kurt & skew statistical functions in ClickHouse®

from scipy.stats import skew, kurtosis

# Creating a dataset

dataset = [10,17,71,6,55,38,27,61,48,46,21,38,2,67,35,77,29,31,27,67,81,82,75,81,31,38,68,95,37,34,65,59,81,28,82,80,35,3,97,42,66,28,85,98,45,15,41,61,24,53,97,86,5,65,84,18,9,32,46,52,69,44,78,98,61,64,26,11,3,19,0,90,28,72,47,8,0,74,38,63,88,43,81,61,34,24,37,53,79,72,5,77,58,3,61,56,1,3,5,61]

print(skew(dataset, axis=0, bias=True), skew(dataset))

# -0.05785361619432152 -0.05785361619432152

WITH arrayJoin([10,17,71,6,55,38,27,61,48,46,21,38,2,67,35,77,29,31,27,67,81,82,75,81,31,38,68,95,37,34,65,59,81,28,82,80,35,3,97,42,66,28,85,98,45,15,41,61,24,53,97,86,5,65,84,18,9,32,46,52,69,44,78,98,61,64,26,11,3,19,0,90,28,72,47,8,0,74,38,63,88,43,81,61,34,24,37,53,79,72,5,77,58,3,61,56,1,3,5,61]) AS value
SELECT skewPop(value) AS ex_1

┌──────────────────ex_1─┐
│ -0.057853616194321014 │
└───────────────────────┘

print(skew(dataset, bias=False))

# -0.05873838908626328

WITH arrayJoin([10, 17, 71, 6, 55, 38, 27, 61, 48, 46, 21, 38, 2, 67, 35, 77, 29, 31, 27, 67, 81, 82, 75, 81, 31, 38, 68, 95, 37, 34, 65, 59, 81, 28, 82, 80, 35, 3, 97, 42, 66, 28, 85, 98, 45, 15, 41, 61, 24, 53, 97, 86, 5, 65, 84, 18, 9, 32, 46, 52, 69, 44, 78, 98, 61, 64, 26, 11, 3, 19, 0, 90, 28, 72, 47, 8, 0, 74, 38, 63, 88, 43, 81, 61, 34, 24, 37, 53, 79, 72, 5, 77, 58, 3, 61, 56, 1, 3, 5, 61]) AS value
SELECT
    skewSamp(value) AS ex_1,
    (pow(count(), 2) * ex_1) / ((count() - 1) * (count() - 2)) AS G

┌─────────────────ex_1─┬────────────────────G─┐
│ -0.05698798509149213 │ -0.05873838908626276 │
└──────────────────────┴──────────────────────┘

print(kurtosis(dataset, bias=True, fisher=False), kurtosis(dataset, bias=True, fisher=True), kurtosis(dataset))

# 1.9020275610791184 -1.0979724389208816 -1.0979724389208816

WITH arrayJoin([10, 17, 71, 6, 55, 38, 27, 61, 48, 46, 21, 38, 2, 67, 35, 77, 29, 31, 27, 67, 81, 82, 75, 81, 31, 38, 68, 95, 37, 34, 65, 59, 81, 28, 82, 80, 35, 3, 97, 42, 66, 28, 85, 98, 45, 15, 41, 61, 24, 53, 97, 86, 5, 65, 84, 18, 9, 32, 46, 52, 69, 44, 78, 98, 61, 64, 26, 11, 3, 19, 0, 90, 28, 72, 47, 8, 0, 74, 38, 63, 88, 43, 81, 61, 34, 24, 37, 53, 79, 72, 5, 77, 58, 3, 61, 56, 1, 3, 5, 61]) AS value
SELECT
    kurtPop(value) AS pearson,
    pearson - 3 AS fisher

┌────────────pearson─┬──────────────fisher─┐
│ 1.9020275610791124 │ -1.0979724389208876 │
└────────────────────┴─────────────────────┘

print(kurtosis(dataset, bias=False))

# -1.0924286152713967

WITH arrayJoin([10, 17, 71, 6, 55, 38, 27, 61, 48, 46, 21, 38, 2, 67, 35, 77, 29, 31, 27, 67, 81, 82, 75, 81, 31, 38, 68, 95, 37, 34, 65, 59, 81, 28, 82, 80, 35, 3, 97, 42, 66, 28, 85, 98, 45, 15, 41, 61, 24, 53, 97, 86, 5, 65, 84, 18, 9, 32, 46, 52, 69, 44, 78, 98, 61, 64, 26, 11, 3, 19, 0, 90, 28, 72, 47, 8, 0, 74, 38, 63, 88, 43, 81, 61, 34, 24, 37, 53, 79, 72, 5, 77, 58, 3, 61, 56, 1, 3, 5, 61]) AS value
SELECT
    kurtSamp(value) AS ex_1,
    (((pow(count(), 2) * (count() + 1)) / (((count() - 1) * (count() - 2)) * (count() - 3))) * ex_1) - ((3 * pow(count() - 1, 2)) / ((count() - 2) * (count() - 3))) AS G

┌──────────────ex_1─┬───────────────────G─┐
│ 1.864177212613638 │ -1.0924286152714027 │
└───────────────────┴─────────────────────┘