skewness from moments2 into data

[Jinsuk Yang]

Hi,

I am trying to use "moments2" and use the skewness, kurtosis, and SD as my data.
The following is the example of my data (it is just a small part of my complete data). My full data has 24(IDs)*20(years)*12(months)*30(Days)

----------------------- copy starting from the next line -----------------------

* Example generated by -dataex-. To install: ssc install dataex
clear
input float edate byte mnth int yr str5 id double rate
15706 1 2003 "A"        .
15707 1 2003 "A" 1.776182
15708 1 2003 "A" 1.774442
15709 1 2003 "A"        .
15710 1 2003 "A"        .
15711 1 2003 "A"  1.74304
15712 1 2003 "A" 1.741966
15713 1 2003 "A" 1.747326
15714 1 2003 "A" 1.729514
15715 1 2003 "A" 1.723984
15716 1 2003 "A"        .
15717 1 2003 "A"        .
15718 1 2003 "A" 1.716656
15719 1 2003 "A" 1.712678
15720 1 2003 "A" 1.712331
15721 1 2003 "A" 1.706551
15722 1 2003 "A"  1.69095
15723 1 2003 "A"        .
15724 1 2003 "A"        .
15725 1 2003 "A" 1.694922
15726 1 2003 "A" 1.702244
15727 1 2003 "A" 1.704889
15728 1 2003 "A" 1.690992
15729 1 2003 "A" 1.690931
15730 1 2003 "A"        .
15731 1 2003 "A"        .
15732 1 2003 "A" 1.687029
15733 1 2003 "A" 1.699389
15734 1 2003 "A" 1.692584
15735 1 2003 "A" 1.701247
15736 1 2003 "A" 1.700906
15737 2 2003 "A"        .
15738 2 2003 "A"        .
15739 2 2003 "A" 1.715444
15740 2 2003 "A" 1.696636
15741 2 2003 "A" 1.688818
15742 2 2003 "A" 1.693517
15743 2 2003 "A" 1.694411
15744 2 2003 "A"        .
15745 2 2003 "A"        .
15746 2 2003 "A" 1.686714
15747 2 2003 "A" 1.698113
15748 2 2003 "A" 1.689498
15749 2 2003 "A" 1.693252
15750 2 2003 "A" 1.684981
15751 2 2003 "A"        .
15752 2 2003 "A"        .
15753 2 2003 "A" 1.696342
15754 2 2003 "A" 1.693112
15755 2 2003 "A" 1.687039
15756 2 2003 "A" 1.677878
15757 2 2003 "A" 1.668297
15758 2 2003 "A"        .
15759 2 2003 "A"        .
15760 2 2003 "A" 1.661226
15761 2 2003 "A" 1.651105
15762 2 2003 "A" 1.651353
15763 2 2003 "A" 1.644982
15764 2 2003 "A" 1.652384
15706 1 2003 "B"        .
15707 1 2003 "B"  7.11009
15708 1 2003 "B" 7.148095
15709 1 2003 "B"        .
15710 1 2003 "B"        .
15711 1 2003 "B" 7.082285
15712 1 2003 "B" 7.125659
15713 1 2003 "B" 7.159198
15714 1 2003 "B" 7.071191
15715 1 2003 "B" 7.073217
15716 1 2003 "B"        .
15717 1 2003 "B"        .
15718 1 2003 "B" 7.042848
15719 1 2003 "B" 7.024203
15720 1 2003 "B" 7.059662
15721 1 2003 "B" 7.035498
15722 1 2003 "B" 6.979253
15723 1 2003 "B"        .
15724 1 2003 "B"        .
15725 1 2003 "B" 6.977377
15726 1 2003 "B" 6.977659
15727 1 2003 "B" 6.937955
15728 1 2003 "B" 6.913173
15729 1 2003 "B" 6.897533
15730 1 2003 "B"        .
15731 1 2003 "B"        .
15732 1 2003 "B" 6.841766
15733 1 2003 "B" 6.881199
15734 1 2003 "B" 6.840817
15735 1 2003 "B" 6.917008
15736 1 2003 "B"  6.87574
15737 2 2003 "B"        .
15738 2 2003 "B"        .
15739 2 2003 "B" 6.932333
15740 2 2003 "B" 6.870911
15741 2 2003 "B"  6.81549
15742 2 2003 "B"  6.87441
15743 2 2003 "B" 6.887571
15744 2 2003 "B"        .
15745 2 2003 "B"        .
15746 2 2003 "B" 6.876665
end
format %d edate

------------------ copy up to and including the previous line ------------------


To find skewness by id, mnth, and yr, I used the following command: "bys id mnth yr: moments2 rate"

-> id = A, mnth = 1, yr = 2003
----------------------------------------------------------
n = 22 | mean SD skewness kurtosis
----------+-----------------------------------------------
exchrate | 1.715 0.026 1.155 0.519
----------------------------------------------------------
-> id = A, mnth = 2, yr = 2003
----------------------------------------------------------
n = 20 | mean SD skewness kurtosis
----------+-----------------------------------------------
exchrate | 1.681 0.020 -0.591 -0.621
----------------------------------------------------------
-> id = B, mnth = 1, yr = 2003
---------------------------------------------------------
n = 22 | mean SD skewness kurtosis
----------+-----------------------------------------------
exchrate | 6.999 0.100 -0.057 -1.214
----------------------------------------------------------
-> id = B, mnth = 2, yr = 2003
----------------------------------------------------------
n = 20 | mean SD skewness kurtosis
----------+-----------------------------------------------
exchrate | 6.899 0.033 -0.652 0.260
----------------------------------------------------------

What I want to do is to use the skewness as data. I would like to create a data set like the following:


edate mnth yr id rate skewness SD kurtosis
.
.
15712 1 2003 "A" 1.741966 1.155 0.026 0.519
15713 1 2003 "A" 1.747326 1.155 0.026 0.519
.
.
15740 2 2003 "A" 1.696636 -0.591 0.020 -0.621
15741 2 2003 "A" 1.688818 -0.591 0.020 -0.621
.
.
15707 1 2003 "B" 7.110090 -0.057 0.100 -1.214
15708 1 2003 "B" 7.148095 -0.057 0.100 -1.214
.
.
15739 2 2003 "B" 6.932333 -0.652 0.033 0.260
15740 2 2003 "B" 6.870911 -0.652 0.033 0.260

Is there any way I can do it in more efficient way?
I always appreciate your help and time.

[Nick Cox]

What is moments2? https://www.statalist.org/forums/help#stata applies. You're asked to explain the provenance of community-contributed commands you refer to.

[Jinsuk Yang]

I apologize for the lack of explanation and hope the following information is enough.

I am using moments2 from SSC in STATA 14.2.

package moments2 from http://fmwww.bc.edu/RePEc/bocode/m
TITLE
'MOMENTS2': module to compute skewness and kurtosis measures

DESCRIPTION/AUTHOR(S)

moments2 calculates various measures of skewness and kurtosis.
Based on Nicholas Cox's moments, it also calculates mean and
standard deviation for a list of variables. moments2 differs
from moments only in allowing different measures of skewness and
kurtosis and making the measures used in SAS and SPSS the
default.

KW: moments
KW: kurtosis
KW: skewness
KW: summary statistics

Requires: Stata version 8.2

Distribution-Date: 20130119

Author: Dirk Enzmann, University of Hamburg
Support: email [email protected]

Thanks a lot.

[Nick Cox]

Thanks for the detail. moments2 has documented capability to save results as a matrix, whence svmat in principle could be used.

But I have to say that calling it up repeatedly as you do seems very roundabout and isn't compatible with saving as matrices.

I'd use rangestat (SSC) as you aren't using any of the extra definitions supported by moments2.

. sysuse auto, clear
(1978 Automobile Data)

. rangestat (mean) mpg (sd) mpg (skewness) mpg (kurtosis) mpg, int(rep78 0 0)

. tabdisp rep78, c(mpg_*)

------------------------------------------------------------------------------
Repair    |
Record    |
1978      |     mean of mpg        sd of mpg  skewness of mpg  kurtosis of mpg
----------+-------------------------------------------------------------------
        1 |              21        4.2426407                0                1
        2 |          19.125        3.7583241        .22412358        1.6421611
        3 |       19.433333        4.1413252        .35552274         3.081041
        4 |       21.666667        4.9348699       -.13262994        1.9664636
        5 |       27.363636        8.7323849       -.01518308        1.5515859
        . |                                                                   
------------------------------------------------------------------------------

At worst you need to define an interval variable:

egen interval = group(id  mnth yr), label

[Jinsuk Yang]

Thanks for the advice. And, it works perfectly.
But, I have one more question. The skewness and kurtosis of mpg from rangestat and those from moments2 are different. And, the moments2 provides the same skewness and kurtosis generated by Excel program.

. sysuse auto, clear
(1978 Automobile Data)

. rangestat (mean) mpg (sd) mpg (skewness) mpg (kurtosis) mpg, int(rep78 0 0)

. tabdisp rep78, c(mpg_*)

------------------------------------------------------------------------------
Repair    |
Record    |
1978      |     mean of mpg        sd of mpg  skewness of mpg  kurtosis of mpg
----------+-------------------------------------------------------------------
        1 |              21        4.2426407                0                1
        2 |          19.125        3.7583241        .22412358        1.6421611
        3 |       19.433333        4.1413252        .35552274         3.081041
        4 |       21.666667        4.9348699       -.13262994        1.9664636
        5 |       27.363636        8.7323849       -.01518308        1.5515859
        . |                                                                  
------------------------------------------------------------------------------

 bys rep78: moments2 mpg

-------------------------------------------------------------------------------------------------------------------------------
-> rep78 = 1

--------------------------------------------------------------
        n = 2 |       mean          SD    skewness    kurtosis
--------------+-----------------------------------------------
Mileage (mpg) |     21.000       4.243                        
--------------------------------------------------------------

-------------------------------------------------------------------------------------------------------------------------------
-> rep78 = 2

--------------------------------------------------------------
        n = 8 |       mean          SD    skewness    kurtosis
--------------+-----------------------------------------------
Mileage (mpg) |     19.125       3.758       0.280      -1.451
--------------------------------------------------------------

-------------------------------------------------------------------------------------------------------------------------------
-> rep78 = 3

--------------------------------------------------------------
       n = 30 |       mean          SD    skewness    kurtosis
--------------+-----------------------------------------------
Mileage (mpg) |     19.433       4.141       0.375       0.327
--------------------------------------------------------------

-------------------------------------------------------------------------------------------------------------------------------
-> rep78 = 4

--------------------------------------------------------------
       n = 18 |       mean          SD    skewness    kurtosis
--------------+-----------------------------------------------
Mileage (mpg) |     21.667       4.935      -0.145      -0.966
--------------------------------------------------------------

-------------------------------------------------------------------------------------------------------------------------------
-> rep78 = 5

--------------------------------------------------------------
       n = 11 |       mean          SD    skewness    kurtosis
--------------+-----------------------------------------------
Mileage (mpg) |     27.364       8.732      -0.018      -1.581
--------------------------------------------------------------

-------------------------------------------------------------------------------------------------------------------------------

From Excel:

rep78	mean	SD	skewness	kurtosis
1	21	4.2426
2	19.125	3.758324095	0.279531215	-1.451461687
3	19.43333333	4.141325236	0.374514797	0.326528863
4	21.66666667	4.934869925	-0.145004776	-0.965967701
5	27.3636363	8.732384866	-0.017693498	-1.580690186

Does this comparison imply that moments2 is better?
If so, I must use moments2 and use the skewness and kurtosis as data. Any advice will be greatly appreciated.

Thanks a lot.

[Nick Cox]

If you want to take MS Excel as a reference standard, then so be it. Really, not my choice and not my recommendation.

There are different formulas for skewness and kurtosis, hinging on

1. correction factors to make estimates more nearly unbiased that bite most in small samples

2. whether 3 is subtracted in reporting kurtosis (which summarize doesn't do and rangestat doesn't do but moments2 and Excel apparently do).

The help for rangestat documents its choices with a reference to

https://www.stata-journal.com/sjpdf....iclenum=st0204

which I am partial to as a survey of the main issues.

As far as #1 is concerned expecting good estimates of skewness and kurtosis from small samples is extreme statistical optimism, given their dependence on third and fourth powers of deviations. I chose the auto data as a convenient mutual sandbox but the reservation remains.