数量数据的非参数化分布

利用 WeatherData 获取芝加哥市从 2014 年初到 2015 年末的风速测量的时间序列.

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wsts = WeatherData["Chicago", "WindSpeed", {DateObject[{2014, 1, 1}], DateObject[{2015, 12, 31}]}]

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用 Histogram 来可视化风速的分布.

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Histogram[wsts, PlotTheme -> "Detailed", FrameLabel -> Automatic]

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提取风速值，用插值法补齐缺失数据.

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winds = Values[TimeSeries[wsts, MissingDataMethod -> "Interpolation"]]

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用 SmoothKernelDistribution 构建芝加哥市风速的非参数化模型，要确保风速不能是负值.

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ws\[ScriptCapitalD] = SmoothKernelDistribution[winds, Automatic, {"Bounded", Quantity[0, ("Kilometers")/("Hours")], "Gaussian"}]

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用作为风速的函数的风力发电机功率输出的非参数化模型，来估计安装在当地的 GE 1.5 兆瓦风力发电机的平均输出功率.

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turbine = Interpolation[ QuantityArray[{{0.`, 0.`}, {0.5`, 0.`}, {1.`, 0.`}, {1.5`, 0.`}, {2.`, 0.`}, {2.5`, 0.`}, {3.`, 0.`}, {3.5`, 0.`}, {4.`, 36.`}, {4.5`, 66.`}, {5.`, 104.`}, {5.5`, 150.`}, {6.`, 205.`}, {6.5`, 269.`}, {7.`, 344.`}, {7.5`, 428.`}, {8.`, 528.`}, {8.5`, 644.`}, {9.`, 774.`}, {9.5`, 926.5`}, {10.`, 1079.`}, {10.5`, 1211.`}, {11.`, 1342.`}, {11.5`, 1401.`}, {12.`, 1460.`}, {12.5`, 1477.`}, {13.`, 1494.`}, {13.5`, 1500.`}, {30.`, 1500.`}}, {"Meters"/"Seconds", "Kilowatts"}] // Normal, InterpolationOrder -> 1];

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NExpectation[turbine[v], v \[Distributed] ws\[ScriptCapitalD]]

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