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quantileExactWeightedInterpolated

Computes quantile of a numeric data sequence using linear interpolation, taking into account the weight of each element.

To get the interpolated value, all the passed values are combined into an array, which are then sorted by their corresponding weights. Quantile interpolation is then performed using the weighted percentile method by building a cumulative distribution based on weights and then a linear interpolation is performed using the weights and the values to compute the quantiles.

When using multiple quantile* functions with different levels in a query, the internal states are not combined (that is, the query works less efficiently than it could). In this case, use the quantiles function.

We strongly recommend using quantileExactWeightedInterpolated instead of quantileInterpolatedWeighted because quantileExactWeightedInterpolated is more accurate than quantileInterpolatedWeighted. Here is an example:

SELECT
    quantileExactWeightedInterpolated(0.99)(number, 1),
    quantile(0.99)(number),
    quantileInterpolatedWeighted(0.99)(number, 1)
FROM numbers(9)


┌─quantileExactWeightedInterpolated(0.99)(number, 1)─┬─quantile(0.99)(number)─┬─quantileInterpolatedWeighted(0.99)(number, 1)─┐
│                                               7.92 │                   7.92 │                                             8 │
└────────────────────────────────────────────────────┴────────────────────────┴───────────────────────────────────────────────┘

Syntax

quantileExactWeightedInterpolated(level)(expr, weight)

Alias: medianExactWeightedInterpolated.

Arguments

  • level — Level of quantile. Optional parameter. Constant floating-point number from 0 to 1. We recommend using a level value in the range of [0.01, 0.99]. Default value: 0.5. At level=0.5 the function calculates median.
  • expr — Expression over the column values resulting in numeric data types, Date or DateTime.
  • weight — Column with weights of sequence members. Weight is a number of value occurrences with Unsigned integer types.

Returned value

  • Quantile of the specified level.

Type:

  • Float64 for numeric data type input.
  • Date if input values have the Date type.
  • DateTime if input values have the DateTime type.

Example

Input table:

┌─n─┬─val─┐
│ 0 │   3 │
│ 1 │   2 │
│ 2 │   1 │
│ 5 │   4 │
└───┴─────┘

Result:

┌─quantileExactWeightedInterpolated(n, val)─┐
│                                       1.5 │
└───────────────────────────────────────────┘

See Also