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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_density.wasp
Title produced by softwareKernel Density Estimation
Date of computationMon, 11 Feb 2013 10:43:06 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Feb/11/t1360597419chdixssghltkoge.htm/, Retrieved Mon, 29 Apr 2024 15:46:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=206259, Retrieved Mon, 29 Apr 2024 15:46:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact111

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Histogram] [consumptieprijzen...] [2013-02-07 09:26:39] [449b5e808e718ae5c894f4cdc1419746]
- R P   [Histogram] [consumptieprijzen...] [2013-02-11 15:38:55] [449b5e808e718ae5c894f4cdc1419746]
- RM D      [Kernel Density Estimation] [consumptieprijzen...] [2013-02-11 15:43:06] [c26e09c8434f533bb784f50bf3cf5b76] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206259&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206259&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206259&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Properties of Density Trace
Bandwidth0.0142089774595625
#Observations72

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.0142089774595625 \tabularnewline
#Observations & 72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206259&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.0142089774595625[/C][/ROW]
[ROW][C]#Observations[/C][C]72[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206259&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206259&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Properties of Density Trace
Bandwidth0.0142089774595625
#Observations72






Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.51621669809613810.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 0.594547504897042 & 11.4866524391173 \tabularnewline
Epanechnikov & 0.596458012379991 & 10.7636577496208 \tabularnewline
Rectangular & 0.516216698096138 & 10.1581952472075 \tabularnewline
Triangular & 0.590344388434554 & 11.5647686736729 \tabularnewline
Biweight & 0.596075910883401 & 10.9783777041667 \tabularnewline
Cosine & 0.595693809386811 & 11.0489189686393 \tabularnewline
Optcosine & 0.596458012379991 & 10.8241781265658 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206259&T=2

[TABLE]
[ROW][C]Maximum Density Values[/C][/ROW]
[ROW][C]Kernel[/C][C]x-value[/C][C]max. density[/C][/ROW]
[ROW][C]Gaussian[/C][C]0.594547504897042[/C][C]11.4866524391173[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]0.596458012379991[/C][C]10.7636577496208[/C][/ROW]
[ROW][C]Rectangular[/C][C]0.516216698096138[/C][C]10.1581952472075[/C][/ROW]
[ROW][C]Triangular[/C][C]0.590344388434554[/C][C]11.5647686736729[/C][/ROW]
[ROW][C]Biweight[/C][C]0.596075910883401[/C][C]10.9783777041667[/C][/ROW]
[ROW][C]Cosine[/C][C]0.595693809386811[/C][C]11.0489189686393[/C][/ROW]
[ROW][C]Optcosine[/C][C]0.596458012379991[/C][C]10.8241781265658[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206259&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206259&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.51621669809613810.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658






Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.51659879959272810.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 0.594547504897042 & 11.4866524391173 \tabularnewline
Epanechnikov & 0.596458012379991 & 10.7636577496208 \tabularnewline
Rectangular & 0.516598799592728 & 10.1581952472075 \tabularnewline
Triangular & 0.590344388434554 & 11.5647686736729 \tabularnewline
Biweight & 0.596075910883401 & 10.9783777041667 \tabularnewline
Cosine & 0.595693809386811 & 11.0489189686393 \tabularnewline
Optcosine & 0.596458012379991 & 10.8241781265658 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206259&T=3

[TABLE]
[ROW][C]Maximum Density Values[/C][/ROW]
[ROW][C]Kernel[/C][C]x-value[/C][C]max. density[/C][/ROW]
[ROW][C]Gaussian[/C][C]0.594547504897042[/C][C]11.4866524391173[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]0.596458012379991[/C][C]10.7636577496208[/C][/ROW]
[ROW][C]Rectangular[/C][C]0.516598799592728[/C][C]10.1581952472075[/C][/ROW]
[ROW][C]Triangular[/C][C]0.590344388434554[/C][C]11.5647686736729[/C][/ROW]
[ROW][C]Biweight[/C][C]0.596075910883401[/C][C]10.9783777041667[/C][/ROW]
[ROW][C]Cosine[/C][C]0.595693809386811[/C][C]11.0489189686393[/C][/ROW]
[ROW][C]Optcosine[/C][C]0.596458012379991[/C][C]10.8241781265658[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206259&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206259&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.51659879959272810.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658






Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.51774510408249710.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 0.594547504897042 & 11.4866524391173 \tabularnewline
Epanechnikov & 0.596458012379991 & 10.7636577496208 \tabularnewline
Rectangular & 0.517745104082497 & 10.1581952472075 \tabularnewline
Triangular & 0.590344388434554 & 11.5647686736729 \tabularnewline
Biweight & 0.596075910883401 & 10.9783777041667 \tabularnewline
Cosine & 0.595693809386811 & 11.0489189686393 \tabularnewline
Optcosine & 0.596458012379991 & 10.8241781265658 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206259&T=4

[TABLE]
[ROW][C]Maximum Density Values[/C][/ROW]
[ROW][C]Kernel[/C][C]x-value[/C][C]max. density[/C][/ROW]
[ROW][C]Gaussian[/C][C]0.594547504897042[/C][C]11.4866524391173[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]0.596458012379991[/C][C]10.7636577496208[/C][/ROW]
[ROW][C]Rectangular[/C][C]0.517745104082497[/C][C]10.1581952472075[/C][/ROW]
[ROW][C]Triangular[/C][C]0.590344388434554[/C][C]11.5647686736729[/C][/ROW]
[ROW][C]Biweight[/C][C]0.596075910883401[/C][C]10.9783777041667[/C][/ROW]
[ROW][C]Cosine[/C][C]0.595693809386811[/C][C]11.0489189686393[/C][/ROW]
[ROW][C]Optcosine[/C][C]0.596458012379991[/C][C]10.8241781265658[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206259&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206259&T=4

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.51774510408249710.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658






Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.51889140857226610.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 0.594547504897042 & 11.4866524391173 \tabularnewline
Epanechnikov & 0.596458012379991 & 10.7636577496208 \tabularnewline
Rectangular & 0.518891408572266 & 10.1581952472075 \tabularnewline
Triangular & 0.590344388434554 & 11.5647686736729 \tabularnewline
Biweight & 0.596075910883401 & 10.9783777041667 \tabularnewline
Cosine & 0.595693809386811 & 11.0489189686393 \tabularnewline
Optcosine & 0.596458012379991 & 10.8241781265658 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206259&T=5

[TABLE]
[ROW][C]Maximum Density Values[/C][/ROW]
[ROW][C]Kernel[/C][C]x-value[/C][C]max. density[/C][/ROW]
[ROW][C]Gaussian[/C][C]0.594547504897042[/C][C]11.4866524391173[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]0.596458012379991[/C][C]10.7636577496208[/C][/ROW]
[ROW][C]Rectangular[/C][C]0.518891408572266[/C][C]10.1581952472075[/C][/ROW]
[ROW][C]Triangular[/C][C]0.590344388434554[/C][C]11.5647686736729[/C][/ROW]
[ROW][C]Biweight[/C][C]0.596075910883401[/C][C]10.9783777041667[/C][/ROW]
[ROW][C]Cosine[/C][C]0.595693809386811[/C][C]11.0489189686393[/C][/ROW]
[ROW][C]Optcosine[/C][C]0.596458012379991[/C][C]10.8241781265658[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206259&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206259&T=5

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.51889140857226610.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658






Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.51927351006885610.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 0.594547504897042 & 11.4866524391173 \tabularnewline
Epanechnikov & 0.596458012379991 & 10.7636577496208 \tabularnewline
Rectangular & 0.519273510068856 & 10.1581952472075 \tabularnewline
Triangular & 0.590344388434554 & 11.5647686736729 \tabularnewline
Biweight & 0.596075910883401 & 10.9783777041667 \tabularnewline
Cosine & 0.595693809386811 & 11.0489189686393 \tabularnewline
Optcosine & 0.596458012379991 & 10.8241781265658 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206259&T=6

[TABLE]
[ROW][C]Maximum Density Values[/C][/ROW]
[ROW][C]Kernel[/C][C]x-value[/C][C]max. density[/C][/ROW]
[ROW][C]Gaussian[/C][C]0.594547504897042[/C][C]11.4866524391173[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]0.596458012379991[/C][C]10.7636577496208[/C][/ROW]
[ROW][C]Rectangular[/C][C]0.519273510068856[/C][C]10.1581952472075[/C][/ROW]
[ROW][C]Triangular[/C][C]0.590344388434554[/C][C]11.5647686736729[/C][/ROW]
[ROW][C]Biweight[/C][C]0.596075910883401[/C][C]10.9783777041667[/C][/ROW]
[ROW][C]Cosine[/C][C]0.595693809386811[/C][C]11.0489189686393[/C][/ROW]
[ROW][C]Optcosine[/C][C]0.596458012379991[/C][C]10.8241781265658[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206259&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206259&T=6

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.51927351006885610.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658






Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.52003771306203610.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 0.594547504897042 & 11.4866524391173 \tabularnewline
Epanechnikov & 0.596458012379991 & 10.7636577496208 \tabularnewline
Rectangular & 0.520037713062036 & 10.1581952472075 \tabularnewline
Triangular & 0.590344388434554 & 11.5647686736729 \tabularnewline
Biweight & 0.596075910883401 & 10.9783777041667 \tabularnewline
Cosine & 0.595693809386811 & 11.0489189686393 \tabularnewline
Optcosine & 0.596458012379991 & 10.8241781265658 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206259&T=7

[TABLE]
[ROW][C]Maximum Density Values[/C][/ROW]
[ROW][C]Kernel[/C][C]x-value[/C][C]max. density[/C][/ROW]
[ROW][C]Gaussian[/C][C]0.594547504897042[/C][C]11.4866524391173[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]0.596458012379991[/C][C]10.7636577496208[/C][/ROW]
[ROW][C]Rectangular[/C][C]0.520037713062036[/C][C]10.1581952472075[/C][/ROW]
[ROW][C]Triangular[/C][C]0.590344388434554[/C][C]11.5647686736729[/C][/ROW]
[ROW][C]Biweight[/C][C]0.596075910883401[/C][C]10.9783777041667[/C][/ROW]
[ROW][C]Cosine[/C][C]0.595693809386811[/C][C]11.0489189686393[/C][/ROW]
[ROW][C]Optcosine[/C][C]0.596458012379991[/C][C]10.8241781265658[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206259&T=7

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206259&T=7

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.52003771306203610.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658






Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.52041981455862510.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 0.594547504897042 & 11.4866524391173 \tabularnewline
Epanechnikov & 0.596458012379991 & 10.7636577496208 \tabularnewline
Rectangular & 0.520419814558625 & 10.1581952472075 \tabularnewline
Triangular & 0.590344388434554 & 11.5647686736729 \tabularnewline
Biweight & 0.596075910883401 & 10.9783777041667 \tabularnewline
Cosine & 0.595693809386811 & 11.0489189686393 \tabularnewline
Optcosine & 0.596458012379991 & 10.8241781265658 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206259&T=8

[TABLE]
[ROW][C]Maximum Density Values[/C][/ROW]
[ROW][C]Kernel[/C][C]x-value[/C][C]max. density[/C][/ROW]
[ROW][C]Gaussian[/C][C]0.594547504897042[/C][C]11.4866524391173[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]0.596458012379991[/C][C]10.7636577496208[/C][/ROW]
[ROW][C]Rectangular[/C][C]0.520419814558625[/C][C]10.1581952472075[/C][/ROW]
[ROW][C]Triangular[/C][C]0.590344388434554[/C][C]11.5647686736729[/C][/ROW]
[ROW][C]Biweight[/C][C]0.596075910883401[/C][C]10.9783777041667[/C][/ROW]
[ROW][C]Cosine[/C][C]0.595693809386811[/C][C]11.0489189686393[/C][/ROW]
[ROW][C]Optcosine[/C][C]0.596458012379991[/C][C]10.8241781265658[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206259&T=8

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206259&T=8

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.52041981455862510.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658






Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.52080191605521510.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 0.594547504897042 & 11.4866524391173 \tabularnewline
Epanechnikov & 0.596458012379991 & 10.7636577496208 \tabularnewline
Rectangular & 0.520801916055215 & 10.1581952472075 \tabularnewline
Triangular & 0.590344388434554 & 11.5647686736729 \tabularnewline
Biweight & 0.596075910883401 & 10.9783777041667 \tabularnewline
Cosine & 0.595693809386811 & 11.0489189686393 \tabularnewline
Optcosine & 0.596458012379991 & 10.8241781265658 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206259&T=9

[TABLE]
[ROW][C]Maximum Density Values[/C][/ROW]
[ROW][C]Kernel[/C][C]x-value[/C][C]max. density[/C][/ROW]
[ROW][C]Gaussian[/C][C]0.594547504897042[/C][C]11.4866524391173[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]0.596458012379991[/C][C]10.7636577496208[/C][/ROW]
[ROW][C]Rectangular[/C][C]0.520801916055215[/C][C]10.1581952472075[/C][/ROW]
[ROW][C]Triangular[/C][C]0.590344388434554[/C][C]11.5647686736729[/C][/ROW]
[ROW][C]Biweight[/C][C]0.596075910883401[/C][C]10.9783777041667[/C][/ROW]
[ROW][C]Cosine[/C][C]0.595693809386811[/C][C]11.0489189686393[/C][/ROW]
[ROW][C]Optcosine[/C][C]0.596458012379991[/C][C]10.8241781265658[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206259&T=9

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206259&T=9

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.52080191605521510.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658






Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.52271242353816410.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 0.594547504897042 & 11.4866524391173 \tabularnewline
Epanechnikov & 0.596458012379991 & 10.7636577496208 \tabularnewline
Rectangular & 0.522712423538164 & 10.1581952472075 \tabularnewline
Triangular & 0.590344388434554 & 11.5647686736729 \tabularnewline
Biweight & 0.596075910883401 & 10.9783777041667 \tabularnewline
Cosine & 0.595693809386811 & 11.0489189686393 \tabularnewline
Optcosine & 0.596458012379991 & 10.8241781265658 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206259&T=10

[TABLE]
[ROW][C]Maximum Density Values[/C][/ROW]
[ROW][C]Kernel[/C][C]x-value[/C][C]max. density[/C][/ROW]
[ROW][C]Gaussian[/C][C]0.594547504897042[/C][C]11.4866524391173[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]0.596458012379991[/C][C]10.7636577496208[/C][/ROW]
[ROW][C]Rectangular[/C][C]0.522712423538164[/C][C]10.1581952472075[/C][/ROW]
[ROW][C]Triangular[/C][C]0.590344388434554[/C][C]11.5647686736729[/C][/ROW]
[ROW][C]Biweight[/C][C]0.596075910883401[/C][C]10.9783777041667[/C][/ROW]
[ROW][C]Cosine[/C][C]0.595693809386811[/C][C]11.0489189686393[/C][/ROW]
[ROW][C]Optcosine[/C][C]0.596458012379991[/C][C]10.8241781265658[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206259&T=10

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206259&T=10

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.52271242353816410.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658






Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.52309452503475410.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 0.594547504897042 & 11.4866524391173 \tabularnewline
Epanechnikov & 0.596458012379991 & 10.7636577496208 \tabularnewline
Rectangular & 0.523094525034754 & 10.1581952472075 \tabularnewline
Triangular & 0.590344388434554 & 11.5647686736729 \tabularnewline
Biweight & 0.596075910883401 & 10.9783777041667 \tabularnewline
Cosine & 0.595693809386811 & 11.0489189686393 \tabularnewline
Optcosine & 0.596458012379991 & 10.8241781265658 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206259&T=11

[TABLE]
[ROW][C]Maximum Density Values[/C][/ROW]
[ROW][C]Kernel[/C][C]x-value[/C][C]max. density[/C][/ROW]
[ROW][C]Gaussian[/C][C]0.594547504897042[/C][C]11.4866524391173[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]0.596458012379991[/C][C]10.7636577496208[/C][/ROW]
[ROW][C]Rectangular[/C][C]0.523094525034754[/C][C]10.1581952472075[/C][/ROW]
[ROW][C]Triangular[/C][C]0.590344388434554[/C][C]11.5647686736729[/C][/ROW]
[ROW][C]Biweight[/C][C]0.596075910883401[/C][C]10.9783777041667[/C][/ROW]
[ROW][C]Cosine[/C][C]0.595693809386811[/C][C]11.0489189686393[/C][/ROW]
[ROW][C]Optcosine[/C][C]0.596458012379991[/C][C]10.8241781265658[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206259&T=11

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206259&T=11

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.52309452503475410.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658






Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.52347662653134410.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 0.594547504897042 & 11.4866524391173 \tabularnewline
Epanechnikov & 0.596458012379991 & 10.7636577496208 \tabularnewline
Rectangular & 0.523476626531344 & 10.1581952472075 \tabularnewline
Triangular & 0.590344388434554 & 11.5647686736729 \tabularnewline
Biweight & 0.596075910883401 & 10.9783777041667 \tabularnewline
Cosine & 0.595693809386811 & 11.0489189686393 \tabularnewline
Optcosine & 0.596458012379991 & 10.8241781265658 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206259&T=12

[TABLE]
[ROW][C]Maximum Density Values[/C][/ROW]
[ROW][C]Kernel[/C][C]x-value[/C][C]max. density[/C][/ROW]
[ROW][C]Gaussian[/C][C]0.594547504897042[/C][C]11.4866524391173[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]0.596458012379991[/C][C]10.7636577496208[/C][/ROW]
[ROW][C]Rectangular[/C][C]0.523476626531344[/C][C]10.1581952472075[/C][/ROW]
[ROW][C]Triangular[/C][C]0.590344388434554[/C][C]11.5647686736729[/C][/ROW]
[ROW][C]Biweight[/C][C]0.596075910883401[/C][C]10.9783777041667[/C][/ROW]
[ROW][C]Cosine[/C][C]0.595693809386811[/C][C]11.0489189686393[/C][/ROW]
[ROW][C]Optcosine[/C][C]0.596458012379991[/C][C]10.8241781265658[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206259&T=12

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206259&T=12

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.52347662653134410.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658






Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.52385872802793310.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 0.594547504897042 & 11.4866524391173 \tabularnewline
Epanechnikov & 0.596458012379991 & 10.7636577496208 \tabularnewline
Rectangular & 0.523858728027933 & 10.1581952472075 \tabularnewline
Triangular & 0.590344388434554 & 11.5647686736729 \tabularnewline
Biweight & 0.596075910883401 & 10.9783777041667 \tabularnewline
Cosine & 0.595693809386811 & 11.0489189686393 \tabularnewline
Optcosine & 0.596458012379991 & 10.8241781265658 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206259&T=13

[TABLE]
[ROW][C]Maximum Density Values[/C][/ROW]
[ROW][C]Kernel[/C][C]x-value[/C][C]max. density[/C][/ROW]
[ROW][C]Gaussian[/C][C]0.594547504897042[/C][C]11.4866524391173[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]0.596458012379991[/C][C]10.7636577496208[/C][/ROW]
[ROW][C]Rectangular[/C][C]0.523858728027933[/C][C]10.1581952472075[/C][/ROW]
[ROW][C]Triangular[/C][C]0.590344388434554[/C][C]11.5647686736729[/C][/ROW]
[ROW][C]Biweight[/C][C]0.596075910883401[/C][C]10.9783777041667[/C][/ROW]
[ROW][C]Cosine[/C][C]0.595693809386811[/C][C]11.0489189686393[/C][/ROW]
[ROW][C]Optcosine[/C][C]0.596458012379991[/C][C]10.8241781265658[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206259&T=13

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206259&T=13

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Maximum Density Values
Kernelx-valuemax. density
Gaussian0.59454750489704211.4866524391173
Epanechnikov0.59645801237999110.7636577496208
Rectangular0.52385872802793310.1581952472075
Triangular0.59034438843455411.5647686736729
Biweight0.59607591088340110.9783777041667
Cosine0.59569380938681111.0489189686393
Optcosine0.59645801237999110.8241781265658


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 25 ; par2 = yes ; par3 = 512 ;
Parameters (R input):
par1 = 0 ; par2 = no ; par3 = 512 ;
R code (references can be found in the software module):
if (par1 == '0') bw <- 'nrd0'
if (par1 != '0') bw <- as.numeric(par1)
par3 <- as.numeric(par3)
mydensity <- array(NA, dim=c(par3,8))
bitmap(file='density1.png')
mydensity1<-density(x,bw=bw,kernel='gaussian',na.rm=TRUE)
mydensity[,8] = signif(mydensity1$x,3)
mydensity[,1] = signif(mydensity1$y,3)
plot(mydensity1,main='Gaussian Kernel',xlab=xlab,ylab=ylab)
grid()
dev.off()
mydensity1
bitmap(file='density2.png')
mydensity2<-density(x,bw=bw,kernel='epanechnikov',na.rm=TRUE)
mydensity[,2] = signif(mydensity2$y,3)
plot(mydensity2,main='Epanechnikov Kernel',xlab=xlab,ylab=ylab)
grid()
dev.off()
bitmap(file='density3.png')
mydensity3<-density(x,bw=bw,kernel='rectangular',na.rm=TRUE)
mydensity[,3] = signif(mydensity3$y,3)
plot(mydensity3,main='Rectangular Kernel',xlab=xlab,ylab=ylab)
grid()
dev.off()
bitmap(file='density4.png')
mydensity4<-density(x,bw=bw,kernel='triangular',na.rm=TRUE)
mydensity[,4] = signif(mydensity4$y,3)
plot(mydensity4,main='Triangular Kernel',xlab=xlab,ylab=ylab)
grid()
dev.off()
bitmap(file='density5.png')
mydensity5<-density(x,bw=bw,kernel='biweight',na.rm=TRUE)
mydensity[,5] = signif(mydensity5$y,3)
plot(mydensity5,main='Biweight Kernel',xlab=xlab,ylab=ylab)
grid()
dev.off()
bitmap(file='density6.png')
mydensity6<-density(x,bw=bw,kernel='cosine',na.rm=TRUE)
mydensity[,6] = signif(mydensity6$y,3)
plot(mydensity6,main='Cosine Kernel',xlab=xlab,ylab=ylab)
grid()
dev.off()
bitmap(file='density7.png')
mydensity7<-density(x,bw=bw,kernel='optcosine',na.rm=TRUE)
mydensity[,7] = signif(mydensity7$y,3)
plot(mydensity7,main='Optcosine Kernel',xlab=xlab,ylab=ylab)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Properties of Density Trace',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Bandwidth',header=TRUE)
a<-table.element(a,mydensity1$bw)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'#Observations',header=TRUE)
a<-table.element(a,mydensity1$n)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Maximum Density Values',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Kernel',1,TRUE)
a<-table.element(a,'x-value',1,TRUE)
a<-table.element(a,'max. density',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Gaussian',1,TRUE)
a<-table.element(a,mydensity1$x[mydensity1$y==max(mydensity1$y)],1)
a<-table.element(a,mydensity1$y[mydensity1$y==max(mydensity1$y)],1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Epanechnikov',1,TRUE)
a<-table.element(a,mydensity2$x[mydensity2$y==max(mydensity2$y)],1)
a<-table.element(a,mydensity2$y[mydensity2$y==max(mydensity2$y)],1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Rectangular',1,TRUE)
a<-table.element(a,mydensity3$x[mydensity3$y==max(mydensity3$y)],1)
a<-table.element(a,mydensity3$y[mydensity3$y==max(mydensity3$y)],1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Triangular',1,TRUE)
a<-table.element(a,mydensity4$x[mydensity4$y==max(mydensity4$y)],1)
a<-table.element(a,mydensity4$y[mydensity4$y==max(mydensity4$y)],1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biweight',1,TRUE)
a<-table.element(a,mydensity5$x[mydensity5$y==max(mydensity5$y)],1)
a<-table.element(a,mydensity5$y[mydensity5$y==max(mydensity5$y)],1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Cosine',1,TRUE)
a<-table.element(a,mydensity6$x[mydensity6$y==max(mydensity6$y)],1)
a<-table.element(a,mydensity6$y[mydensity6$y==max(mydensity6$y)],1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Optcosine',1,TRUE)
a<-table.element(a,mydensity7$x[mydensity7$y==max(mydensity7$y)],1)
a<-table.element(a,mydensity7$y[mydensity7$y==max(mydensity7$y)],1)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')
if (par2=='yes') {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Kernel Density Values',8,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'x-value',1,TRUE)
a<-table.element(a,'Gaussian',1,TRUE)
a<-table.element(a,'Epanechnikov',1,TRUE)
a<-table.element(a,'Rectangular',1,TRUE)
a<-table.element(a,'Triangular',1,TRUE)
a<-table.element(a,'Biweight',1,TRUE)
a<-table.element(a,'Cosine',1,TRUE)
a<-table.element(a,'Optcosine',1,TRUE)
a<-table.row.end(a)
for(i in 1:par3) {
a<-table.row.start(a)
a<-table.element(a,mydensity[i,8],1,TRUE)
for(j in 1:7) {
a<-table.element(a,mydensity[i,j],1)
}
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
}