tdigest() (aggregation function)

Article
08/12/2024

Applies to: ✅ Microsoft Fabric ✅ Azure Data Explorer ✅ Azure Monitor ✅ Microsoft Sentinel

Calculates the intermediate results of percentiles() across the group.

Note

This function is used in conjunction with the summarize operator.

For more information, see the underlying algorithm (T-Digest) and the estimated error.

Important

The results of tdigest() and tdigest_merge() can be stored and later retrieved. For example, you may want to create daily percentiles summary, which can then be used to calculate weekly percentiles. However, the precise binary representation of these results may change over time, and is not documented. There's no guarantee that these functions will produce identical results for identical inputs.

Syntax

tdigest(expr [, weight])

Learn more about syntax conventions.

Parameters

Name	Type	Required	Description
expr	`string`	✔️	The expression used for the aggregation calculation.
weight	`string`		The weights of the values for the aggregation calculation.

Returns

The Intermediate results of weighted percentiles of *expr* across the group.

Tip

Use the aggregation function tdigest_merge() to merge the output of tdigest again across another group.
Use the function percentile_tdigest() to calculate the percentile/percentilew of the tdigest results.

Examples

Results per state

This example shows the results of the tdigest percentiles sorted by state.

Run the query

StormEvents
| summarize tdigest(DamageProperty) by State

The results table shown includes only the first 10 rows.

State	tdigest_DamageProperty
NEBRASKA	[[7],[800,250,300000,5000,240000,1500000,20000,550000,0,75000,100000,1000,10000,30000,13000,2000000,1000000,650000,125000,35000,7000,2500000,4000000,450000,85000,460000,500000,6000,150000,350000,4000,72500,1200000,180000,400000,25000,50000,2000,45000,8000,120000,200000,40000,1200,15000,55000,3000,250000],[5,1,3,72,1,1,44,1,1351,12,24,17,46,13,6,1,2,1,2,6,8,1,1,1,2,1,4,2,6,1,2,2,1,1,2,26,18,12,2,2,1,7,6,4,28,4,6,6]]
MINNESOTA	[[7],[700,500,2000000,2500,1200000,12000000,16000,7000000,0,300000,425000,750,6000,30000,10000,22000000,10000000,9600000,600000,50000,4000,27000000,35000000,4000000,400000,5000000,6000000,3000,750000,2500000,2000,250000,11000000,38000000,3000000,20000,120000,1000,100000,5000,500000,1000000,60000,800,15000,200000,1500,1500000,900000],[1,3,1,3,1,2,1,1,1793,1,1,2,2,2,3,1,1,1,2,2,1,1,1,1,2,1,2,1,1,1,6,1,1,1,3,5,1,5,2,5,2,2,1,2,2,2,2,1,1]]
KANSAS	[[7],[667,200,6000000,3400,80000,300000,18875,210000,0,45857,750000,37500000,10000,81150000,15000000,6400000,2570000,225000,59400,25000,5000,400000,7000000,4500000,2500000,6500000,200000,4500,70000,122500,2785,12000000,1900000,18200000,150000,1150000,27000000,2000,30000,2000000,250000000,75000,26000,1500,1500000,1000000,2500,100000,21600000,50000,335000,600000,175000,500000,160000,51000,40000,20000,15000,252500,7520,350000,250000,3400000,1000,338000,16000000,106000,4840000,305000,540000,337500,9800000,45000,12500,700000,4000000,71000,30000000,35000,3700000,22000,56000],[12,2,2,5,2,3,8,1,2751,7,2,1,37,1,1,1,1,2,5,12,33,8,1,1,1,2,10,1,5,2,7,1,4,1,5,1,1,9,11,4,1,5,2,6,4,8,2,23,1,44,2,3,2,3,1,1,1,18,5,2,5,1,7,1,25,1,1,3,1,1,1,2,6,1,1,2,1,1,1,3,1,1,1]]
NEW MEXICO	[[7],[600,500,2500000,7000,1500,28000,40000,10000,0,500000,20000,1000,21000,70000,25000,3500000,200000,16500000,50000,100000,15000,4000,5000,2000],[1,3,1,1,1,1,1,7,466,1,7,4,1,1,2,1,1,1,1,2,1,4,10,8]]
KENTUCKY	[[7],[600,200,700000,5000,400000,12000,15000,100000,0,60000,80000,1000,9000,20000,10000,50000,30000,300000,120000,25000,7000,3000,500000,11500000,75000,35000,8000,6000,150000,1500000,4000,56000,1911,250000,2500000,18000,45000,2000],[6,2,1,42,1,3,9,8,999,2,1,52,1,21,37,25,7,2,3,14,11,35,1,1,6,10,9,10,4,1,13,1,9,3,1,2,1,37]]
VIRGINIA	[[7],[536,500,125000,3000,100000,7250,8000,60000,0,40000,50000,956,6000,11500,7000,25000,15000,98000,70000,12000,4000,2000,120000,1000000,45000,16000,5000,3500,75000,175000,2500,30000,1000,80000,300000,10000,20000,1500],[7,11,1,48,2,2,2,1,1025,2,6,9,2,2,1,5,16,1,3,5,12,122,1,1,1,1,64,2,2,1,1,7,209,3,2,42,19,6]]
OREGON	[[7],[5000,1000,60000,434000,20000,50000,100000,500000,0,1500000,20400000,6000,62600000],[8,2,1,1,1,1,3,1,401,1,1,1,1]]
ALASKA	[[7],[5000,1000,25000,700000,12060,15000,100000,1600000,0,10000],[5,1,1,1,1,2,1,2,242,1]]
CONNECTICUT	[[7],[5000,1000,2000000,0,50000,750000,6000],[1,1,1,142,1,1,1]]
NEVADA	[[7],[5000,1000,200000,1000000,30000,40000,297000,5000000,0,10000],[4,2,1,1,1,1,1,1,148,3]]

Convert pre-existing centroids

The following example shows how one can convert pre-existing T-Digest centroids for long-term storage. The V column holds the value of each centroid, and the W column is its weight (relative count). The tdigest() aggregate function is then applied to convert the data in table DT into the internal representation, and percentile_tdigest() is used to demonstrate how ot find the 50-tile value.

let DT=datatable(V:real, W:long) [
    1.0, 1,
    2.0, 2
];
DT
| summarize TD=tdigest(V, W)
| project P50=percentile_tdigest(TD, 50)

P50
2

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