Normal Distribution with Different Means and Variances
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Plot[Table[PDF[NormalDistribution[μ,1.5],x],{μ,{-1,1,2}}]//Evaluate,{x,-6,6},FillingAxis]​​Plot[Table[PDF[NormalDistribution[0,σ],x],{σ,{.75,1,2}}]//Evaluate,{x,-6,6},FillingAxis]​​Manipulate[​​Plot[PDF[NormalDistribution[μ,σ],x],{x,-5,5},AxesOrigin{0,0},PlotRange{{-5,5},{0,0.4}}],​​{{μ,0},-4,4},{{σ,2},1,3}]
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μ
σ
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How well normal describes SP500 Returns?
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sp500=FinancialData["SP500","FractionalChange",​​{{2000,1,1},{2009,1,1},"Day"}];​​edist=EstimatedDistribution[sp500,NormalDistribution[μ,σ]]
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QuantityDistribution[NormalDistribution[-0.0118302,1.36004],
%
]
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hist=Histogram[sp500,Automatic,"PDF"];​​Show[hist,​​Plot[Table[PDF[NormalDistribution[-0.0118302,σ],x],{σ,0.8,1.5,0.3}]//Evaluate,{x,-3,3},PlotStyleThick,PlotRangeAll]​​]​​Manipulate[​​Show[​​Histogram[FinancialData["SP500","FractionalChange",{{2000,1,1},{2009,1,1},"Day"}],Automatic,"PDF"],​​ Plot[PDF[NormalDistribution[-0.0118302,σ],x],{x,-10,12},PlotStyleThick,PlotRangeAll]],​​{{σ,1.36004},0.5,2}​​]
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σ
ShowHistogram[Missing[NotAvailable],Automatic,PDF],
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How about Chicago wind speed?
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chit=Log[WeatherData["KORD","WindSpeed",{{2007,1,1},{2007,12,31},"Day"}]];​​hist=Histogram[chit,Automatic,"PDF"];​​edist=EstimatedDistribution[chit,​​NormalDistribution[μ,σ]];​​Show[hist,Plot[PDF[edist,x],{x,1,4},PlotStyleThick,​​PlotRangeAll]]
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How about pressure?
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chit=Log[WeatherData["KORD","Pressure",{{2007,1,1},{2007,12,31},"Day"}]];​​hist=Histogram[chit,Automatic,"PDF"];​​edist=EstimatedDistribution[chit,​​NormalDistribution[μ,σ]]​​Show[hist,Plot[PDF[edist,x],{x,6.8,7},PlotStyleThick,​​PlotRangeAll]]
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NormalDistribution[6.92465,0.0064028]
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pub=CloudPublish[EvaluationNotebook[]]
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CloudObject
https://www.wolframcloud.com/obj/144c13ec-0a36-4a22-9797-a917a7988baa
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