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Author's title

Author

*Unverified author*

R Software Module

rwasp_density.wasp

Title produced by software

Kernel Density Estimation

Date of computation

Mon, 25 Feb 2013 11:29:48 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Feb/25/t1361809812vbe5s03q35rupps.htm/, Retrieved Fri, 03 May 2024 09:39:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=206911, Retrieved Fri, 03 May 2024 09:39:10 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

145

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Univariate Data Series] [] [2013-02-25 15:21:43] [7c1d781e3a487991a6ec5bf00026d672]
- RMP     [Kernel Density Estimation] [] [2013-02-25 16:29:48] [b2d056cfd8f58045d93980b40d00d0d0] [Current]

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Dataseries X:

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Histogram

Boxplots

1.95
1.95
1.94
2.02
2.09
2.14
2.14
2.13
2.13
2.14
2.17
2.18
2.19
2.2
2.2
2.22
2.21
2.21
2.21
2.2
2.21
2.2
2.23
2.27
2.3
2.33
2.3
2.32
2.29
2.25
2.24
2.22
2.28
2.38
2.4
2.44
2.44
2.48
2.54
2.58
2.58
2.57
2.58
2.59
2.58
2.59
2.59
2.58
2.58
2.57
2.57
2.56
2.56
2.52
2.51
2.52
2.52
2.48
2.5
2.5
2.5
2.52
2.5
2.49
2.5
2.46
2.49
2.49
2.5
2.51
2.55
2.62
2.65
2.65
2.65
2.65
2.66
2.66
2.66
2.67
2.66
2.67

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206911&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206911&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206911&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Properties of Density Trace
Bandwidth	0.0747266691394119
#Observations	82

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.0747266691394119 \tabularnewline
#Observations & 82 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206911&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.0747266691394119[/C][/ROW]
[ROW][C]#Observations[/C][C]82[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206911&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206911&T=1

As an alternative you can also use a QR Code:

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

Properties of Density Trace
Bandwidth	0.0747266691394119
#Observations	82

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.54366978774085	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 2.54828176431555 & 2.2326248589208 \tabularnewline
Epanechnikov & 2.55519972917761 & 2.17725218271442 \tabularnewline
Rectangular & 2.54366978774085 & 2.2142046477775 \tabularnewline
Triangular & 2.55981170575231 & 2.18036264569899 \tabularnewline
Biweight & 2.55289374089026 & 2.18965280806873 \tabularnewline
Cosine & 2.55289374089026 & 2.19427604668676 \tabularnewline
Optcosine & 2.55289374089026 & 2.17900167937722 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206911&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]2.54828176431555[/C][C]2.2326248589208[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]2.55519972917761[/C][C]2.17725218271442[/C][/ROW]
[ROW][C]Rectangular[/C][C]2.54366978774085[/C][C]2.2142046477775[/C][/ROW]
[ROW][C]Triangular[/C][C]2.55981170575231[/C][C]2.18036264569899[/C][/ROW]
[ROW][C]Biweight[/C][C]2.55289374089026[/C][C]2.18965280806873[/C][/ROW]
[ROW][C]Cosine[/C][C]2.55289374089026[/C][C]2.19427604668676[/C][/ROW]
[ROW][C]Optcosine[/C][C]2.55289374089026[/C][C]2.17900167937722[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206911&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206911&T=2

As an alternative you can also use a QR Code:

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

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.54366978774085	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.5459757760282	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 2.54828176431555 & 2.2326248589208 \tabularnewline
Epanechnikov & 2.55519972917761 & 2.17725218271442 \tabularnewline
Rectangular & 2.5459757760282 & 2.2142046477775 \tabularnewline
Triangular & 2.55981170575231 & 2.18036264569899 \tabularnewline
Biweight & 2.55289374089026 & 2.18965280806873 \tabularnewline
Cosine & 2.55289374089026 & 2.19427604668676 \tabularnewline
Optcosine & 2.55289374089026 & 2.17900167937722 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206911&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]2.54828176431555[/C][C]2.2326248589208[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]2.55519972917761[/C][C]2.17725218271442[/C][/ROW]
[ROW][C]Rectangular[/C][C]2.5459757760282[/C][C]2.2142046477775[/C][/ROW]
[ROW][C]Triangular[/C][C]2.55981170575231[/C][C]2.18036264569899[/C][/ROW]
[ROW][C]Biweight[/C][C]2.55289374089026[/C][C]2.18965280806873[/C][/ROW]
[ROW][C]Cosine[/C][C]2.55289374089026[/C][C]2.19427604668676[/C][/ROW]
[ROW][C]Optcosine[/C][C]2.55289374089026[/C][C]2.17900167937722[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206911&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206911&T=3

As an alternative you can also use a QR Code:

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

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.5459757760282	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.54828176431555	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 2.54828176431555 & 2.2326248589208 \tabularnewline
Epanechnikov & 2.55519972917761 & 2.17725218271442 \tabularnewline
Rectangular & 2.54828176431555 & 2.2142046477775 \tabularnewline
Triangular & 2.55981170575231 & 2.18036264569899 \tabularnewline
Biweight & 2.55289374089026 & 2.18965280806873 \tabularnewline
Cosine & 2.55289374089026 & 2.19427604668676 \tabularnewline
Optcosine & 2.55289374089026 & 2.17900167937722 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206911&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]2.54828176431555[/C][C]2.2326248589208[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]2.55519972917761[/C][C]2.17725218271442[/C][/ROW]
[ROW][C]Rectangular[/C][C]2.54828176431555[/C][C]2.2142046477775[/C][/ROW]
[ROW][C]Triangular[/C][C]2.55981170575231[/C][C]2.18036264569899[/C][/ROW]
[ROW][C]Biweight[/C][C]2.55289374089026[/C][C]2.18965280806873[/C][/ROW]
[ROW][C]Cosine[/C][C]2.55289374089026[/C][C]2.19427604668676[/C][/ROW]
[ROW][C]Optcosine[/C][C]2.55289374089026[/C][C]2.17900167937722[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206911&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206911&T=4

As an alternative you can also use a QR Code:

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

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.54828176431555	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.5505877526029	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 2.54828176431555 & 2.2326248589208 \tabularnewline
Epanechnikov & 2.55519972917761 & 2.17725218271442 \tabularnewline
Rectangular & 2.5505877526029 & 2.2142046477775 \tabularnewline
Triangular & 2.55981170575231 & 2.18036264569899 \tabularnewline
Biweight & 2.55289374089026 & 2.18965280806873 \tabularnewline
Cosine & 2.55289374089026 & 2.19427604668676 \tabularnewline
Optcosine & 2.55289374089026 & 2.17900167937722 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206911&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]2.54828176431555[/C][C]2.2326248589208[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]2.55519972917761[/C][C]2.17725218271442[/C][/ROW]
[ROW][C]Rectangular[/C][C]2.5505877526029[/C][C]2.2142046477775[/C][/ROW]
[ROW][C]Triangular[/C][C]2.55981170575231[/C][C]2.18036264569899[/C][/ROW]
[ROW][C]Biweight[/C][C]2.55289374089026[/C][C]2.18965280806873[/C][/ROW]
[ROW][C]Cosine[/C][C]2.55289374089026[/C][C]2.19427604668676[/C][/ROW]
[ROW][C]Optcosine[/C][C]2.55289374089026[/C][C]2.17900167937722[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206911&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206911&T=5

As an alternative you can also use a QR Code:

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

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.5505877526029	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.55289374089026	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 2.54828176431555 & 2.2326248589208 \tabularnewline
Epanechnikov & 2.55519972917761 & 2.17725218271442 \tabularnewline
Rectangular & 2.55289374089026 & 2.2142046477775 \tabularnewline
Triangular & 2.55981170575231 & 2.18036264569899 \tabularnewline
Biweight & 2.55289374089026 & 2.18965280806873 \tabularnewline
Cosine & 2.55289374089026 & 2.19427604668676 \tabularnewline
Optcosine & 2.55289374089026 & 2.17900167937722 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206911&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]2.54828176431555[/C][C]2.2326248589208[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]2.55519972917761[/C][C]2.17725218271442[/C][/ROW]
[ROW][C]Rectangular[/C][C]2.55289374089026[/C][C]2.2142046477775[/C][/ROW]
[ROW][C]Triangular[/C][C]2.55981170575231[/C][C]2.18036264569899[/C][/ROW]
[ROW][C]Biweight[/C][C]2.55289374089026[/C][C]2.18965280806873[/C][/ROW]
[ROW][C]Cosine[/C][C]2.55289374089026[/C][C]2.19427604668676[/C][/ROW]
[ROW][C]Optcosine[/C][C]2.55289374089026[/C][C]2.17900167937722[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206911&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206911&T=6

As an alternative you can also use a QR Code:

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

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.55289374089026	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.55519972917761	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 2.54828176431555 & 2.2326248589208 \tabularnewline
Epanechnikov & 2.55519972917761 & 2.17725218271442 \tabularnewline
Rectangular & 2.55519972917761 & 2.2142046477775 \tabularnewline
Triangular & 2.55981170575231 & 2.18036264569899 \tabularnewline
Biweight & 2.55289374089026 & 2.18965280806873 \tabularnewline
Cosine & 2.55289374089026 & 2.19427604668676 \tabularnewline
Optcosine & 2.55289374089026 & 2.17900167937722 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206911&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]2.54828176431555[/C][C]2.2326248589208[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]2.55519972917761[/C][C]2.17725218271442[/C][/ROW]
[ROW][C]Rectangular[/C][C]2.55519972917761[/C][C]2.2142046477775[/C][/ROW]
[ROW][C]Triangular[/C][C]2.55981170575231[/C][C]2.18036264569899[/C][/ROW]
[ROW][C]Biweight[/C][C]2.55289374089026[/C][C]2.18965280806873[/C][/ROW]
[ROW][C]Cosine[/C][C]2.55289374089026[/C][C]2.19427604668676[/C][/ROW]
[ROW][C]Optcosine[/C][C]2.55289374089026[/C][C]2.17900167937722[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206911&T=7

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206911&T=7

As an alternative you can also use a QR Code:

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

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.55519972917761	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.55750571746496	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 2.54828176431555 & 2.2326248589208 \tabularnewline
Epanechnikov & 2.55519972917761 & 2.17725218271442 \tabularnewline
Rectangular & 2.55750571746496 & 2.2142046477775 \tabularnewline
Triangular & 2.55981170575231 & 2.18036264569899 \tabularnewline
Biweight & 2.55289374089026 & 2.18965280806873 \tabularnewline
Cosine & 2.55289374089026 & 2.19427604668676 \tabularnewline
Optcosine & 2.55289374089026 & 2.17900167937722 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206911&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]2.54828176431555[/C][C]2.2326248589208[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]2.55519972917761[/C][C]2.17725218271442[/C][/ROW]
[ROW][C]Rectangular[/C][C]2.55750571746496[/C][C]2.2142046477775[/C][/ROW]
[ROW][C]Triangular[/C][C]2.55981170575231[/C][C]2.18036264569899[/C][/ROW]
[ROW][C]Biweight[/C][C]2.55289374089026[/C][C]2.18965280806873[/C][/ROW]
[ROW][C]Cosine[/C][C]2.55289374089026[/C][C]2.19427604668676[/C][/ROW]
[ROW][C]Optcosine[/C][C]2.55289374089026[/C][C]2.17900167937722[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206911&T=8

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206911&T=8

As an alternative you can also use a QR Code:

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

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.55750571746496	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.55981170575231	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 2.54828176431555 & 2.2326248589208 \tabularnewline
Epanechnikov & 2.55519972917761 & 2.17725218271442 \tabularnewline
Rectangular & 2.55981170575231 & 2.2142046477775 \tabularnewline
Triangular & 2.55981170575231 & 2.18036264569899 \tabularnewline
Biweight & 2.55289374089026 & 2.18965280806873 \tabularnewline
Cosine & 2.55289374089026 & 2.19427604668676 \tabularnewline
Optcosine & 2.55289374089026 & 2.17900167937722 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206911&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]2.54828176431555[/C][C]2.2326248589208[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]2.55519972917761[/C][C]2.17725218271442[/C][/ROW]
[ROW][C]Rectangular[/C][C]2.55981170575231[/C][C]2.2142046477775[/C][/ROW]
[ROW][C]Triangular[/C][C]2.55981170575231[/C][C]2.18036264569899[/C][/ROW]
[ROW][C]Biweight[/C][C]2.55289374089026[/C][C]2.18965280806873[/C][/ROW]
[ROW][C]Cosine[/C][C]2.55289374089026[/C][C]2.19427604668676[/C][/ROW]
[ROW][C]Optcosine[/C][C]2.55289374089026[/C][C]2.17900167937722[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206911&T=9

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206911&T=9

As an alternative you can also use a QR Code:

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

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.55981170575231	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.56211769403966	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 2.54828176431555 & 2.2326248589208 \tabularnewline
Epanechnikov & 2.55519972917761 & 2.17725218271442 \tabularnewline
Rectangular & 2.56211769403966 & 2.2142046477775 \tabularnewline
Triangular & 2.55981170575231 & 2.18036264569899 \tabularnewline
Biweight & 2.55289374089026 & 2.18965280806873 \tabularnewline
Cosine & 2.55289374089026 & 2.19427604668676 \tabularnewline
Optcosine & 2.55289374089026 & 2.17900167937722 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206911&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]2.54828176431555[/C][C]2.2326248589208[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]2.55519972917761[/C][C]2.17725218271442[/C][/ROW]
[ROW][C]Rectangular[/C][C]2.56211769403966[/C][C]2.2142046477775[/C][/ROW]
[ROW][C]Triangular[/C][C]2.55981170575231[/C][C]2.18036264569899[/C][/ROW]
[ROW][C]Biweight[/C][C]2.55289374089026[/C][C]2.18965280806873[/C][/ROW]
[ROW][C]Cosine[/C][C]2.55289374089026[/C][C]2.19427604668676[/C][/ROW]
[ROW][C]Optcosine[/C][C]2.55289374089026[/C][C]2.17900167937722[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206911&T=10

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206911&T=10

As an alternative you can also use a QR Code:

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

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.56211769403966	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.56442368232701	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 2.54828176431555 & 2.2326248589208 \tabularnewline
Epanechnikov & 2.55519972917761 & 2.17725218271442 \tabularnewline
Rectangular & 2.56442368232701 & 2.2142046477775 \tabularnewline
Triangular & 2.55981170575231 & 2.18036264569899 \tabularnewline
Biweight & 2.55289374089026 & 2.18965280806873 \tabularnewline
Cosine & 2.55289374089026 & 2.19427604668676 \tabularnewline
Optcosine & 2.55289374089026 & 2.17900167937722 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206911&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]2.54828176431555[/C][C]2.2326248589208[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]2.55519972917761[/C][C]2.17725218271442[/C][/ROW]
[ROW][C]Rectangular[/C][C]2.56442368232701[/C][C]2.2142046477775[/C][/ROW]
[ROW][C]Triangular[/C][C]2.55981170575231[/C][C]2.18036264569899[/C][/ROW]
[ROW][C]Biweight[/C][C]2.55289374089026[/C][C]2.18965280806873[/C][/ROW]
[ROW][C]Cosine[/C][C]2.55289374089026[/C][C]2.19427604668676[/C][/ROW]
[ROW][C]Optcosine[/C][C]2.55289374089026[/C][C]2.17900167937722[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206911&T=11

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206911&T=11

As an alternative you can also use a QR Code:

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

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.56442368232701	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.56672967061436	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 2.54828176431555 & 2.2326248589208 \tabularnewline
Epanechnikov & 2.55519972917761 & 2.17725218271442 \tabularnewline
Rectangular & 2.56672967061436 & 2.2142046477775 \tabularnewline
Triangular & 2.55981170575231 & 2.18036264569899 \tabularnewline
Biweight & 2.55289374089026 & 2.18965280806873 \tabularnewline
Cosine & 2.55289374089026 & 2.19427604668676 \tabularnewline
Optcosine & 2.55289374089026 & 2.17900167937722 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206911&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]2.54828176431555[/C][C]2.2326248589208[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]2.55519972917761[/C][C]2.17725218271442[/C][/ROW]
[ROW][C]Rectangular[/C][C]2.56672967061436[/C][C]2.2142046477775[/C][/ROW]
[ROW][C]Triangular[/C][C]2.55981170575231[/C][C]2.18036264569899[/C][/ROW]
[ROW][C]Biweight[/C][C]2.55289374089026[/C][C]2.18965280806873[/C][/ROW]
[ROW][C]Cosine[/C][C]2.55289374089026[/C][C]2.19427604668676[/C][/ROW]
[ROW][C]Optcosine[/C][C]2.55289374089026[/C][C]2.17900167937722[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206911&T=12

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206911&T=12

As an alternative you can also use a QR Code:

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

Maximum Density Values
Kernel	x-value	max. density
Gaussian	2.54828176431555	2.2326248589208
Epanechnikov	2.55519972917761	2.17725218271442
Rectangular	2.56672967061436	2.2142046477775
Triangular	2.55981170575231	2.18036264569899
Biweight	2.55289374089026	2.18965280806873
Cosine	2.55289374089026	2.19427604668676
Optcosine	2.55289374089026	2.17900167937722

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Figure 5

PNG link

Postscript link

PDF link

Figure 6

PNG link

Postscript link

PDF link

Figure 7

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 0 ; par2 = no ; par3 = 512 ;

Parameters (R input):

par1 = 0 ; par2 = no ; par3 = 512 ;

R code (references can be found in the software module):

par3 <- '512'
par2 <- 'no'
par1 <- '0'
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')
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code