我有一个数据文件，其中包含100 256 个值，范围大约从 0.01 到 3。我想绘制此数据集的密度。我绘制了理论（渐近分布）以供参考。我尝试使用 [hist=density] 选项，但它似乎无法正确归一化。
我们：
\documentclass[]{article}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\pgfmathsetmacro\M{256}
\pgfmathsetmacro\T{512}
\pgfmathsetmacro\c{\M/\T}
\pgfmathsetmacro\a{ (1-sqrt{\c})^2 }
\pgfmathsetmacro\b{ (1+sqrt{\c})^2 }
\begin{axis}[]
\addplot [domain=\a:\b, samples=401]{ (1 / (2*pi*\c*x)) * sqrt{max(x-\a,0)} * sqrt{ max(\b-x,0)}};
\addplot [hist={density,bins=12,data min=0,data max=3}] table [y index=0] {
2.84792527e+00
2.79971300e+00
2.75767416e+00
2.70242300e+00
2.63474982e+00
2.59112703e+00
2.58169006e+00
2.55872660e+00
2.50714780e+00
2.47939450e+00
2.45540054e+00
2.44807366e+00
2.39869010e+00
2.38551068e+00
2.36071654e+00
2.32497123e+00
2.29341151e+00
2.20198818e+00
2.26704476e+00
2.24770329e+00
2.23883343e+00
2.17155548e+00
2.14851869e+00
2.12234916e+00
2.11434171e+00
2.10296781e+00
2.08434324e+00
2.06187359e+00
2.04121062e+00
2.02674162e+00
2.00116870e+00
1.97414690e+00
1.86391772e+00
1.95819315e+00
1.87970695e+00
1.90289119e+00
1.91374844e+00
1.93106762e+00
1.93453101e+00
1.84736272e+00
1.83451621e+00
1.81579733e+00
1.79746771e+00
1.77324373e+00
1.77591396e+00
1.75389693e+00
1.73632737e+00
1.71546129e+00
1.70649338e+00
1.70902234e+00
1.67391959e+00
1.65833738e+00
1.64774043e+00
1.63668526e+00
1.61796348e+00
1.56738001e+00
1.60193044e+00
1.57845268e+00
1.59057702e+00
1.55485577e+00
1.47873974e+00
1.49340294e+00
1.50267231e+00
1.53386269e+00
1.51979168e+00
1.52503667e+00
1.39142933e+00
1.40132624e+00
1.45745146e+00
1.42332545e+00
1.43487108e+00
1.44369011e+00
1.37909372e+00
1.36653525e+00
1.36166819e+00
1.31151678e+00
1.34572767e+00
1.33291913e+00
1.32218248e+00
1.30052933e+00
1.29376312e+00
1.24943283e+00
1.25805378e+00
1.26974936e+00
1.27652793e+00
1.24218264e+00
1.23015005e+00
1.22280541e+00
1.21187412e+00
1.19787246e+00
1.18224724e+00
1.19084037e+00
1.17022557e+00
9.35412607e-02
1.01126689e-01
1.05046944e-01
1.14640343e+00
1.14043759e+00
1.12821814e+00
1.12323195e+00
1.10807967e+00
1.10339326e+00
1.09178614e+00
1.10600437e-01
1.17731747e-01
1.24266049e-01
1.27153618e-01
1.30847665e-01
1.34807606e-01
1.08193357e+00
1.07153220e+00
1.06051855e+00
1.03323835e+00
1.04720251e+00
1.02451344e+00
1.38801514e-01
1.44349972e-01
1.47735282e-01
1.52610351e-01
1.58219230e-01
1.59985173e-01
1.66222439e-01
1.69911973e-01
1.01664939e+00
1.00923683e+00
1.00460464e+00
9.88497443e-01
9.92123832e-01
9.82364322e-01
9.71801376e-01
9.57434308e-01
9.38667240e-01
9.29565397e-01
9.48983040e-01
9.18951540e-01
9.13876580e-01
1.75229379e-01
1.81038000e-01
1.82687431e-01
1.85693748e-01
9.00846949e-01
8.94817920e-01
8.86782414e-01
8.72470822e-01
8.65317436e-01
8.60003967e-01
1.90750406e-01
1.93583505e-01
1.99589582e-01
2.03355998e-01
2.08235131e-01
2.04995761e-01
8.54237972e-01
8.38019062e-01
8.30602872e-01
8.25107075e-01
8.22235928e-01
8.11973258e-01
8.06110049e-01
7.82969173e-01
7.94341980e-01
2.17336532e-01
2.22492951e-01
2.29378688e-01
2.31412052e-01
2.37269579e-01
2.44569780e-01
2.47479574e-01
7.69630529e-01
7.90996270e-01
2.54803964e-01
7.42313790e-01
7.65172955e-01
7.54705998e-01
7.56934758e-01
7.30326874e-01
7.13491444e-01
2.57078873e-01
2.61146223e-01
2.63164382e-01
2.69880427e-01
2.71051599e-01
7.25560296e-01
7.05977400e-01
6.72653509e-01
6.61137426e-01
6.53955772e-01
6.97464788e-01
6.85441160e-01
6.87531104e-01
6.94202771e-01
2.78592672e-01
2.74923086e-01
2.84629896e-01
2.89965333e-01
2.99153394e-01
3.02679471e-01
3.08903091e-01
3.16598056e-01
3.19550433e-01
6.45028317e-01
6.39678575e-01
6.30148206e-01
3.26900436e-01
3.33051638e-01
3.40591869e-01
3.47608462e-01
6.18681609e-01
5.94874880e-01
6.04131709e-01
6.15394881e-01
6.09297544e-01
6.24899639e-01
5.85961018e-01
5.82262352e-01
5.63451820e-01
5.69384105e-01
3.37010860e-01
3.55447439e-01
3.63433252e-01
3.68066820e-01
3.71597992e-01
3.50862089e-01
3.80250912e-01
3.89908305e-01
3.93942564e-01
4.11209197e-01
4.00779182e-01
5.73555187e-01
4.33220043e-01
4.05788444e-01
4.49729506e-01
5.50658052e-01
5.24581614e-01
5.28757940e-01
5.09345085e-01
5.06674917e-01
4.54050375e-01
4.66052390e-01
4.72312620e-01
4.81922511e-01
3.30540618e-01
5.55127447e-01
3.84951530e-01
5.40326182e-01
5.31938577e-01
4.26837646e-01
4.39155048e-01
4.23378545e-01
4.24972665e-01
4.98169056e-01
4.94796789e-01
4.58194651e-01
4.78098490e-01
4.90495477e-01
5.44041046e-01
};
\end{axis}
\end{tikzpicture}
\end{document}
这让我
如您所见，我有 12 个箱子，范围为 3，因此每个条形的宽度为 0.25 个单位。所有条形的宽度都低于 0.2，所以我的面积肯定小于 12 * 0.25 * 0.2 = 0.6。
直方图应该被标准化，因此面积为 1 才能被视为密度，所以我遗漏了什么吗？
（我可以使用八度对直方图进行标准化，然后只需将此直方图提供给 pgfplots 进行正常绘图，但似乎 hist=density 选项应该自动执行此操作）
有任何想法吗？