TimescaleDB API referenceHyperfunctionsStatistical and regression analysis

## Introduction

Perform common statistical analyses, such as calculating averages and standard deviations, using this group of functions. These functions are similar to the PostgreSQL statistical aggregates, but they include more features and are easier to use in continuous aggregates and window functions.

These functions work on one-dimensional data. To work with two-dimensional data, for example to perform linear regression, see the two-dimensional `stats_agg` functions.

## Functions in this group

### Aggregate

stats_agg (one variable)
Aggregate data into an intermediate statistical aggregate form for further calculation

### Accessor

average
Calculate the average from a one-dimensional statistical aggregate
kurtosis
Calculate the kurtosis from a one-dimensional statistical aggregate
num_vals
Calculate the number of values in a one-dimensional statistical aggregate
skewness
Calculate the skewness from a one-dimensional statistical aggregate
stddev
Calculate the standard deviation from a one-dimensional statistical aggregate
sum
Calculate the sum from a one-dimensional statistical aggregate
variance
Calculate the variance from a one-dimensional statistical aggregate

### Rollup

rolling
Combine multiple one-dimensional statistical aggregates to calculate rolling window aggregates
rollup
Combine multiple one-dimensional statistical aggregates

## Function details

`stats_agg(    value DOUBLE PRECISION) RETURNS StatsSummary1D`

This is the first step for performing any statistical aggregate calculations on one-dimensional data. Use `stats_agg` to create an intermediate aggregate (`StatsSummary1D`) from your data. This intermediate form can then be used by one or more accessors in this group to compute final results. Optionally, multiple such intermediate aggregate objects can be combined using `rollup()` or `rolling()` before an accessor is applied.

`stats_agg` is well suited for creating a continuous aggregate that can serve multiple purposes later. For example, you can create a continuous aggregate using `stats_agg` to calculate average and sum. Later, you can reuse the same `StatsSummary1D` objects to calculate standard deviation from the same continuous aggregate.

Required arguments
NameTypeDescription
`value``DOUBLE PRECISION`The variable to use for the statistical aggregate.
Returns
ColumnTypeDescription
`stats_agg``StatsSummary1D`The statistical aggregate, containing data about the variables in an intermediate form. Pass the aggregate to accessor functions in the statistical aggregates API to perform final calculations. Or, pass the aggregate to rollup functions to combine multiple statistical aggregates into larger aggregates.
`average(  summary StatsSummary1D) RETURNS DOUBLE PRECISION`

Calculate a simple average (or mean) from the values in a statistical aggregate.

Required arguments
NameTypeDescription
`summary``StatsSummary1D`The statistical aggregate produced by a `stats_agg` call
Returns
ColumnTypeDescription
`average``DOUBLE PRECISION`The average of the values in the statistical aggregate
Examples

Calculate the average of the integers from 0 to 100:

`SELECT average(stats_agg(data))  FROM generate_series(0, 100) data;`
`average-----------50`
`kurtosis(  summary StatsSummary1D,  [ method TEXT ]) DOUBLE PRECISION`

Calculate the kurtosis from the values in a statistical aggregate. The kurtosis is the fourth statistical moment. It is a measure of “tailedness” of a data distribution compared to a normal distribution.

Required arguments
NameTypeDescription
`summary``StatsSummary1D`The statistical aggregate produced by a `stats_agg` call
Optional arguments
NameTypeDescription
`method``TEXT`The method used for calculating the kurtosis. The two options are `population` and `sample`, which can be abbreviated to `pop` or `samp`. Defaults to `sample`.
Returns
ColumnTypeDescription
`kurtosis``DOUBLE PRECISION`The kurtosis of the values in the statistical aggregate
Examples

Calculate the kurtosis of a sample containing the integers from 0 to 100:

`SELECT kurtosis(stats_agg(data))  FROM generate_series(0, 100) data;`
`kurtosis----------1.78195`
`num_vals(  summary StatsSummary1D) RETURNS BIGINT`

Calculate the number of values contained in a statistical aggregate.

Required arguments
NameTypeDescription
`summary``StatsSummary1D`The statistical aggregate produced by a `stats_agg` call
Returns
ColumnTypeDescription
`num_vals``DOUBLE PRECISION`The number of values in the statistical aggregate
Examples

Calculate the number of values from 0 to 100, inclusive:

`SELECT num_vals(stats_agg(data))  FROM generate_series(0, 100) data;`
`num_vals--------101`
`skewness(  summary StatsSummary1D,  [ method TEXT ]) RETURNS DOUBLE PRECISION`

Calculate the skewness from the values in a statistical aggregate. The skewness is the third statistical moment. It is a measure of asymmetry in a data distribution.

Required arguments
NameTypeDescription
`summary``StatsSummary1D`The statistical aggregate produced by a `stats_agg` call
Optional arguments
NameTypeDescription
`method``TEXT`The method used for calculating the skewness. The two options are `population` and `sample`, which can be abbreviated to `pop` or `samp`. Defaults to `sample`.
Returns
ColumnTypeDescription
`skewness``DOUBLE PRECISION`The skewness of the values in the statistical aggregate
Examples

Calculate the skewness of a sample containing the integers from 0 to 100:

`SELECT skewness(stats_agg(data))  FROM generate_series(0, 100) data;`
`skewness_x----------0`
`stddev(  summary StatsSummary1D,  [ method TEXT ]) RETURNS DOUBLE PRECISION`

Calculate the standard deviation from the values in a statistical aggregate.

Required arguments
NameTypeDescription
`summary``StatsSummary1D`The statistical aggregate produced by a `stats_agg` call
Optional arguments
NameTypeDescription
`method``TEXT`The method used for calculating the standard deviation. The two options are `population` and `sample`, which can be abbreviated to `pop` or `samp`. Defaults to `sample`.
Returns
ColumnTypeDescription
`stddev``DOUBLE PRECISION`The standard deviation of the values in the statistical aggregate
Examples

Calculate the standard deviation of a sample containing the integers from 0 to 100:

`SELECT stddev(stats_agg(data))  FROM generate_series(0, 100) data;`
`stddev_y--------29.3002`
`sum(  summary StatsSummary1D) RETURNS DOUBLE PRECISION`

Calculate the sum of the values contained in a statistical aggregate.

Required arguments
NameTypeDescription
`summary``StatsSummary1D`The statistical aggregate produced by a `stats_agg` call
Returns
ColumnTypeDescription
`sum``DOUBLE PRECISION`The sum of the values in the statistical aggregate
Examples

Calculate the sum of the integers from 0 to 100:

`SELECT sum(stats_agg(data))  FROM generate_series(0, 100) data;`
`sum-----5050`
`variance(  summary StatsSummary1D,  [ method TEXT ]) RETURNS DOUBLE PRECISION`

Calculate the variance from the values in a statistical aggregate.

Required arguments
NameTypeDescription
`summary``StatsSummary1D`The statistical aggregate produced by a `stats_agg` call
Optional arguments
NameTypeDescription
`method``TEXT`The method used for calculating the standard deviation. The two options are `population` and `sample`, which can be abbreviated to `pop` or `samp`. Defaults to `sample`.
Returns
ColumnTypeDescription
`variance``DOUBLE PRECISION`The variance of the values in the statistical aggregate
Examples

Calculate the variance of a sample containing the integers from 0 to 100:

`SELECT variance(stats_agg(data))  FROM generate_series(0, 100) data;`
`variance----------858.5`
`rolling(    ss StatsSummary1D) RETURNS StatsSummary1D`

Combine multiple intermediate statistical aggregate (`StatsSummary1D`) objects into a single `StatsSummary1D` object. It is optimized for use in a window function context for computing tumbling window statistical aggregates.

###### Note

This is especially useful for computing tumbling window aggregates from a continuous aggregate. It can be orders of magnitude faster because it uses inverse transition and combine functions, with the possibility that bigger floating point errors can occur in unusual scenarios. For re-aggregation in a non-window function context, such as combining hourly buckets into daily buckets, see `rollup()`.

Required arguments
NameTypeDescription
`summary``StatsSummary1D`The statistical aggregate produced by a `stats_agg` call
Returns
ColumnTypeDescription
`rolling``StatsSummary1D`A new statistical aggregate produced by combining the input statistical aggregates
Examples

Combine hourly continuous aggregates to create a tumbling window daily aggregate. Calculate the average and standard deviation using the appropriate accessors:

```CREATE MATERIALIZED VIEW foo_hourlyWITH (timescaledb.continuous)AS SELECT  time_bucket('1h'::interval, ts) AS bucket,  stats_agg(value) as statsFROM fooGROUP BY 1;
SELECT  bucket,  average(rolling(stats) OVER (ORDER BY bucket RANGE '1 day' PRECEDING)),  stddev(rolling(stats) OVER (ORDER BY bucket RANGE '1 day' PRECEDING)),FROM foo_hourly;```
`rollup(    ss StatsSummary1D) RETURNS StatsSummary1D`

Combine multiple intermediate statistical aggregate (`StatsSummary1D`) objects produced by `stats_agg` (one variable) into a single intermediate `StatsSummary1D` object. For example, you can use `rollup` to combine statistical aggregates from 15-minute buckets into daily buckets. For use in window functions, see `rolling()`.

Required arguments
NameTypeDescription
`summary``StatsSummary1D`The statistical aggregate produced by a `stats_agg` call
Returns
ColumnTypeDescription
`rollup``StatsSummary1D`A new statistical aggregate produced by combining the input statistical aggregates

## Extended examples

Create a statistical aggregate to summarize daily statistical data about the variable `val1`. Use the statistical aggregate to calculate average, standard deviation, and skewness of the variable:

`WITH t as (    SELECT        time_bucket('1 day'::interval, ts) as dt,        stats_agg(val1) AS stats1D    FROM foo    WHERE id = 'bar'    GROUP BY time_bucket('1 day'::interval, ts))SELECT    average(stats1D),    stddev(stats1D),    skewness(stats1D)FROM t;`

Keywords