当我在 matplotlib.pyplot.hist() 中使用“density=True”参数时，为什么我没有得到标准化值

Question

我有以下数据，我正在尝试使用他的数据和 matplotlib.pyplot.hist() 函数来拟合 PDF。

bs_slope_reps
array([0.0520316 , 0.05160929, 0.04848691, 0.04998295, 0.04404885,
       0.05063528, 0.04436635, 0.05471181, 0.05150545, 0.05034114,
       0.05333551, 0.04964237, 0.05050637, 0.04982179, 0.04841369,
       0.05135721, 0.04896658, 0.05583844, 0.04737563, 0.05067793,
       0.04635896, 0.05067058, 0.0429712 , 0.04961807, 0.04835286,
       0.05139547, 0.04640738, 0.05020543, 0.05572707, 0.04808664,
       0.05064092, 0.04960493, 0.04748579, 0.05263983, 0.05279465,
       0.049672  , 0.05248898, 0.05154026, 0.047722  , 0.04928005,
       0.04950495, 0.05137217, 0.05081193, 0.04764161, 0.05456121,
       0.0523411 , 0.04566333, 0.04970461, 0.05189497, 0.04786661,
       0.04611002, 0.04833256, 0.04968685, 0.04729923, 0.05402039,
       0.05308427, 0.04582401, 0.05233882, 0.05070356, 0.05338896,
       0.0539938 , 0.04554897, 0.0485493 , 0.051148  , 0.04709942,
       0.04797971, 0.05329998, 0.04791984, 0.0487534 , 0.04778987,
       0.04612894, 0.0498524 , 0.05275295, 0.05014263, 0.05146684,
       0.04989203, 0.04977884, 0.04555686, 0.04849763, 0.0499492 ,
       0.0431869 , 0.05177775, 0.04765351, 0.05294277, 0.05324382,
       0.05440251, 0.04943524, 0.05881614, 0.05344215, 0.05225652,
       0.05076026, 0.05454493, 0.0511924 , 0.05276151, 0.04622118,
       0.04892746, 0.05426056, 0.050171  , 0.0467458 , 0.05401329,
       0.05146726, 0.04847862, 0.05040234, 0.04953278, 0.0482813 ,
       0.05271867, 0.0510187 , 0.05157167, 0.04861981, 0.04828292,
       0.04850384, 0.04939776, 0.05066815, 0.04830298, 0.04965386,
       0.04949991, 0.0539839 , 0.04553934, 0.04643377, 0.05090904,
       0.04869974, 0.05089623, 0.05019059, 0.0485673 , 0.04691444,
       0.05332229, 0.05042144, 0.05051362, 0.04895553, 0.04744161,
       0.04859037, 0.0493465 , 0.0488008 , 0.05231724, 0.05518981,
       0.04681006, 0.05029493, 0.05110057, 0.04767872, 0.04937095,
       0.0524756 , 0.05113148, 0.04726702, 0.0480495 , 0.04960746,
       0.04537505, 0.04731028, 0.05629919, 0.05232977, 0.05111447,
       0.04570114, 0.05006477, 0.04949715, 0.04533517, 0.05047006,
       0.04682233, 0.04846041, 0.05059028, 0.0460438 , 0.05388126,
       0.04378466, 0.048276  , 0.04526832, 0.05213078, 0.04913582,
       0.05015408, 0.04921747, 0.04760582, 0.04838669, 0.05283185,
       0.04497601, 0.04901067, 0.05354468, 0.05168816, 0.04562744,
       0.04319781, 0.05004012, 0.05339087, 0.04489087, 0.05095208,
       0.05327525, 0.0452265 , 0.04918115, 0.05388768, 0.04978407,
       0.04489241, 0.05159438, 0.04632876, 0.04714244, 0.04870325,
       0.04788938, 0.04407355, 0.04751146, 0.04993667, 0.05365527,
       0.05293167, 0.04958151, 0.04481716, 0.04835846, 0.05019251,
       0.0445879 , 0.05554031, 0.05084581, 0.04591604, 0.05021242,
       0.04843221, 0.05261338, 0.05259107, 0.04819529, 0.0466933 ,
       0.04838755, 0.05124261, 0.0534444 , 0.05041736, 0.04935596,
       0.04819474, 0.04900961, 0.04594862, 0.05424005, 0.05318035,
       0.05481001, 0.04667292, 0.04875687, 0.05554243, 0.0507825 ,
       0.04941086, 0.04968849, 0.04758964, 0.05226413, 0.05051193,
       0.04839188, 0.04939746, 0.05333251, 0.04997078, 0.04644216,
       0.05030446, 0.04885201, 0.04743469, 0.04725879, 0.04902101,
       0.05172672, 0.05274773, 0.04848581, 0.04866886, 0.04736317,
       0.05306121, 0.050653  , 0.05029069, 0.04957173, 0.04801235,
       0.04979022, 0.05003965, 0.04850477, 0.04374289, 0.0465281 ,
       0.04387934, 0.05146633, 0.04934409, 0.05048213, 0.04874064,
       0.0517513 , 0.05128024, 0.04944209, 0.04888407, 0.05077473,
       0.04957108, 0.04931158, 0.04573551, 0.05482341, 0.04855035,
       0.04901622, 0.04983627, 0.0472557 , 0.04947764, 0.04698017,
       0.04947366, 0.0515415 , 0.04898971, 0.04645964, 0.04613201,
       0.05320363, 0.05328655, 0.05161196, 0.05220259, 0.05173935,
       0.05346232, 0.05316519, 0.05045331, 0.04942012, 0.04653559,
       0.04630915, 0.05082626, 0.05013578, 0.05099166, 0.05149157,
       0.04980349, 0.05125401, 0.05170271, 0.05656241, 0.04993871,
       0.04748124, 0.05573249, 0.05399041, 0.04932821, 0.04820483,
       0.04786794, 0.05274393, 0.05298585, 0.04896901, 0.04747096,
       0.05741472, 0.05420834, 0.04870523, 0.04592647, 0.05529823,
       0.04771641, 0.04737671, 0.05019528, 0.05069891, 0.04923077,
       0.04496967, 0.05362649, 0.04685166, 0.04716789, 0.05175453,
       0.04869038, 0.04644694, 0.05120672, 0.05319481, 0.05458965,
       0.05196997, 0.04910628, 0.05439416, 0.04670172, 0.04555069,
       0.0505049 , 0.05196277, 0.05823439, 0.05114317, 0.05070024,
       0.05665107, 0.0495306 , 0.05172963, 0.05018011, 0.05140056,
       0.05357441, 0.0537774 , 0.0441439 , 0.04876871, 0.05063552,
       0.05369826, 0.04937306, 0.04952938, 0.05254119, 0.04551079,
       0.0457304 , 0.04952427, 0.05028471, 0.05141945, 0.05351535,
       0.05050873, 0.04800063, 0.04720164, 0.04884971, 0.05135419,
       0.05160356, 0.04604888, 0.0529981 , 0.04977256, 0.04523448,
       0.05208725, 0.05313274, 0.05413813, 0.05508746, 0.05390183,
       0.05047701, 0.0513307 , 0.05284478, 0.05016473, 0.04813696,
       0.05056617, 0.04612449, 0.04883637, 0.05356193, 0.04893187,
       0.05018272, 0.05027251, 0.0501143 , 0.04261922, 0.05180099,
       0.05435355, 0.05152862, 0.04866125, 0.04699904, 0.04877365,
       0.04696819, 0.052512  , 0.04908491, 0.05081994, 0.04679027,
       0.05131938, 0.04941195, 0.05267099, 0.05223494, 0.0478726 ,
       0.04907661, 0.04760451, 0.04793462, 0.0526982 , 0.04870881,
       0.05149775, 0.05593673, 0.05354955, 0.0553809 , 0.04617826,
       0.05466793, 0.0541615 , 0.04981911, 0.05071435, 0.05003726,
       0.04424241, 0.04871905, 0.04593134, 0.05608876, 0.05265227,
       0.04724178, 0.05613748, 0.05148353, 0.04612124, 0.05142259,
       0.05321131, 0.05182609, 0.04938966, 0.05476937, 0.05294885,
       0.05351947, 0.04856854, 0.04953822, 0.04817237, 0.04944105,
       0.04962188, 0.04794024, 0.04731367, 0.05146914, 0.05152919,
       0.04354601, 0.05305154, 0.05573179, 0.04938139, 0.04923531,
       0.0471789 , 0.04610962, 0.05087648, 0.04907873, 0.05072657,
       0.0490785 , 0.04861006, 0.05000054, 0.04902744, 0.04990386,
       0.05400148, 0.04918693, 0.0444911 , 0.04947195, 0.05090897,
       0.04894251, 0.05645236, 0.04700956, 0.05240244, 0.04211827,
       0.04611662, 0.05337947, 0.05473492, 0.04897319, 0.05024453,
       0.04878357, 0.05025965, 0.04656844, 0.05829623, 0.05681263,
       0.04640974, 0.04889029, 0.05282684, 0.04985636, 0.04887466,
       0.04813986, 0.04984758, 0.05168634, 0.04706482, 0.05033689,
       0.04933082, 0.05531448, 0.04912529, 0.05223116, 0.05452812,
       0.05075942, 0.05026772, 0.04599448, 0.0497711 , 0.0492381 ,
       0.04491251, 0.05873477, 0.04987302, 0.05241024, 0.04957075,
       0.04559973, 0.05194943, 0.04799646, 0.04876582, 0.04738106,
       0.05266071, 0.04652703, 0.05137693, 0.05363929, 0.04964638,
       0.050628  , 0.05271703, 0.05003416, 0.04871179, 0.04764007,
       0.05494945, 0.04870519, 0.05015828, 0.04841085, 0.04904419,
       0.05208887, 0.04900261, 0.05005589, 0.04477594, 0.04555916,
       0.05536126, 0.05268228, 0.04636362, 0.05025851, 0.04677208,
       0.04834265, 0.04873473, 0.04785136, 0.05018433, 0.05176   ,
       0.04646484, 0.04967791, 0.04789048, 0.0445605 , 0.04599846,
       0.05071997, 0.05072142, 0.04890159, 0.04868793, 0.0440235 ,
       0.05148176, 0.04905514, 0.05213364, 0.04683977, 0.05301817,
       0.04954075, 0.0511674 , 0.0452312 , 0.04956976, 0.04783761,
       0.04960534, 0.04905361, 0.05035869, 0.04985139, 0.04923417,
       0.04993366, 0.04904327, 0.04710691, 0.05397292, 0.05018352,
       0.05143658, 0.05183038, 0.04771311, 0.0564536 , 0.04802102,
       0.0491623 , 0.0517517 , 0.04976597, 0.0551865 , 0.05010598,
       0.04387606, 0.04561828, 0.0472429 , 0.0563065 , 0.05517411,
       0.04807942, 0.04426639, 0.04843217, 0.04920751, 0.04966598,
       0.04601344, 0.05043266, 0.05078886, 0.04767609, 0.05056729,
       0.05331595, 0.04508704, 0.04971964, 0.05082888, 0.05666934,
       0.05077989, 0.05355629, 0.05032215, 0.04455816, 0.04740633,
       0.05418673, 0.05195268, 0.04762953, 0.05470922, 0.04893129,
       0.05222928, 0.05414122, 0.0498379 , 0.04971149, 0.04717252,
       0.04935652, 0.04879633, 0.04916839, 0.04691701, 0.04791618,
       0.05036595, 0.0423537 , 0.05024822, 0.05017752, 0.05047447,
       0.05313954, 0.04696201, 0.05130618, 0.04955395, 0.05118816,
       0.0503743 , 0.05035741, 0.05336276, 0.04844283, 0.05217633,
       0.04666974, 0.04710334, 0.04959153, 0.0472958 , 0.04485941,
       0.05011367, 0.05322357, 0.05239311, 0.05149964, 0.04719446,
       0.04761175, 0.04597545, 0.04920868, 0.05288653, 0.04863549,
       0.0504015 , 0.05160588, 0.04453383, 0.05181224, 0.05015808,
       0.04882117, 0.05070062, 0.05751477, 0.0501814 , 0.05145818,
       0.05644023, 0.04939426, 0.05116706, 0.04734703, 0.04469711,
       0.05307641, 0.05227265, 0.05343145, 0.04716246, 0.0491238 ,
       0.04867434, 0.05045739, 0.04926089, 0.04813057, 0.05003028,
       0.05455248, 0.04477953, 0.05026449, 0.04743791, 0.05533145,
       0.04434371, 0.05048137, 0.05100697, 0.0492002 , 0.05021425,
       0.04874232, 0.05240968, 0.05261992, 0.04992837, 0.04684891,
       0.04638037, 0.05095142, 0.04656938, 0.05038266, 0.05654889,
       0.05128602, 0.04806998, 0.0517994 , 0.05533163, 0.0488396 ,
       0.05148388, 0.05107077, 0.04851391, 0.05305751, 0.04988156,
       0.04845005, 0.05007255, 0.0474026 , 0.05309936, 0.04641772,
       0.05335613, 0.0470733 , 0.05264876, 0.04753171, 0.04976961,
       0.04832941, 0.04946124, 0.04923486, 0.05046895, 0.04979288,
       0.05163191, 0.05351713, 0.04627264, 0.0454957 , 0.04560088,
       0.04908973, 0.05473868, 0.05520245, 0.05080742, 0.0492271 ,
       0.05019832, 0.05395024, 0.0509336 , 0.05148978, 0.05306048,
       0.05229978, 0.05111206, 0.04990677, 0.04979838, 0.05120098,
       0.05157117, 0.05190742, 0.04857297, 0.04546461, 0.05462838,
       0.04814052, 0.04974051, 0.0477786 , 0.04503909, 0.04861047,
       0.05437192, 0.04710632, 0.05018699, 0.0506187 , 0.05120855,
       0.0493607 , 0.04692951, 0.04760006, 0.05264787, 0.05224679,
       0.0468424 , 0.05028156, 0.0528942 , 0.04921373, 0.0456806 ,
       0.04855214, 0.04561752, 0.04887425, 0.04530341, 0.05012243,
       0.05098379, 0.05100879, 0.05006397, 0.04786183, 0.05203239,
       0.04740276, 0.04832747, 0.05445062, 0.04853116, 0.05118304,
       0.05200768, 0.04763745, 0.05028129, 0.05057894, 0.05257327,
       0.05413822, 0.04196039, 0.05359292, 0.04388526, 0.04612312,
       0.05273238, 0.04889462, 0.04932389, 0.04976385, 0.05350721,
       0.04973466, 0.04182006, 0.0467437 , 0.04825851, 0.04883357,
       0.04881905, 0.04883624, 0.0539815 , 0.0501227 , 0.05089328,
       0.05148859, 0.05333563, 0.05055896, 0.05250723, 0.04813036,
       0.05171658, 0.04747486, 0.04946287, 0.04960541, 0.04814821,
       0.05137911, 0.04829283, 0.05011817, 0.05035914, 0.04778591,
       0.05076631, 0.04934004, 0.04656203, 0.05051715, 0.05062515,
       0.05072469, 0.04944654, 0.05118618, 0.05119579, 0.04982452,
       0.05433756, 0.05212711, 0.04520884, 0.0525749 , 0.05038374,
       0.05153686, 0.05048039, 0.05112254, 0.04682323, 0.04961076,
       0.05136758, 0.0498312 , 0.04867948, 0.05134655, 0.04957444,
       0.04899914, 0.04727669, 0.05083326, 0.04896603, 0.04906398,
       0.04912633, 0.0483007 , 0.05184981, 0.05021544, 0.05063822,
       0.04992925, 0.05078383, 0.04981756, 0.05128878, 0.05072189,
       0.04806347, 0.04977112, 0.04829239, 0.0459417 , 0.05120437,
       0.05388453, 0.0470215 , 0.05722456, 0.04950006, 0.04855051,
       0.04948396, 0.04492763, 0.05074503, 0.04803561, 0.05094024,
       0.05088358, 0.0522854 , 0.05601979, 0.05037027, 0.04855916,
       0.04934486, 0.0505051 , 0.05049802, 0.04357715, 0.04645471,
       0.04978429, 0.05039716, 0.05001028, 0.05034128, 0.05065485,
       0.05160139, 0.04655229, 0.05149285, 0.05138582, 0.04984373,
       0.0439411 , 0.05176945, 0.05392174, 0.04021903, 0.0512692 ,
       0.04984669, 0.04535836, 0.05060852, 0.05005249, 0.0506264 ,
       0.05267486, 0.05146678, 0.04485558, 0.05017329, 0.04882123,
       0.04996398, 0.05473791, 0.05134235, 0.04287953, 0.04905952,
       0.05297333, 0.05219767, 0.04705759, 0.04675108, 0.04727322,
       0.04043231, 0.04452577, 0.04724299, 0.04874545, 0.04889464,
       0.05264893, 0.04833297, 0.04547528, 0.04910529, 0.04985518,
       0.05023881, 0.04719862, 0.05000084, 0.04920479, 0.04687058,
       0.04605366, 0.05357044, 0.04758176, 0.04929915, 0.05038631,
       0.0456238 , 0.04915684, 0.04915346, 0.05015444, 0.05201954,
       0.04997501, 0.0513198 , 0.0487747 , 0.05223705, 0.04947735,
       0.04346266, 0.04446523, 0.04716383, 0.05076577, 0.04804447,
       0.05274723, 0.0540584 , 0.04699266, 0.04711365, 0.04990008,
       0.04825097, 0.05005842, 0.05384307, 0.04832396, 0.05166611,
       0.05507575, 0.04704514, 0.05158264, 0.04954908, 0.05007777,
       0.04647167, 0.05099536, 0.04869678, 0.04997785, 0.0512901 ,
       0.05152356, 0.04954016, 0.04706537, 0.04398199, 0.04834248,
       0.04835895, 0.04772419, 0.05182251, 0.05033011, 0.04767486,
       0.0444403 , 0.05076767, 0.05197773, 0.04455714, 0.05267023,
       0.0538807 , 0.04985273, 0.05280511, 0.0487214 , 0.05073462,
       0.04854203, 0.05095348, 0.05661026, 0.05092068, 0.05131957])

plt.hist(bs_slope_reps, bins=50, density=True)
plt.xlabel('slope')
plt.ylabel('PDF')
plt.show()

我希望 Y 轴值在 0 和 1 之间进行归一化，但该图产生的值高于 1 的值高达 170+。为什么会这样？我对许多其他数据集进行了同样的尝试，到目前为止，在所有其他情况下，该图都符合预期，具有标准化的 y 轴值。任何输入将不胜感激。