Generating kurtosis as a new variable

[Esther Chau]

Hello all,

Thank you very much in advance for your help.

I am trying to generate kurtosis as a new variable. In my dataset, groups are identified by "mov_id," year is identified by k_round, and the value for each year is k_year_sum.
You see there is a -1 in the year (i.e., k_round) because there are cases (i.e., k_year_sum) happened before a release of the product.

I need to calculate kurtosis for each group because I want to compare the pattern across groups.

Question 1: I tried using two codes (with different "intervals") to generate kurtosis as a new variable and the values are different. (I am sorry it's stupid but) why is that? Which one should I use?

The codes:
(a)

rangestat (kurtosis) k_year_sum, interval(k_round -1 8) by(mov_id)

or (b)

rangestat (kurtosis) k_year_sum, interval(count_year 1 10) by(mov_id)

Question 2: With both of these codes, the result generated in each row is different and I don't understand why. I thought I could have just one value for the entire group id (i.e., mov_id).

Question 3: I also tried using the "sum, detail" command to see the kurtosis value, and yet the value is once again different.

The code I used:

bysort mov_id: sum k_year_sum, detail

Part of my data looks like this:

* Example generated by -dataex-. For more info, type help dataex
clear
input float(mov_id k_round count_year k_year_sum)
517 -1  1  92
517  0  2 133
517  1  3   6
517  2  4   8
517  3  5   1
517  4  6   4
517  5  7   3
517  6  8   5
517  7  9   7
517  8 10   6
521 -1  1  69
521  0  2 150
521  1  3   6
521  2  4   1
521  3  5   4
521  4  6   2
521  5  7   6
521  6  8   8
521  7  9  13
521  8 10   3
729 -1  1  59
729  0  2 157
729  1  3   9
729  2  4   6
729  3  5  44
729  4  6   1
729  5  7   6
729  6  8  20
729  7  9   8
729  8 10   7
757 -1  1 192
757  0  2 114
757  1  3   4
757  2  4   6
757  3  5  19
757  4  6   1
757  5  7   9
757  6  8  12
757  7  9   8
757  8 10   2
end

Thank you very much for helping. Really appreciate it.

[Nick Cox]

In the option of rangestat (from SSC, as you are asked to explain)

interval(varname #1 #2)

#1 and #2 are offsets, not literal values. So you are asking tor the interval

[current value of varname MINUS #1, current value of varname PLUS #2]

which may well differ according to varname.

I think you need just

 
 rangestat (kurtosis) k_year_sum, interval(mov_id 0 0)

which is rangestat's slightly quirky way to implement identifier-wise calculations.

See also https://journals.sagepub.com/doi/pdf...867X1001000311 for possibly surprising limits on kurtosis from small samples.

L-moments have less bizarre sampling behaviour.

[Esther Chau]

Thank you very much indeed, Nick! The code works perfectly!!