如何从向量中获得概率密度 function？

Question

我有一个要转换为概率密度 function 的向量。 平均值是 1. 我该怎么做 plot 这个？

向量：

x <- 
c(0.7601401, 0.8607037, 0.8748152, 0.885415, 0.8904619, 0.899021, 
0.9034128, 0.9050411, 0.9093876, 0.9141021, 0.9172803, 0.9209636, 
0.9238607, 0.9268591, 0.9293789, 0.9313833, 0.9335163, 0.9360798, 
0.9406245, 0.9427261, 0.9441703, 0.9473808, 0.9502454, 0.9518683, 
0.9540568, 0.955987, 0.9580035, 0.9617511, 0.9635325, 0.964507, 
0.9674928, 0.9692979, 0.9705296, 0.9732977, 0.9754498, 0.977204, 
0.9793093, 0.9821249, 0.9841156, 0.9864521, 0.9873941, 0.9883275, 
0.9904071, 0.9920552, 0.9946789, 0.9967097, 0.997695, 0.9992215, 
1.001643, 1.0038606, 1.006269, 1.0077312, 1.0091087, 1.0100767, 
1.0113615, 1.0124576, 1.0154025, 1.017386, 1.0189122, 1.021932, 
1.0238598, 1.0258631, 1.0273012, 1.0294901, 1.031085, 1.0336801, 
1.0371085, 1.0387533, 1.0406862, 1.0436292, 1.0453442, 1.0471563, 
1.0514885, 1.0531803, 1.055339, 1.059578, 1.0643068, 1.0668389, 
1.0694237, 1.073174, 1.0759322, 1.0786821, 1.0846407, 1.0904819, 
1.0968733, 1.1039872, 1.1081845, 1.1144191, 1.124116, 1.1378536, 
1.1631801, 0.8238456, 0.8621417, 0.8750536, 0.8864652, 0.8913426, 
0.899054, 0.9034444, 0.9052496, 0.9096515, 0.9141042, 0.9174039, 
0.9215185, 0.9240734, 0.9272829, 0.9294991, 0.9315397, 0.9335967, 
0.9370766, 0.9408574, 0.9427551, 0.9444246, 0.9474299, 0.9503871, 
0.9520593, 0.9541102, 0.9560759, 0.9586173, 0.9618885, 0.9636027, 
0.9653304, 0.9677295, 0.9693085, 0.9706549, 0.9735909, 0.9757686, 
0.9772445, 0.9795081, 0.9823502, 0.9843492, 0.9866112, 0.9874782, 
0.9883432, 0.9904612, 0.99227, 0.9948917, 0.9968164, 0.9979785, 
0.999409, 1.0017522, 1.0038956, 1.0064009, 1.007936, 1.0092714, 
1.0101577, 1.0113745, 1.0124722, 1.015455, 1.0174442, 1.0190047, 
1.0221244, 1.0241163, 1.0262672, 1.0274717, 1.0295358, 1.0311976, 
1.0337105, 1.0376287, 1.0391993, 1.0412049, 1.043784, 1.0458161, 
1.0471989, 1.0515136, 1.0532311, 1.0553901, 1.0598511, 1.0647286, 
1.0674053, 1.0695112, 1.0731966, 1.0765993, 1.0804314, 1.0846581, 
1.0915069, 1.0983415, 1.1041094, 1.1087707, 1.1153954, 1.1244647, 
1.1387218, 1.1631806, 0.8268138, 0.8625675, 0.8751377, 0.886809, 
0.8920388, 0.8991269, 0.9034886, 0.9060083, 0.9102798, 0.9143602, 
0.9178468, 0.9221248, 0.9241217, 0.9273233, 0.929575, 0.9316477, 
0.9337809, 0.9374138, 0.9410309, 0.9429906, 0.9455161, 0.9475521, 
0.9506105, 0.9522978, 0.9541801, 0.9567138, 0.9588403, 0.961889, 
0.9637248, 0.9658144, 0.9678051, 0.9694083, 0.9708232, 0.9737623, 
0.9757794, 0.9772462, 0.9799384, 0.9826819, 0.9844438, 0.9866957, 
0.9875501, 0.9884927, 0.9905356, 0.992504, 0.9952807, 0.9970651, 
0.9979877, 0.9996339, 1.0018148, 1.0039266, 1.0064778, 1.0080148, 
1.0093728, 1.0101958, 1.0115577, 1.0128605, 1.0155767, 1.0176005, 
1.0191159, 1.0222069, 1.0241286, 1.0263724, 1.0275547, 1.0298965, 
1.0314567, 1.0347959, 1.0377489, 1.0392566, 1.0413151, 1.043814, 
1.0462065, 1.0472742, 1.0516567, 1.0533239, 1.0556568, 1.0599784, 
1.0648656, 1.0674582, 1.0695187, 1.0737822, 1.0767733, 1.0805175, 
1.085116, 1.0919541, 1.0987864, 1.1045691, 1.1090898, 1.1155974, 
1.1244743, 1.1403648, 1.1653051, 0.8287487, 0.8632563, 0.8783957, 
0.8872595, 0.8921496, 0.8991388, 0.9038431, 0.9063199, 0.9106785, 
0.9144, 0.9189027, 0.9223262, 0.924352, 0.9275484, 0.9296723, 
0.932303, 0.9340644, 0.9375086, 0.9410767, 0.9431117, 0.9455282, 
0.9476748, 0.9506839, 0.9524355, 0.9542676, 0.9570338, 0.9591047, 
0.9620121, 0.9638592, 0.9660401, 0.9678991, 0.9695856, 0.9710773, 
0.9740787, 0.9760428, 0.9773099, 0.9800677, 0.9830478, 0.9845491, 
0.9868047, 0.9876641, 0.9885819, 0.990765, 0.9929082, 0.9953852, 
0.9972524, 0.9980094, 0.999655, 1.0019781, 1.0041123, 1.0065022, 
1.0080436, 1.0093745, 1.0102597, 1.011591, 1.0133388, 1.0160004, 
1.0177403, 1.0197461, 1.0223301, 1.0243601, 1.0264419, 1.0277154, 
1.0300746, 1.0315714, 1.0348406, 1.0377535, 1.0396123, 1.0416248, 
1.0438679, 1.0463796, 1.0473053, 1.0518621, 1.0535013, 1.0566508, 
1.0602571, 1.0649945, 1.0675837, 1.0696383, 1.0737915, 1.0768286, 
1.0807683, 1.0866947, 1.0922428, 1.0993173, 1.1053873, 1.1097462, 
1.1160662, 1.1245894, 1.1439087, 1.1653756, 0.8336881, 0.8641065, 
0.8801013, 0.8873061, 0.892528, 0.8992721, 0.9040462, 0.9064932, 
0.9118009, 0.9147806, 0.9194353, 0.922346, 0.924704, 0.9279243, 
0.9298283, 0.9325862, 0.9345334, 0.9376213, 0.9413217, 0.9435098, 
0.9457126, 0.948086, 0.9507289, 0.9526298, 0.9544503, 0.9570495, 
0.9594515, 0.9622223, 0.9639176, 0.9664818, 0.9681109, 0.9697204, 
0.9715772, 0.974512, 0.9761773, 0.9774122, 0.9801115, 0.9830508, 
0.9848412, 0.9868423, 0.987876, 0.9886175, 0.9911154, 0.9930527, 
0.995429, 0.9972859, 0.9980303, 1.000341, 1.0023467, 1.0041273, 
1.0066877, 1.0081464, 1.0094208, 1.0103294, 1.0117416, 1.0134278, 
1.0162053, 1.0179561, 1.0202328, 1.0227929, 1.0244661, 1.0266619, 
1.0278932, 1.0301724, 1.0318422, 1.034844, 1.0378449, 1.0396893, 
1.0416388, 1.0441611, 1.0464143, 1.0485936, 1.0520624, 1.0535133, 
1.0568916, 1.0602833, 1.0652996, 1.0678024, 1.0700347, 1.0739087, 
1.0768747, 1.0811584, 1.08706, 1.092342, 1.0994397, 1.1057555, 
1.1101622, 1.1197734, 1.1260845, 1.144113, 1.1656149, 0.8364483, 
0.8665228, 0.8801799, 0.8876104, 0.8951142, 0.9004983, 0.9041605, 
0.9067967, 0.9123546, 0.9151016, 0.9195613, 0.9224414, 0.9250538, 
0.9280133, 0.9299708, 0.9326035, 0.9346515, 0.9380998, 0.9414107, 
0.9435515, 0.9461568, 0.9482194, 0.9508463, 0.9527514, 0.9546165, 
0.9571445, 0.9596505, 0.9624602, 0.963954, 0.9665085, 0.9682382, 
0.9699198, 0.9716006, 0.974844, 0.9761914, 0.9775793, 0.9801981, 
0.9835029, 0.9848844, 0.9869101, 0.9878904, 0.988621, 0.9913567, 
0.9933158, 0.9955091, 0.9973969, 0.9982784, 1.0004438, 1.0024634, 
1.0043027, 1.006941, 1.0081515, 1.0094608, 1.0103653, 1.0117473, 
1.0142556, 1.0165854, 1.0181703, 1.0205428, 1.022822, 1.0245166, 
1.02681, 1.0278956, 1.0302434, 1.032, 1.0355287, 1.037906, 1.0401162, 
1.041886, 1.0442367, 1.0464702, 1.0486031, 1.0521055, 1.0540157, 
1.0570109, 1.0605447, 1.0654882, 1.0679469, 1.0700915, 1.0746908, 
1.076962, 1.0811779, 1.0880499, 1.0925217, 1.1000415, 1.1068352, 
1.1103446, 1.1198258, 1.1278557, 1.144615, 1.1659478, 0.8428518, 
0.8685433, 0.8806388, 0.8878492, 0.8957898, 0.9008499, 0.9041908, 
0.907718, 0.9124535, 0.9154017, 0.9195873, 0.9228693, 0.9252186, 
0.9280587, 0.9302431, 0.9327066, 0.9346733, 0.9382416, 0.9415437, 
0.943858, 0.9463773, 0.9482644, 0.9510351, 0.9529947, 0.9548508, 
0.9571599, 0.9597816, 0.9632479, 0.9640826, 0.9667552, 0.9688842, 
0.9699332, 0.972455, 0.9748674, 0.9765135, 0.9782475, 0.9804558, 
0.9835081, 0.9849378, 0.9869651, 0.9879891, 0.9886996, 0.9913707, 
0.9933895, 0.9958194, 0.9974753, 0.9984636, 1.0005798, 1.0027019, 
1.0043733, 1.007001, 1.008266, 1.0097909, 1.0104785, 1.0119673, 
1.0145991, 1.0166569, 1.0182844, 1.0211453, 1.0231898, 1.0245254, 
1.0268803, 1.0279336, 1.0304433, 1.0322581, 1.035589, 1.0382374, 
1.0401349, 1.0422173, 1.0444101, 1.0465514, 1.0486237, 1.0521174, 
1.054423, 1.057825, 1.0606672, 1.0656468, 1.0684325, 1.0709319, 
1.0749488, 1.0770775, 1.0820547, 1.0881332, 1.0925439, 1.1000816, 
1.1069162, 1.1106217, 1.120701, 1.1302275, 1.1459233, 1.168602, 
0.8488214, 0.8702316, 0.8809238, 0.8890422, 0.8958309, 0.9019966, 
0.9042307, 0.9079107, 0.9132285, 0.9154252, 0.9198471, 0.9230071, 
0.9253286, 0.9283751, 0.9304839, 0.9327088, 0.9348709, 0.9382659, 
0.9417193, 0.943864, 0.9466926, 0.9485074, 0.9511567, 0.9532046, 
0.9554877, 0.9574181, 0.9600951, 0.963362, 0.9643226, 0.9667904, 
0.9689357, 0.9699377, 0.9726418, 0.9749534, 0.9766888, 0.9786503, 
0.9816446, 0.9836604, 0.9850502, 0.9869678, 0.9880833, 0.9894534, 
0.9914227, 0.9937725, 0.9962026, 0.9975144, 0.9987734, 1.0006365, 
1.0029989, 1.0047337, 1.0071024, 1.0086273, 1.0098207, 1.0110381, 
1.0119714, 1.01463, 1.0166717, 1.0183924, 1.0212439, 1.0234931, 
1.0245751, 1.0269182, 1.0286172, 1.0306589, 1.0322592, 1.0359487, 
1.038269, 1.0402549, 1.0422949, 1.0445157, 1.0466529, 1.0487325, 
1.0523088, 1.0546675, 1.0584369, 1.0618338, 1.0658283, 1.0687319, 
1.0712981, 1.0750357, 1.0777228, 1.082814, 1.0896652, 1.092878, 
1.1002284, 1.1072211, 1.1112157, 1.1210507, 1.1331503, 1.1510694, 
1.1729349, 0.8533762, 0.8705291, 0.882901, 0.8898704, 0.8964921, 
0.9026909, 0.9043496, 0.9082536, 0.9132482, 0.9167392, 0.9200439, 
0.923801, 0.9257428, 0.9287926, 0.9310369, 0.9327569, 0.935825, 
0.9396949, 0.9418288, 0.9439139, 0.9468012, 0.9487367, 0.9513136, 
0.9534568, 0.9557201, 0.9577258, 0.9606246, 0.9634036, 0.9644277, 
0.9668756, 0.9689947, 0.9699737, 0.9726901, 0.9749863, 0.9768128, 
0.9790117, 0.9817103, 0.9837448, 0.9853122, 0.98713, 0.9881006, 
0.9896077, 0.9918675, 0.9939561, 0.9962435, 0.9975984, 0.9988964, 
1.0007611, 1.0032765, 1.0052762, 1.0072548, 1.008838, 1.0098927, 
1.011057, 1.0120007, 1.0153072, 1.0167114, 1.0183976, 1.0217836, 
1.0235315, 1.0250021, 1.0270587, 1.0287792, 1.0308106, 1.032815, 
1.0363681, 1.0384448, 1.0403337, 1.0423298, 1.0446048, 1.046717, 
1.0487547, 1.0527611, 1.0548012, 1.0586172, 1.0622363, 1.0665121, 
1.0690857, 1.0720846, 1.0755489, 1.0784088, 1.0840459, 1.089944, 
1.093356, 1.1004089, 1.1073085, 1.1124143, 1.1211267, 1.1339292, 
1.1517573, 1.198363, 0.8571564, 0.8726188, 0.8845936, 0.8898835, 
0.8980876, 0.9028112, 0.9044216, 0.9086289, 0.9133134, 0.9168552, 
0.9203877, 0.9238087, 0.926413, 0.929035, 0.9313117, 0.9330642, 
0.9358536, 0.9400013, 0.9420459, 0.9439535, 0.9469293, 0.9491097, 
0.9513609, 0.9535177, 0.9557438, 0.9577505, 0.9608692, 0.9634749, 
0.9644502, 0.9669999, 0.9690555, 0.9703173, 0.9727357, 0.9750629, 
0.9769616, 0.9790537, 0.9817755, 0.9837511, 0.9856411, 0.9872352, 
0.9882029, 0.990218, 0.9919514, 0.9941591, 0.9965548, 0.9976154, 
0.9990174, 1.0010466, 1.003395, 1.0055957, 1.007304, 1.0089384, 
1.0099392, 1.0112263, 1.012146, 1.0153451, 1.0171438, 1.0186295, 
1.0217893, 1.0236026, 1.0256126, 1.0271073, 1.0289151, 1.0309176, 
1.033115, 1.036525, 1.0385212, 1.0406626, 1.0429921, 1.0447711, 
1.0468007, 1.0501243, 1.0527771, 1.0549067, 1.0590568, 1.0635208, 
1.066646, 1.0691815, 1.0725159, 1.0756145, 1.0784323, 1.0844119, 
1.0900761, 1.0937593, 1.1018746, 1.1080635, 1.112721, 1.1223554, 
1.1342245, 1.1589387, 1.3267105, 0.8593686, 0.8738442, 0.8847164, 
0.8900729, 0.8985823, 0.9030722, 0.9047745, 0.9089145, 0.9133781, 
0.9170319, 0.9205633, 0.9238323, 0.92677, 0.929173, 0.931353, 
0.933437, 0.9359658, 0.9403774, 0.9424343, 0.9441537, 0.9472636, 
0.9497636, 0.9514515, 0.9539961, 0.955913, 0.9577903, 0.9613333, 
0.9635, 0.9644766, 0.9672279, 0.9690912, 0.9704478, 0.9730493, 
0.975256, 0.9771195, 0.9792525, 0.982091, 0.9839065, 0.9862609, 
0.9872484, 0.9882653, 0.9902789, 0.9919861, 0.9944648, 0.996593, 
0.9976709, 0.9992019, 1.0012796, 1.0036569, 1.0061553, 1.0075918, 
1.0089733, 1.0100455, 1.0112892, 1.0124005, 1.0153452, 1.0172939, 
1.0186304, 1.0218203, 1.0238237, 1.0256419, 1.0272337, 1.0289253, 
1.0310775, 1.0333971, 1.0365301, 1.0386841, 1.0406816, 1.04333, 
1.0448819, 1.0471028, 1.0501926, 1.0528722, 1.0551719, 1.059271, 
1.0638416, 1.0667384, 1.0691885, 1.0729292, 1.0756769, 1.0786645, 
1.0844603, 1.0902495, 1.0940123, 1.1037544, 1.1080977, 1.1140658, 
1.1234296, 1.1354923, 1.1600791)

Answer 1

您可以使用?density function 计算 kernel 密度估计值，使用默认高斯 kernel 来获得非参数估计值。

x <- density(vector)

plot(x)

Answer 2

请注意，您还可以使用基础ecdf function 生成经验 cdf。 这允许您计算任何 x 的 F(x)。 例如

x <- rnorm(1000)
cdf <- ecdf(x)
plot(cdf)
f <- cdf(0.5)
f 
[1] 0.692