SmoothKernelDistribution
RandomChoice
PDF
Quantile
ExampleData

Probability & Statistics
Mathematics
Data Science

Snowfall Estimation with Bootstrap Confidence Bands

Analyze annual snowfall data and quantify uncertainty using bootstrap resampling

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This example estimates the probability density function (PDF) of annual snowfall accumulation in Buffalo, New York, using historical data. A bootstrap resampling procedure is applied to quantify uncertainty in the estimated density, resulting in a 95% confidence band around the PDF.

Load the description of the dataset, which contains historical annual snowfall measurements for Buffalo, New York:

In[1]:=

ExampleData[{"Statistics","BuffaloSnow"},"Description"];

Out[1]=

Snowfall records for Buffalo, New York from 1910 to 1972.

Extract the snowfall data and represent it as a quantity array measured in inches:

In[2]:=

data=QuantityArray[ExampleData[{"Statistics","BuffaloSnow"}],"Inches"]

Out[2]=

QuantityArray

Dimensions: {63}

Unit: Inches



Estimate the probability density of snowfall accumulation using kernel density estimation:

In[3]:=

=SmoothKernelDistribution[data]

Out[3]=

DataDistribution

Type: SmoothKernel

Data points: 63



Generate 250 bootstrap resamples by randomly sampling, with replacement, from the observed snowfall data:

In[4]:=

bSamp=RandomChoice[Normal[data],{250,Length[data]}];

Fit a kernel density estimate to each bootstrap resample to obtain a collection of density functions:

In[5]:=



=SmoothKernelDistribution/@bSamp;

Evaluate each bootstrap density on a common grid:

In[6]:=

rng=Range[10.,150];pdf=Table[PDF[i,Quantity[rng,"Inches"]],{i,



}];

Compute pointwise 2.5 % and 97.5 % quantiles to form a 95 % confidence band:

In[7]:=

High=Table[Quantile[i,.975],{i,Transpose[pdf]}];Low=Table[Quantile[i,.025],{i,Transpose[pdf]}];

Plot the estimated probability density function together with the 95% bootstrap confidence band:

In[8]:=

Show[Plot[PDF[,Quantity[x,"Inches"]],{x,0,150},PlotRangeAll,AxesLabel{"in"}],ListLinePlot[{Transpose[{rng,High}],Transpose[{rng,Low}]},PlotStyle{{Dashed,Gray}},Filling{1{2}}]]

Out[8]=

Related Symbols

SmoothKernelDistribution
RandomChoice
PDF
Quantile
ExampleData

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Contributed by: Wolfram Staff

Wolfram Language Example Repository

Snowfall Estimation with Bootstrap Confidence Bands

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