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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Moduleskewkurt.wasp
Title produced by softwareSkewness and Kurtosis
Date of computationThu, 10 Jan 2008 05:09:16 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Jan/10/t11999672896n34uu5iqf6okei.htm/, Retrieved Wed, 15 May 2024 09:59:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7942, Retrieved Wed, 15 May 2024 09:59:37 +0000
QR Codes:

Original text written by user:ARIMA is not working-graphp error
IsPrivate?No (this computation is public)
User-defined keywordsMLE,ARIMA,skewness,percentiles,plot
Estimated Impact337

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Skewness and Kurtosis] [First Test] [2008-01-10 12:09:16] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1
7
11
6
2
27
3
8
2
4
4
2
3
6
18
12
3
6
23
24
5
9
7
9
5
7
10
18
12
27
7
16
14
7
1
5
4
2
8
2
6
23
20
3
2
3
3
4
6
25
16
9
3

Tables (Output of Computation)





Skewness and Kurtosis - Ungrouped Data
Skewness MeasureValueKurtosis MeasureValue
FISHER 3rd Cent. Mom.451.842313FISHER 4th Cent. Mom.9133.840104
FISHER beta 11.329626FISHER beta 23.185351
FISHER gamma 11.153094FISHER gamma 20.185351
FISHER gamma 1 (S.E.)0.336463FISHER gamma 2 (S.E.)0.672927
FISHER Test 13.427103FISHER Test 20.275440
FISHER Test 1 Probability0.000600FISHER Test 2 Probability0.779400
Pearson 21.164605
Yule using Quartile definition:Weighted Average at Xnp0.314286
Yule using Quartile definition:Weighted Average at X(n+1)p0.333333
Yule using Quartile definition:Empirical Distribution Function0.333333
Yule using Quartile definition:Empirical Distribution Function - Averaging0.333333
Yule using Quartile definition:Empirical Distribution Function - Interpolation0.333333
Yule using Quartile definition:Closest Observation0.333333
Yule using Quartile definition:True Basic - Statistics Graphics Toolkit0.333333
Yule using Quartile definition:MS Excel (old versions)0.333333
Skewness Measure (small sample)ValueKurtosis Measure (small sample)Value
Skewness (small sample)1.186955Kurtosis (small sample)0.326457
Skewness S.E. (small sample)0.327446Kurtosis S.E. (small sample)0.644420
TEST 1 (small sample)3.624891TEST 1 (small sample)0.506590
TEST 1 Prob. (small sample)0.000200TEST 1 Prob. (small sample)0.610000
Observations53

\begin{tabular}{lllllllll}
\hline

Skewness and Kurtosis - Ungrouped Data \tabularnewline

Skewness Measure
ValueKurtosis MeasureValue \tabularnewline FISHER 3rd Cent. Mom.451.842313 & FISHER 4th Cent. Mom.9133.840104 \tabularnewline FISHER beta 11.329626 & FISHER beta 23.185351 \tabularnewline FISHER gamma 11.153094 & FISHER gamma 20.185351 \tabularnewline FISHER gamma 1 (S.E.)0.336463 & FISHER gamma 2 (S.E.)0.672927 \tabularnewline FISHER Test 13.427103 & FISHER Test 20.275440 \tabularnewline FISHER Test 1 Probability0.000600 & FISHER Test 2 Probability0.779400 \tabularnewline Pearson 21.164605 & & \tabularnewline Yule using Quartile definition:Weighted Average at Xnp0.314286 & & \tabularnewline Yule using Quartile definition:Weighted Average at X(n+1)p0.333333 & & \tabularnewline Yule using Quartile definition:Empirical Distribution Function0.333333 & & \tabularnewline Yule using Quartile definition:Empirical Distribution Function - Averaging0.333333 & & \tabularnewline Yule using Quartile definition:Empirical Distribution Function - Interpolation0.333333 & & \tabularnewline Yule using Quartile definition:Closest Observation0.333333 & & \tabularnewline Yule using Quartile definition:True Basic - Statistics Graphics Toolkit0.333333 & & \tabularnewline Yule using Quartile definition:MS Excel (old versions)0.333333 & & \tabularnewline Skewness Measure (small sample)ValueKurtosis Measure (small sample)Value \tabularnewline Skewness (small sample)1.186955 & Kurtosis (small sample)0.326457 \tabularnewline Skewness S.E. (small sample)0.327446 & Kurtosis S.E. (small sample)0.644420 \tabularnewline TEST 1 (small sample)3.624891 & TEST 1 (small sample)0.506590 \tabularnewline TEST 1 Prob. (small sample)0.000200 & TEST 1 Prob. (small sample)0.610000 \tabularnewline Observations53 \tabularnewline & \tabularnewline & \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=7942&T=0

[TABLE]

[ROW][C]Skewness and Kurtosis - Ungrouped Data[/C][/ROW]

[ROW][C]Skewness Measure[/C]
Value[/C]Kurtosis Measure[/C]Value[/C][/ROW] [ROW][C]FISHER 3rd Cent. Mom.[/C]451.842313[/C][C]FISHER 4th Cent. Mom.[/C]9133.840104[/C][/ROW] [ROW][C]FISHER beta 1[/C]1.329626[/C][C]FISHER beta 2[/C]3.185351[/C][/ROW] [ROW][C]FISHER gamma 1[/C]1.153094[/C][C]FISHER gamma 2[/C]0.185351[/C][/ROW] [ROW][C]FISHER gamma 1 (S.E.)[/C]0.336463[/C][C]FISHER gamma 2 (S.E.)[/C]0.672927[/C][/ROW] [ROW][C]FISHER Test 1[/C]3.427103[/C][C]FISHER Test 2[/C]0.275440[/C][/ROW] [ROW][C]FISHER Test 1 Probability[/C]0.000600[/C][C]FISHER Test 2 Probability[/C]0.779400[/C][/ROW] [ROW][C]Pearson 2[/C]1.164605[/C][C][/C][C][/C][/ROW] [ROW][C]Yule using Quartile definition:Weighted Average at Xnp[/C]0.314286[/C][C][/C][C][/C][/ROW] [ROW][C]Yule using Quartile definition:Weighted Average at X(n+1)p[/C]0.333333[/C][C][/C][C][/C][/ROW] [ROW][C]Yule using Quartile definition:Empirical Distribution Function[/C]0.333333[/C][C][/C][C][/C][/ROW] [ROW][C]Yule using Quartile definition:Empirical Distribution Function - Averaging[/C]0.333333[/C][C][/C][C][/C][/ROW] [ROW][C]Yule using Quartile definition:Empirical Distribution Function - Interpolation[/C]0.333333[/C][C][/C][C][/C][/ROW] [ROW][C]Yule using Quartile definition:Closest Observation[/C]0.333333[/C][C][/C][C][/C][/ROW] [ROW][C]Yule using Quartile definition:True Basic - Statistics Graphics Toolkit[/C]0.333333[/C][C][/C][C][/C][/ROW] [ROW][C]Yule using Quartile definition:MS Excel (old versions)[/C]0.333333[/C][C][/C][C][/C][/ROW] [ROW][C]Skewness Measure (small sample)[/C]Value[/C]Kurtosis Measure (small sample)[/C]Value[/C][/ROW] [ROW][C]Skewness (small sample)[/C]1.186955[/C][C]Kurtosis (small sample)[/C]0.326457[/C][/ROW] [ROW][C]Skewness S.E. (small sample)[/C]0.327446[/C][C]Kurtosis S.E. (small sample)[/C]0.644420[/C][/ROW] [ROW][C]TEST 1 (small sample)[/C]3.624891[/C][C]TEST 1 (small sample)[/C]0.506590[/C][/ROW] [ROW][C]TEST 1 Prob. (small sample)[/C]0.000200[/C][C]TEST 1 Prob. (small sample)[/C]0.610000[/C][/ROW] [ROW][C]Observations[/C]53[/C][/ROW] [ROW][C] [/C][C] [/C][/ROW] [ROW][C] [/C][C] [/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=7942&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7942&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:

Skewness and Kurtosis - Ungrouped Data
Skewness MeasureValueKurtosis MeasureValue
FISHER 3rd Cent. Mom.451.842313FISHER 4th Cent. Mom.9133.840104
FISHER beta 11.329626FISHER beta 23.185351
FISHER gamma 11.153094FISHER gamma 20.185351
FISHER gamma 1 (S.E.)0.336463FISHER gamma 2 (S.E.)0.672927
FISHER Test 13.427103FISHER Test 20.275440
FISHER Test 1 Probability0.000600FISHER Test 2 Probability0.779400
Pearson 21.164605
Yule using Quartile definition:Weighted Average at Xnp0.314286
Yule using Quartile definition:Weighted Average at X(n+1)p0.333333
Yule using Quartile definition:Empirical Distribution Function0.333333
Yule using Quartile definition:Empirical Distribution Function - Averaging0.333333
Yule using Quartile definition:Empirical Distribution Function - Interpolation0.333333
Yule using Quartile definition:Closest Observation0.333333
Yule using Quartile definition:True Basic - Statistics Graphics Toolkit0.333333
Yule using Quartile definition:MS Excel (old versions)0.333333
Skewness Measure (small sample)ValueKurtosis Measure (small sample)Value
Skewness (small sample)1.186955Kurtosis (small sample)0.326457
Skewness S.E. (small sample)0.327446Kurtosis S.E. (small sample)0.644420
TEST 1 (small sample)3.624891TEST 1 (small sample)0.506590
TEST 1 Prob. (small sample)0.000200TEST 1 Prob. (small sample)0.610000
Observations53






Trimmed Skewness and Kurtosis (small sample) - Ungrouped Data
Skewness Measure (small sample)ValueProbabilityKurtosis Measure (small sample)ValueProbability
Trim. Skewness (0/53)1.1870000.000200Trim. Kurtosis (0/53)0.3265000.610000
Trim. Skewness (1/53)1.2142000.000200Trim. Kurtosis (1/53)0.4659000.471600
Trim. Skewness (2/53)1.2139000.000400Trim. Kurtosis (2/53)0.4881000.459200
Trim. Skewness (3/53)1.2230000.000400Trim. Kurtosis (3/53)0.6032000.373400
Trim. Skewness (4/53)1.2268000.000600Trim. Kurtosis (4/53)0.7219000.298400
Trim. Skewness (5/53)1.2200000.000800Trim. Kurtosis (5/53)0.8282000.242000
Trim. Skewness (6/53)1.1063000.002600Trim. Kurtosis (6/53)0.4391000.541800
Trim. Skewness (7/53)1.0723000.004600Trim. Kurtosis (7/53)0.4020000.582400
Trim. Skewness (8/53)1.0987000.004600Trim. Kurtosis (8/53)0.6177000.412200
Trim. Skewness (9/53)0.9964000.012000Trim. Kurtosis (9/53)0.4486000.562000
Trim. Skewness (10/53)0.9543000.019200Trim. Kurtosis (10/53)0.5948000.453200
Trim. Skewness (11/53)0.7097000.091000Trim. Kurtosis (11/53)-0.0134000.984000
Trim. Skewness (12/53)0.5179000.230200Trim. Kurtosis (12/53)-0.3903000.638400
Trim. Skewness (13/53)0.4928000.267000Trim. Kurtosis (13/53)-0.2277000.787200
Trim. Skewness (14/53)0.3399000.459200Trim. Kurtosis (14/53)-0.4537000.610000
Trim. Skewness (15/53)0.2507000.596200Trim. Kurtosis (15/53)-0.7717000.406600
Trim. Skewness (16/53)0.1026000.833600Trim. Kurtosis (16/53)-0.8137000.400800
Trim. Skewness (17/53)0.1142000.825800Trim. Kurtosis (17/53)-0.4972000.617000
Trim. Skewness (18/53)0.1206000.825800Trim. Kurtosis (18/53)-0.0993000.920400

\begin{tabular}{lllllllll}
\hline

Trimmed Skewness and Kurtosis (small sample) - Ungrouped Data \tabularnewline

Skewness Measure (small sample)
ValueProbabilityKurtosis Measure (small sample)ValueProbability \tabularnewline Trim. Skewness (0/53)1.1870000.000200 & Trim. Kurtosis (0/53)0.3265000.610000 \tabularnewline Trim. Skewness (1/53)1.2142000.000200 & Trim. Kurtosis (1/53)0.4659000.471600 \tabularnewline Trim. Skewness (2/53)1.2139000.000400 & Trim. Kurtosis (2/53)0.4881000.459200 \tabularnewline Trim. Skewness (3/53)1.2230000.000400 & Trim. Kurtosis (3/53)0.6032000.373400 \tabularnewline Trim. Skewness (4/53)1.2268000.000600 & Trim. Kurtosis (4/53)0.7219000.298400 \tabularnewline Trim. Skewness (5/53)1.2200000.000800 & Trim. Kurtosis (5/53)0.8282000.242000 \tabularnewline Trim. Skewness (6/53)1.1063000.002600 & Trim. Kurtosis (6/53)0.4391000.541800 \tabularnewline Trim. Skewness (7/53)1.0723000.004600 & Trim. Kurtosis (7/53)0.4020000.582400 \tabularnewline Trim. Skewness (8/53)1.0987000.004600 & Trim. Kurtosis (8/53)0.6177000.412200 \tabularnewline Trim. Skewness (9/53)0.9964000.012000 & Trim. Kurtosis (9/53)0.4486000.562000 \tabularnewline Trim. Skewness (10/53)0.9543000.019200 & Trim. Kurtosis (10/53)0.5948000.453200 \tabularnewline Trim. Skewness (11/53)0.7097000.091000 & Trim. Kurtosis (11/53)-0.0134000.984000 \tabularnewline Trim. Skewness (12/53)0.5179000.230200 & Trim. Kurtosis (12/53)-0.3903000.638400 \tabularnewline Trim. Skewness (13/53)0.4928000.267000 & Trim. Kurtosis (13/53)-0.2277000.787200 \tabularnewline Trim. Skewness (14/53)0.3399000.459200 & Trim. Kurtosis (14/53)-0.4537000.610000 \tabularnewline Trim. Skewness (15/53)0.2507000.596200 & Trim. Kurtosis (15/53)-0.7717000.406600 \tabularnewline Trim. Skewness (16/53)0.1026000.833600 & Trim. Kurtosis (16/53)-0.8137000.400800 \tabularnewline Trim. Skewness (17/53)0.1142000.825800 & Trim. Kurtosis (17/53)-0.4972000.617000 \tabularnewline Trim. Skewness (18/53)0.1206000.825800 & Trim. Kurtosis (18/53)-0.0993000.920400 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=7942&T=1

[TABLE]

[ROW][C]Trimmed Skewness and Kurtosis (small sample) - Ungrouped Data[/C][/ROW]

[ROW][C]Skewness Measure (small sample)[/C]
Value[/C]Probability[/C]Kurtosis Measure (small sample)[/C]Value[/C]Probability[/C][/ROW] [ROW][C]Trim. Skewness (0/53)[/C]1.187000[/C]0.000200[/C][C]Trim. Kurtosis (0/53)[/C]0.326500[/C]0.610000[/C][/ROW] [ROW][C]Trim. Skewness (1/53)[/C]1.214200[/C]0.000200[/C][C]Trim. Kurtosis (1/53)[/C]0.465900[/C]0.471600[/C][/ROW] [ROW][C]Trim. Skewness (2/53)[/C]1.213900[/C]0.000400[/C][C]Trim. Kurtosis (2/53)[/C]0.488100[/C]0.459200[/C][/ROW] [ROW][C]Trim. Skewness (3/53)[/C]1.223000[/C]0.000400[/C][C]Trim. Kurtosis (3/53)[/C]0.603200[/C]0.373400[/C][/ROW] [ROW][C]Trim. Skewness (4/53)[/C]1.226800[/C]0.000600[/C][C]Trim. Kurtosis (4/53)[/C]0.721900[/C]0.298400[/C][/ROW] [ROW][C]Trim. Skewness (5/53)[/C]1.220000[/C]0.000800[/C][C]Trim. Kurtosis (5/53)[/C]0.828200[/C]0.242000[/C][/ROW] [ROW][C]Trim. Skewness (6/53)[/C]1.106300[/C]0.002600[/C][C]Trim. Kurtosis (6/53)[/C]0.439100[/C]0.541800[/C][/ROW] [ROW][C]Trim. Skewness (7/53)[/C]1.072300[/C]0.004600[/C][C]Trim. Kurtosis (7/53)[/C]0.402000[/C]0.582400[/C][/ROW] [ROW][C]Trim. Skewness (8/53)[/C]1.098700[/C]0.004600[/C][C]Trim. Kurtosis (8/53)[/C]0.617700[/C]0.412200[/C][/ROW] [ROW][C]Trim. Skewness (9/53)[/C]0.996400[/C]0.012000[/C][C]Trim. Kurtosis (9/53)[/C]0.448600[/C]0.562000[/C][/ROW] [ROW][C]Trim. Skewness (10/53)[/C]0.954300[/C]0.019200[/C][C]Trim. Kurtosis (10/53)[/C]0.594800[/C]0.453200[/C][/ROW] [ROW][C]Trim. Skewness (11/53)[/C]0.709700[/C]0.091000[/C][C]Trim. Kurtosis (11/53)[/C]-0.013400[/C]0.984000[/C][/ROW] [ROW][C]Trim. Skewness (12/53)[/C]0.517900[/C]0.230200[/C][C]Trim. Kurtosis (12/53)[/C]-0.390300[/C]0.638400[/C][/ROW] [ROW][C]Trim. Skewness (13/53)[/C]0.492800[/C]0.267000[/C][C]Trim. Kurtosis (13/53)[/C]-0.227700[/C]0.787200[/C][/ROW] [ROW][C]Trim. Skewness (14/53)[/C]0.339900[/C]0.459200[/C][C]Trim. Kurtosis (14/53)[/C]-0.453700[/C]0.610000[/C][/ROW] [ROW][C]Trim. Skewness (15/53)[/C]0.250700[/C]0.596200[/C][C]Trim. Kurtosis (15/53)[/C]-0.771700[/C]0.406600[/C][/ROW] [ROW][C]Trim. Skewness (16/53)[/C]0.102600[/C]0.833600[/C][C]Trim. Kurtosis (16/53)[/C]-0.813700[/C]0.400800[/C][/ROW] [ROW][C]Trim. Skewness (17/53)[/C]0.114200[/C]0.825800[/C][C]Trim. Kurtosis (17/53)[/C]-0.497200[/C]0.617000[/C][/ROW] [ROW][C]Trim. Skewness (18/53)[/C]0.120600[/C]0.825800[/C][C]Trim. Kurtosis (18/53)[/C]-0.099300[/C]0.920400[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=7942&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7942&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:

Trimmed Skewness and Kurtosis (small sample) - Ungrouped Data
Skewness Measure (small sample)ValueProbabilityKurtosis Measure (small sample)ValueProbability
Trim. Skewness (0/53)1.1870000.000200Trim. Kurtosis (0/53)0.3265000.610000
Trim. Skewness (1/53)1.2142000.000200Trim. Kurtosis (1/53)0.4659000.471600
Trim. Skewness (2/53)1.2139000.000400Trim. Kurtosis (2/53)0.4881000.459200
Trim. Skewness (3/53)1.2230000.000400Trim. Kurtosis (3/53)0.6032000.373400
Trim. Skewness (4/53)1.2268000.000600Trim. Kurtosis (4/53)0.7219000.298400
Trim. Skewness (5/53)1.2200000.000800Trim. Kurtosis (5/53)0.8282000.242000
Trim. Skewness (6/53)1.1063000.002600Trim. Kurtosis (6/53)0.4391000.541800
Trim. Skewness (7/53)1.0723000.004600Trim. Kurtosis (7/53)0.4020000.582400
Trim. Skewness (8/53)1.0987000.004600Trim. Kurtosis (8/53)0.6177000.412200
Trim. Skewness (9/53)0.9964000.012000Trim. Kurtosis (9/53)0.4486000.562000
Trim. Skewness (10/53)0.9543000.019200Trim. Kurtosis (10/53)0.5948000.453200
Trim. Skewness (11/53)0.7097000.091000Trim. Kurtosis (11/53)-0.0134000.984000
Trim. Skewness (12/53)0.5179000.230200Trim. Kurtosis (12/53)-0.3903000.638400
Trim. Skewness (13/53)0.4928000.267000Trim. Kurtosis (13/53)-0.2277000.787200
Trim. Skewness (14/53)0.3399000.459200Trim. Kurtosis (14/53)-0.4537000.610000
Trim. Skewness (15/53)0.2507000.596200Trim. Kurtosis (15/53)-0.7717000.406600
Trim. Skewness (16/53)0.1026000.833600Trim. Kurtosis (16/53)-0.8137000.400800
Trim. Skewness (17/53)0.1142000.825800Trim. Kurtosis (17/53)-0.4972000.617000
Trim. Skewness (18/53)0.1206000.825800Trim. Kurtosis (18/53)-0.0993000.920400


Figures (Output of Computation)

Input Parameters & R Code

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