DuckDB Extensions
Cauchy functions in the Stochastic DuckDB extension
Function category
Cauchy
15 functionsCauchy distribution — heavy-tailed location/scale family with no defined mean. Used in robust statistics and physics.
Signature
dist_cauchy_cdf(
x: DOUBLE,
y: DOUBLE,
x: DOUBLE
) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
y
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Computes the cumulative distribution function (CDF) of the cauchy distribution. Returns the probability that a random variable X is less than or equal to x.
1
Example 1
SELECT dist_cauchy_cdf(0, 1.0, 0.5);Output
| dist_cauchy_cdf(0, 1.0, 0.5) |
|---|
| 0.6475836176504333 |
Related functions
Signature
dist_cauchy_cdf_complement(
x: DOUBLE,
y: DOUBLE,
x: DOUBLE
) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
y
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Computes the complementary cumulative distribution function (1 - CDF) of the cauchy distribution. Returns the probability that X > x, equivalent to the survival function.
1
Example 1
SELECT dist_cauchy_cdf_complement(0, 1.0, 0.5);Output
| dist_cauchy_cdf_complement(0, 1.0, 0.5) |
|---|
| 0.35241638234956674 |
Related functions
- dist_cauchy_sample() — Generates random samples from the cauchy distribution with specified parameters
- dist_cauchy_pdf() — Computes the probability density function (PDF) of the cauchy distribution
- dist_cauchy_cdf() — Computes the cumulative distribution function (CDF) of the cauchy distribution
- dist_cauchy_quantile() — Computes the quantile function (inverse CDF) of the cauchy distribution
Signature
dist_cauchy_chf(
x: DOUBLE,
y: DOUBLE,
x: DOUBLE
) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
y
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Computes the cumulative hazard function of the cauchy distribution.
1
Example 1
SELECT dist_cauchy_chf(0, 1.0, 0.5);Output
| dist_cauchy_chf(0, 1.0, 0.5) |
|---|
| 1.0429418980620317 |
Related functions
- dist_cauchy_sample() — Generates random samples from the cauchy distribution with specified parameters
- dist_cauchy_pdf() — Computes the probability density function (PDF) of the cauchy distribution
- dist_cauchy_cdf() — Computes the cumulative distribution function (CDF) of the cauchy distribution
- dist_cauchy_quantile() — Computes the quantile function (inverse CDF) of the cauchy distribution
Signature
dist_cauchy_hazard(
x: DOUBLE,
y: DOUBLE,
x: DOUBLE
) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
y
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Computes the hazard function of the cauchy distribution.
1
Example 1
SELECT dist_cauchy_hazard(0, 1.0, 0.5);Output
| dist_cauchy_hazard(0, 1.0, 0.5) |
|---|
| 0.7225768202070803 |
Related functions
- dist_cauchy_sample() — Generates random samples from the cauchy distribution with specified parameters
- dist_cauchy_pdf() — Computes the probability density function (PDF) of the cauchy distribution
- dist_cauchy_cdf() — Computes the cumulative distribution function (CDF) of the cauchy distribution
- dist_cauchy_quantile() — Computes the quantile function (inverse CDF) of the cauchy distribution
Signature
dist_cauchy_log_cdf(
x: DOUBLE,
y: DOUBLE,
x: DOUBLE
) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
y
|
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 cauchy distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.
1
Example 1
SELECT dist_cauchy_log_cdf(0, 1.0, 0.5);Output
| dist_cauchy_log_cdf(0, 1.0, 0.5) |
|---|
| -0.4345073545177282 |
Related functions
- dist_cauchy_sample() — Generates random samples from the cauchy distribution with specified parameters
- dist_cauchy_pdf() — Computes the probability density function (PDF) of the cauchy distribution
- dist_cauchy_cdf() — Computes the cumulative distribution function (CDF) of the cauchy distribution
- dist_cauchy_quantile() — Computes the quantile function (inverse CDF) of the cauchy distribution
Signature
dist_cauchy_log_cdf_complement(
x: DOUBLE,
y: DOUBLE,
x: DOUBLE
) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
y
|
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 cauchy distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.
1
Example 1
SELECT dist_cauchy_log_cdf_complement(0, 1.0, 0.5);Output
| dist_cauchy_log_cdf_complement(0, 1.0, 0.5) |
|---|
| -1.0429418980620317 |
Related functions
- dist_cauchy_sample() — Generates random samples from the cauchy distribution with specified parameters
- dist_cauchy_pdf() — Computes the probability density function (PDF) of the cauchy distribution
- dist_cauchy_cdf() — Computes the cumulative distribution function (CDF) of the cauchy distribution
- dist_cauchy_quantile() — Computes the quantile function (inverse CDF) of the cauchy distribution
Signature
dist_cauchy_log_pdf(
x: DOUBLE,
y: DOUBLE,
x: DOUBLE
) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
y
|
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 cauchy distribution. Useful for numerical stability when dealing with very small probabilities.
1
Example 1
SELECT dist_cauchy_log_pdf(0, 1.0, 0.5);Output
| dist_cauchy_log_pdf(0, 1.0, 0.5) |
|---|
| -1.3678734371636099 |
Related functions
- dist_cauchy_sample() — Generates random samples from the cauchy distribution with specified parameters
- dist_cauchy_pdf() — Computes the probability density function (PDF) of the cauchy distribution
- dist_cauchy_cdf() — Computes the cumulative distribution function (CDF) of the cauchy distribution
- dist_cauchy_quantile() — Computes the quantile function (inverse CDF) of the cauchy distribution
Signature
dist_cauchy_median(x: DOUBLE, y: DOUBLE) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
y
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Returns the median (50th percentile) of the cauchy distribution, which equals the mean.
1
Example 1
SELECT dist_cauchy_median(0.0, 1.0);Output
| dist_cauchy_median(0.0, 1.0) |
|---|
| 0.0 |
Related functions
- dist_cauchy_sample() — Generates random samples from the cauchy distribution with specified parameters
- dist_cauchy_pdf() — Computes the probability density function (PDF) of the cauchy distribution
- dist_cauchy_cdf() — Computes the cumulative distribution function (CDF) of the cauchy distribution
- dist_cauchy_quantile() — Computes the quantile function (inverse CDF) of the cauchy distribution
Signature
dist_cauchy_mode(x: DOUBLE, y: DOUBLE) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
y
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Returns the mode (most likely value) of the cauchy distribution, which equals the mean.
1
Example 1
SELECT dist_cauchy_mode(0.0, 1.0);Output
| dist_cauchy_mode(0.0, 1.0) |
|---|
| 0.0 |
Related functions
- dist_cauchy_sample() — Generates random samples from the cauchy distribution with specified parameters
- dist_cauchy_pdf() — Computes the probability density function (PDF) of the cauchy distribution
- dist_cauchy_cdf() — Computes the cumulative distribution function (CDF) of the cauchy distribution
- dist_cauchy_quantile() — Computes the quantile function (inverse CDF) of the cauchy distribution
Signature
dist_cauchy_pdf(
x: DOUBLE,
y: DOUBLE,
x: DOUBLE
) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
y
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Computes the probability density function (PDF) of the cauchy distribution. Returns the probability densityat point x for a cauchy distribution with specified parameters.
1
Example 1
SELECT dist_cauchy_pdf(0, 1.0, 0.5);Output
| dist_cauchy_pdf(0, 1.0, 0.5) |
|---|
| 0.25464790894703254 |
Related functions
Signature
dist_cauchy_quantile(
x: DOUBLE,
y: DOUBLE,
p: DOUBLE
) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
y
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
p
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Computes the quantile function (inverse CDF) of the cauchy distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.
1
Example 1
SELECT dist_cauchy_quantile(0, 1.0, 0.95);Output
| dist_cauchy_quantile(0, 1.0, 0.95) |
|---|
| 6.313751514675038 |
Related functions
Signature
dist_cauchy_quantile_complement(
x: DOUBLE,
y: DOUBLE,
p: DOUBLE
) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
y
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
p
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Computes the complementary quantile function of the cauchy distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.
1
Example 1
SELECT dist_cauchy_quantile_complement(0, 1.0, 0.95);Output
| dist_cauchy_quantile_complement(0, 1.0, 0.95) |
|---|
| -6.313751514675038 |
Related functions
- dist_cauchy_sample() — Generates random samples from the cauchy distribution with specified parameters
- dist_cauchy_pdf() — Computes the probability density function (PDF) of the cauchy distribution
- dist_cauchy_cdf() — Computes the cumulative distribution function (CDF) of the cauchy distribution
- dist_cauchy_quantile() — Computes the quantile function (inverse CDF) of the cauchy distribution
Signature
dist_cauchy_range(x: DOUBLE, y: DOUBLE) → DOUBLE[2]
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
y
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Returns the range of the cauchy distribution.
1
Example 1
SELECT dist_cauchy_range(0.0, 1.0);Output
| dist_cauchy_range(0.0, 1.0) |
|---|
| (-inf, inf) |
Related functions
- dist_cauchy_sample() — Generates random samples from the cauchy distribution with specified parameters
- dist_cauchy_pdf() — Computes the probability density function (PDF) of the cauchy distribution
- dist_cauchy_cdf() — Computes the cumulative distribution function (CDF) of the cauchy distribution
- dist_cauchy_quantile() — Computes the quantile function (inverse CDF) of the cauchy distribution
Signature
dist_cauchy_sample(x: DOUBLE, y: DOUBLE) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
y
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Generates random samples from the cauchy distribution with specified parameters.
1
Example 1
SELECT dist_cauchy_sample(0.0, 1.0);Output
| dist_cauchy_sample(0.0, 1.0) |
|---|
| -1.2266264270965836 |
Related functions
Signature
dist_cauchy_support(x: DOUBLE, y: DOUBLE) → DOUBLE[2]
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
y
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Returns the support of the cauchy distribution.
1
Example 1
SELECT dist_cauchy_support(0.0, 1.0);Output
| dist_cauchy_support(0.0, 1.0) |
|---|
| (-inf, inf) |
Related functions
- dist_cauchy_sample() — Generates random samples from the cauchy distribution with specified parameters
- dist_cauchy_pdf() — Computes the probability density function (PDF) of the cauchy distribution
- dist_cauchy_cdf() — Computes the cumulative distribution function (CDF) of the cauchy distribution
- dist_cauchy_quantile() — Computes the quantile function (inverse CDF) of the cauchy distribution