Skip to content
DuckDB Extensions All extensions Stochastic

Chi-squared functions in the Stochastic DuckDB extension

Function category

Chi-squared

21 functions

Chi-squared distribution — sum of k squared standard normals. Used in goodness-of-fit and variance tests.

dist_chi_squared_cdf

Scalar function Chi-squared
Signature
dist_chi_squared_cdf(degrees_of_freedom: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the cumulative distribution function (CDF) of the chi_squared distribution. Returns the probability that a random variable X is less than or equal to x.

1 Example 1 
SELECT dist_chi_squared_cdf(5, 3.0);

Output

dist_chi_squared_cdf(5, 3.0)
0.3000141641213725
Related functions

dist_chi_squared_cdf_complement

Scalar function Chi-squared
Signature
dist_chi_squared_cdf_complement(degrees_of_freedom: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the complementary cumulative distribution function (1 - CDF) of the chi_squared distribution. Returns the probability that X > x, equivalent to the survival function.

1 Example 1 
SELECT dist_chi_squared_cdf_complement(5, 3.0);

Output

dist_chi_squared_cdf_complement(5, 3.0)
0.6999858358786275
Related functions

dist_chi_squared_chf

Scalar function Chi-squared
Signature
dist_chi_squared_chf(degrees_of_freedom: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the cumulative hazard function of the chi_squared distribution.

1 Example 1 
SELECT dist_chi_squared_chf(5, 3.0);

Output

dist_chi_squared_chf(5, 3.0)
0.3566951786025554
Related functions

dist_chi_squared_hazard

Scalar function Chi-squared
Signature
dist_chi_squared_hazard(degrees_of_freedom: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the hazard function of the chi_squared distribution.

1 Example 1 
SELECT dist_chi_squared_hazard(5, 3.0);

Output

dist_chi_squared_hazard(5, 3.0)
0.2202620708892502
Related functions

dist_chi_squared_kurtosis

Scalar function Chi-squared
Signature
dist_chi_squared_kurtosis(degrees_of_freedom: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

Returns the kurtosis of the chi_squared distribution.

1 Example 1 
SELECT dist_chi_squared_kurtosis(5);

Output

dist_chi_squared_kurtosis(5)
5.4
Related functions

dist_chi_squared_kurtosis_excess

Scalar function Chi-squared
Signature
dist_chi_squared_kurtosis_excess(degrees_of_freedom: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

Returns the excess kurtosis of the chi_squared distribution.

1 Example 1 
SELECT dist_chi_squared_kurtosis_excess(5);

Output

dist_chi_squared_kurtosis_excess(5)
2.4
Related functions

dist_chi_squared_log_cdf

Scalar function Chi-squared
Signature
dist_chi_squared_log_cdf(degrees_of_freedom: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the natural logarithm of the cumulative distribution function (CDF) of the chi_squared distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.

1 Example 1 
SELECT dist_chi_squared_log_cdf(5, 3.0);

Output

dist_chi_squared_log_cdf(5, 3.0)
-1.203925591702561
Related functions

dist_chi_squared_log_cdf_complement

Scalar function Chi-squared
Signature
dist_chi_squared_log_cdf_complement(degrees_of_freedom: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the chi_squared distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.

1 Example 1 
SELECT dist_chi_squared_log_cdf_complement(5, 3.0);

Output

dist_chi_squared_log_cdf_complement(5, 3.0)
-0.3566951786025554
Related functions

dist_chi_squared_log_pdf

Scalar function Chi-squared
Signature
dist_chi_squared_log_pdf(degrees_of_freedom: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the natural logarithm of the probability density function (log-PDF) of the chi_squared distribution. Useful for numerical stability when dealing with very small probabilities.

1 Example 1 
SELECT dist_chi_squared_log_pdf(5, 3.0);

Output

dist_chi_squared_log_pdf(5, 3.0)
-1.8696323888706177
Related functions

dist_chi_squared_mean

Scalar function Chi-squared
Signature
dist_chi_squared_mean(degrees_of_freedom: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

Returns the mean (μ) of the chi_squared distribution, which is the first moment.

1 Example 1 
SELECT dist_chi_squared_mean(5);

Output

dist_chi_squared_mean(5)
5.0
Related functions

dist_chi_squared_median

Scalar function Chi-squared
Signature
dist_chi_squared_median(degrees_of_freedom: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

Returns the median (50th percentile) of the chi_squared distribution, which equals the mean.

1 Example 1 
SELECT dist_chi_squared_median(5);

Output

dist_chi_squared_median(5)
4.351460191095527
Related functions

dist_chi_squared_mode

Scalar function Chi-squared
Signature
dist_chi_squared_mode(degrees_of_freedom: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

Returns the mode (most likely value) of the chi_squared distribution, which equals the mean.

1 Example 1 
SELECT dist_chi_squared_mode(5);

Output

dist_chi_squared_mode(5)
3.0
Related functions

dist_chi_squared_pdf

Scalar function Chi-squared
Signature
dist_chi_squared_pdf(degrees_of_freedom: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the probability density function (PDF) of the chi_squared distribution. Returns the probability densityat point x for a chi_squared distribution with specified parameters.

1 Example 1 
SELECT dist_chi_squared_pdf(5, 3.0);

Output

dist_chi_squared_pdf(5, 3.0)
0.1541803298037693
Related functions

dist_chi_squared_quantile

Scalar function Chi-squared
Signature
dist_chi_squared_quantile(degrees_of_freedom: DOUBLE, p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Argument p Type DOUBLE Mode Positional Description
Description

Computes the quantile function (inverse CDF) of the chi_squared distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.

1 Example 1 
SELECT dist_chi_squared_quantile(5, 0.95);

Output

dist_chi_squared_quantile(5, 0.95)
11.070497693516351
Related functions

dist_chi_squared_quantile_complement

Scalar function Chi-squared
Signature
dist_chi_squared_quantile_complement(degrees_of_freedom: DOUBLE, p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Argument p Type DOUBLE Mode Positional Description
Description

Computes the complementary quantile function of the chi_squared distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.

1 Example 1 
SELECT dist_chi_squared_quantile_complement(5, 0.05);

Output

dist_chi_squared_quantile_complement(5, 0.05)
11.070497693516355
Related functions

dist_chi_squared_range

Scalar function Chi-squared
Signature
dist_chi_squared_range(degrees_of_freedom: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

Returns the range of the chi_squared distribution.

1 Example 1 
SELECT dist_chi_squared_range(5);

Output

dist_chi_squared_range(5)
(0.0, inf)
Related functions

dist_chi_squared_sample

Scalar function Chi-squared
Signature
dist_chi_squared_sample(degrees_of_freedom: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

Generates random samples from the chi_squared distribution with specified parameters.

1 Example 1 
SELECT dist_chi_squared_sample(5);

Output

dist_chi_squared_sample(5)
5.125173105199968
Related functions

dist_chi_squared_skewness

Scalar function Chi-squared
Signature
dist_chi_squared_skewness(degrees_of_freedom: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

Returns the skewness of the chi_squared distribution.

1 Example 1 
SELECT dist_chi_squared_skewness(5);

Output

dist_chi_squared_skewness(5)
1.2649110640673518
Related functions

dist_chi_squared_stddev

Scalar function Chi-squared
Signature
dist_chi_squared_stddev(degrees_of_freedom: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

Returns the standard deviation (σ) of the chi_squared distribution.

1 Example 1 
SELECT dist_chi_squared_stddev(5);

Output

dist_chi_squared_stddev(5)
3.1622776601683795
Related functions

dist_chi_squared_support

Scalar function Chi-squared
Signature
dist_chi_squared_support(degrees_of_freedom: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

Returns the support of the chi_squared distribution.

1 Example 1 
SELECT dist_chi_squared_support(5);

Output

dist_chi_squared_support(5)
(0.0, 1.7976931348623157e+308)
Related functions

dist_chi_squared_variance

Scalar function Chi-squared
Signature
dist_chi_squared_variance(degrees_of_freedom: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

Returns the variance (σ²) of the chi_squared distribution.

1 Example 1 
SELECT dist_chi_squared_variance(5);

Output

dist_chi_squared_variance(5)
10.0
Related functions