0204,1.4995,-1.108,-1.2138,-1.1342,0.478,-0.4757,-0.7648,0.289,-1.4409,-0.8772,1.3766,0.485,-0.4826,0.097,-0.5814,-1.1696,0,0.6903,-0.0979,-0.1961,-0.5894,-1.087,-0.2997,0.8016,0.5964,1.7787,0.2913,-0.5808,1.2658,-0.6731,-0.1936,-0.485,0.3899,0.7767,-0.6744,-0.291,-0.8755,0.0981,0.3922,-0.3906,0.7843,-0.3891,0.8789,0.7744,0.1921,-0.767,0.1932,0.3857,0.3842,-0.3828,1.0567,-0.3802,-0.2863,0.6699,-0.6654,1.1483,-0.5676,0.1903,0.7597,-0.377,0.1892,1.4164,-0.0931,1.4911,1.3774,1.721,0.6233,0.708,-0.5272,0.3534,0.9683,0.959,-0.4318,1.5611,0.427,1.3605,-0.5034,0.8432,-1.087,-0.1691,0,0.6774,0.9251,3.1667,-0.4039,-1.3788,0.6579,0.9804,0.4045,-2.498,-0.6612,2.3295,-2.7642,1.5886,-0.3292,-1.4864,-4.4426,0.1754,-1.6637,1.5138,-0.7895,-0.0884,0.531,1.4085,-1.1285,0.5268,-0.3493,1.4023,4.2351,0,0.4975,0.5776,-1.4766,0.0833,1.1647,0.7401,1.8776,-0.7212,-0.0807,-0.6462,-1.9512,1.2438,1.0647,0,-0.4052,0.4068,0.9724,-0.0803,0.1606,2.085,0,-0.2357,1.4173,-0.7764,1.1737,-1.6241,-0.6289,-0.2373,1.7446,0.3118,0.3108,-2.0139,0.0791,-3.8705,-0.3287,0.4122,-1.8883,0.1674,-2.2556,-3.8462,-0.8889,1.3453,-2.5664,4.5413,1.0426,1.1178,2.381,-0.6645,1.5886,-0.6584,-0.8285,1.5038,-0.7407,0.8292,2.2204,-0.1609,3.2232,0.5464,0.854,-1.6166,-1.1737,1.2668,-0.7819,3.3885,2.2104,-0.522,-0.6747,-1.9623,3.5412,1.3383,-2.0543,-1.7228,3.6585,0,-0.1471,-1.1782,0.149,1.3393,0,1.9824,-2.4478,1.6236,-3.1227,0.9745,1.1136,0.2203,-0.0733,1.4663,3.9017,-1.9471,2.766,0.6901,-0.6854,1.9324,2.0311,-1.1281,0.1342,3.0831,-3.186,0,2.8207,0.8491,-1.7487,0.4614,-0.1312,2.2996,-0.1927,0.7722,1.788,1.0665,-5.1521,-0.589,2.8966,-4.7345,0.2015,3.6863,2.1978,-1.3283,0.0641,-3.2671,2.5166,-1.4212,-0.9174,-1.6534,-1.8157,3.9711,0,0.8333,0.7576,-0.3418,-3.6351,-1.0676,4.6043,0,1.1004,-1.3605,-1.8621,-2.6001,0,3.824,0.8339,0.3446,3.2967,1.8617,1.1749,-1.2903,0.1307,-3.4595,-0.3381,-7.1913,-0.4386,2.6432,-1.1445,-1.4472,-3.8179,0.687,-2.047,0.6966,-3.5357,-5.0199,3.104,-2.0342,4.5681,2.8594,1.8533,-0.3791,-3.8813,0.1584,-4.664,-1.8242,5.8277,-0.0798,1.278,0.7886,3.2864,-0.6818,-1.0679,-1.2336,-2.498,-0.4003,0.0804,-1.4458,-1.0595,2.4712,-1.9293,0.9016,-3.6556,-1.602,-1.5424,-1.6536,2.7434,1.4643,-0.5093,2.4744,0.4996,2.1541,0.7299,1.2882,-5.2464,-1.2584,-2.209,-5.2129,0.4583,-1.0036,-1.7512,-1.3133,-4.3726,5.0696,5.6764,-2.2381,-2.5641,-1.2218,-1.9029,-2.2308,1.5873,3.3203,0.5671,5.8271,-1.2433,0.7194,-0.3571,0.0896,-1.0743,1.991,1.5084,-0.8741,0.97,-2.0961,0.0892,-1.6043,2.0833,-0.3549,-2.0481,-0.1818,-0.0911,1.1851,-1.2613,1.2774,3.4234,1.4808,1.2876,-4.2373,-3.5398,-1.5596,1.3979,-1.6544,1.4953,-3.1308,-1.9011,-0.4845,-3.1159,-1.1055,-1.8293,2.2774,0.8097,-0.7028,-0.6067,0.4069,0,-3.4448,-1.2592,2.4442,0.4149,0.1033,0.516,-0.616,0.1033,-1.3416,1.569,1.4418,-0.6091,2.145,1.3,-1.6782,0.2008,0.1002,1.001,0,-0.1982,-1.1917,0.7035,3.0938,1.7425,1.0466,1.4124,0.2786,-0.9259,4.486,-1.2522,-1.087,-0.2747,1.3774,3.5326,0.6999,-0.9557,3.3333,0.5942,1.6878,0.4149,-0.6612,-1.9135,-0.6785,4.953,0.1627,0.4874,-0.5659,2.9268,4.4234,-1.8154,-0.6934,-0.3879,0.5452,-1.4717,-1.1006,3.1002,-0.4626,3.5631,1.5707,-1.9882,-0.2254,-0.5271,-1.6654,1.7706,1.1346,-3.3657,-0.0774,-1.0844,1.2529,0.1547,-0.3089,0.4648,-0.3084,0.0773,0.541,0.2306,0.0767,1.7625,-0.3765,-4.9131,3.4181,-1.7679,-2.6604,3.6174,0.7758,-0.5389,2.9412,0.9774,-2.2338,-1.9802,1.3986,-0.0766,-2.454,0,1.1792,1.7094,-0.5348,0.5376,1.0695,-0.6803,-1.9026,-2.0171,-0.7126,1.5949,3.2182,-0.076,1.2177,-0.2256,-0.9043,1.1407,0.9023,2.459,-0.0727,0.5095,-0.0724,3.3333,1.122,-0.6241,0,2.1633,1.2978,-2.2252,-2.1379,1.9732,-2.2806,0.4243,0.1408,-0.1406,0.1408,-0.9142,-1.5614,-0.5047,-1.4493,0.4412,0,0,0.6589,-0.0727,2.0378,-0.9272,0.072,-0.5755,-0.4342,0.8721,-1.8732,0.2203,1.7582,2.1598,-0.1409,1.0586,0.0698,2.2331,0,0.8191,0.677,0.269,-1.1402,1.0176,3.1565,-0.0651,0.3257,-0.3247,-0.3257,0.6536,1.7532,-0.4467,-0.1282,-0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通过初步统计：
总共记录： 1158
负涨幅： 516
正涨幅：611
零涨幅：31
最大负涨幅：-7.1913
最大正涨幅：5.8277
总体收益率：309%。 也就是说从16年11月分买入100万的话， 到2021年7月29日， 挣了309万。
这是大致分析。现在想看下具体服从啥分布：
这里用非参数核密度估计，是最合适的。
用简单的代码，先粗略看下效果， 核密度估计使用的是高斯内核Gaussian kernel
import numpy as np import seaborn as sns import matplotlib.pyplot as plt # data 数据在上面 sns.kdeplot(data=data) plt.show()
从肉眼可以看出，从0处分割，右区稍微大于左区一丢丢。
怎么说呢, 看到这个图不是很满意，总感觉过度平滑了些，这个图左右两边基本上是55开了。现在开始设置带宽。
sns.kdeplot(data=data, bw_adjust=0.2)
从这个图可以看出右边明显比左边大了。 也就是总体正涨幅大于负涨幅。 基本上80%都集中在 -2.5 和 2.5中
看到图了， 有点不甘心， 基金数据量太小了， 想根据这个核密度估计生成一堆随机数，也服从这个分布。
其实原理很简单，就是求这个分布函数的反函数。
google 搜索了一下，发现sklearn有逆采样的API， 真是太方便，不用自己造轮子了。
开始撸一段代码，生成一堆随机数，服从这个这个分布
import numpy as np import seaborn as sns import matplotlib.pyplot as plt from sklearn.neighbors import KernelDensity data=上面的数据 bandwidth=0.2 data = np.array(data) data = data.reshape(1, -1) kde = KernelDensity(kernel='gaussian', bandwidth=bandwidth).fit(data) data2 = kde.sample(n_samples=1) # print(data2) sns.kdeplot(data=data2[0], bw_adjust=bandwidth) plt.show()
生成的前100项数据
[-0.04815941 0.39256206 -0.9863881 0.49870153 -0.0685882 -0.19805829
-0.04881429 -0.06329466 -0.08757228 -0.05626878 0.73477043 0.53225204
-0.38579164 0.83846548 0.47279225 -0.00614553 -0.6908834 -0.84516852
0.10460452 -1.68316156 -0.66628967 -0.21534727 0.98405373 -0.05263706
0.30697309 -2.15871898 -0.35459538 -0.52873768 -1.17071306 0.11299641
0.03853813 -0.20053358 0.35698474 -0.01739235 -0.48132911 0.44775797
-0.061619 -0.6657418 -0.62232173 0.89765569 0.10955856 0.80463848
0.37803424 0.35498848 -0.78111103 0.29430354 -0.69433118 -0.38413522
-0.83943738 -0.83408007 -0.42279157 0.72632924 0.24573081 -0.41170196
0.85835499 0.24643445 -0.51300586 0.74195118 0.59904193 0.19662009
0.42170835 0.30809563 -0.01263777 -0.07373658 0.04519119 0.64315866
-0.39171321 -1.27626658 0.85453185 -1.06308532 1.18232718 0.95965952
0.90415696 1.87500951 -0.86526574 -0.58421233 0.32383176 -0.33258237
-0.47503023 -0.35860991 0.39685402 0.08292457 0.01761468 -0.82799399
0.3078751 1.38049451 -0.24757849 0.60739704 0.49034587 -0.70863595
0.53619962 0.64877759 1.09609066 -0.18906142 -0.48301451 -0.96290755
0.21041798 -0.71870651 -0.24372297 1.75752347]
生成的数据服从的分布和原始数据的分布基本一致。
但是在这里我发现了一个问题， 给入的样本是1158条数据， 只能随机生成1158数据， 太扯淡了。
我的本意随机一堆数，服从这个分布。这个一堆数是任何正整数。 没办法，继续研究,
以下是改造后的代码，支持随机任意个数了。
import numpy as np import seaborn as sns import matplotlib.pyplot as plt from sklearn.neighbors import KernelDensity data=上面的数据 bandwidth=0.2 data = np.array(data) data = data.reshape(-1, 1) kde = KernelDensity(kernel='gaussian', bandwidth=bandwidth).fit(data) data2 = kde.sample(n_samples=1000) # print(data2.flatten()) sns.kdeplot(data=data2.flatten(), bw_adjust=bandwidth) plt.show()
其实之所做这个模型，是因为训练要大量基金数据，1158条数据远远不够， 没有一个几万几十万数据，训练不好一个模型。