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Paper - Skewness en kurtosis

*The author of this computation has been verified*

R Software Module: /skewkurt.wasp (opens new window with default values)

Title produced by software: Skewness and Kurtosis

Date of computation: Tue, 30 Nov 2010 21:51:54 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/30/t1291153971blfov1scg06z8mx.htm/, Retrieved Tue, 30 Nov 2010 22:52:51 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/30/t1291153971blfov1scg06z8mx.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

807 444 412 428 315 168 263 267 228 129 104 122 393 190 280 63 102 265 234 277 73 67 103 290 83 56 236 73 34 139 26 70 40 42 12 211 74 80 83 131 203 56 89 88 39 25 49 149 58 41 90 136 97 63 114 77 6 47 51 85 43 32 25 77 54 251 15 44 73 85 49 38 35 9 34 20 29 11 52 13 29 66 33 15 15 68 100 13 45 14 36 40 68 29 43 30 9 22 19 9

Output produced by software:

Skewness and Kurtosis - Ungrouped Data
Skewness Measure	Value	Kurtosis Measure	Value
FISHER 3rd Cent. Mom.	4.93211e+6	FISHER 4th Cent. Mom.	2.89524e+9
FISHER beta 1	7.278319	FISHER beta 2	12.951722
FISHER gamma 1	2.697836	FISHER gamma 2	9.951722
FISHER gamma 1 (S.E.)	0.244949	FISHER gamma 2 (S.E.)	0.489898
FISHER Test 1	11.013869	FISHER Test 2	20.313868
FISHER Test 1 Probability	0.000000	FISHER Test 2 Probability	0.000000
Pearson 2	0.981110
Yule using Quartile definition: Weighted Average at Xnp	0.261364
Yule using Quartile definition: Weighted Average at X(n+1)p	0.302949
Yule using Quartile definition: Empirical Distribution Function	0.261364
Yule using Quartile definition: Empirical Distribution Function - Averaging	0.289617
Yule using Quartile definition: Empirical Distribution Function - Interpolation	0.275766
Yule using Quartile definition: Closest Observation	0.261364
Yule using Quartile definition: True Basic - Statistics Graphics Toolkit	0.275766
Yule using Quartile definition: MS Excel (old versions)	0.315789
Skewness Measure (small sample)	Value	Kurtosis Measure (small sample)	Value
Skewness (small sample)	2.739095	Kurtosis (small sample)	10.530325
Skewness S.E. (small sample)	0.241380	Kurtosis S.E. (small sample)	0.478331
TEST 1 (small sample)	11.347656	TEST 1 (small sample)	22.014719
TEST 1 Prob. (small sample)	0.000000	TEST 1 Prob. (small sample)	0.000000
Observations	100

Trimmed Skewness and Kurtosis (small sample) - Ungrouped Data
Skewness Measure (small sample)	Value	Probability	Kurtosis Measure (small sample)	Value	Probability
Trim. Skewness (0/100)	2.739100	0.000000	Trim. Kurtosis (0/100)	10.530300	0.000000
Trim. Skewness (1/100)	1.722500	0.000000	Trim. Kurtosis (1/100)	2.454900	0.000000
Trim. Skewness (2/100)	1.686600	0.000000	Trim. Kurtosis (2/100)	2.356300	0.000000
Trim. Skewness (3/100)	1.627900	0.000000	Trim. Kurtosis (3/100)	2.127000	0.000000
Trim. Skewness (4/100)	1.534900	0.000000	Trim. Kurtosis (4/100)	1.679000	0.000800
Trim. Skewness (5/100)	1.399600	0.000000	Trim. Kurtosis (5/100)	0.935700	0.061400
Trim. Skewness (6/100)	1.396400	0.000000	Trim. Kurtosis (6/100)	0.932000	0.065800
Trim. Skewness (7/100)	1.417400	0.000000	Trim. Kurtosis (7/100)	1.047400	0.041400
Trim. Skewness (8/100)	1.444700	0.000000	Trim. Kurtosis (8/100)	1.198300	0.020800
Trim. Skewness (9/100)	1.466600	0.000000	Trim. Kurtosis (9/100)	1.338300	0.010800
Trim. Skewness (10/100)	1.494000	0.000000	Trim. Kurtosis (10/100)	1.519100	0.004200
Trim. Skewness (11/100)	1.511200	0.000000	Trim. Kurtosis (11/100)	1.669700	0.001800
Trim. Skewness (12/100)	1.508100	0.000000	Trim. Kurtosis (12/100)	1.733500	0.001400
Trim. Skewness (13/100)	1.500800	0.000000	Trim. Kurtosis (13/100)	1.809500	0.001000
Trim. Skewness (14/100)	1.506300	0.000000	Trim. Kurtosis (14/100)	1.979500	0.000400
Trim. Skewness (15/100)	1.471400	0.000000	Trim. Kurtosis (15/100)	1.994400	0.000400
Trim. Skewness (16/100)	1.380500	0.000000	Trim. Kurtosis (16/100)	1.766100	0.002000
Trim. Skewness (17/100)	1.292900	0.000000	Trim. Kurtosis (17/100)	1.585100	0.006400
Trim. Skewness (18/100)	1.138500	0.000200	Trim. Kurtosis (18/100)	1.088800	0.064400
Trim. Skewness (19/100)	0.929800	0.002200	Trim. Kurtosis (19/100)	0.335400	0.575400
Trim. Skewness (20/100)	0.789400	0.010400	Trim. Kurtosis (20/100)	-0.104300	0.857200
Trim. Skewness (21/100)	0.728900	0.019800	Trim. Kurtosis (21/100)	-0.227000	0.711400
Trim. Skewness (22/100)	0.695000	0.029200	Trim. Kurtosis (22/100)	-0.248100	0.689200
Trim. Skewness (23/100)	0.637900	0.048800	Trim. Kurtosis (23/100)	-0.324400	0.610000
Trim. Skewness (24/100)	0.572200	0.081800	Trim. Kurtosis (24/100)	-0.415800	0.522200
Trim. Skewness (25/100)	0.458200	0.170600	Trim. Kurtosis (25/100)	-0.662900	0.312400
Trim. Skewness (26/100)	0.351200	0.303000	Trim. Kurtosis (26/100)	-0.903500	0.180200
Trim. Skewness (27/100)	0.273800	0.429600	Trim. Kurtosis (27/100)	-1.058400	0.123600
Trim. Skewness (28/100)	0.260900	0.465400	Trim. Kurtosis (28/100)	-1.048700	0.133600
Trim. Skewness (29/100)	0.228600	0.528600	Trim. Kurtosis (29/100)	-1.056400	0.138800
Trim. Skewness (30/100)	0.173300	0.638400	Trim. Kurtosis (30/100)	-1.105500	0.131000
Trim. Skewness (31/100)	0.097400	0.794800	Trim. Kurtosis (31/100)	-1.191500	0.111800
Trim. Skewness (32/100)	0.020000	0.952200	Trim. Kurtosis (32/100)	-1.297800	0.091000
Trim. Skewness (33/100)	0.003500	0.992000	Trim. Kurtosis (33/100)	-1.279400	0.103200

Charts produced by software:

Parameters (Session):

Parameters (R input):

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

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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