DuckDB Extensions
Extreme Value functions in the Stochastic DuckDB extension
Function category
Extreme Value
19 functionsGeneralized extreme-value (Gumbel) — block-maxima of i.i.d. samples. Used in hydrology, insurance, climate.
Signature
dist_extreme_value_cdf(
real: DOUBLE,
scale: DOUBLE,
x: DOUBLE
) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
real
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
scale
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Computes the cumulative distribution function (CDF) of the extreme_value distribution. Returns the probability that a random variable X is less than or equal to x.
1
Example 1
SELECT dist_extreme_value_cdf(0, 1.0, 0.5);Output
| dist_extreme_value_cdf(0, 1.0, 0.5) |
|---|
| 0.545239211892605 |
Related functions
- dist_extreme_value_sample() — Generates random samples from the extreme_value distribution with specified parameters
- dist_extreme_value_pdf() — Computes the probability density function (PDF) of the extreme_value distribution
- dist_extreme_value_quantile() — Computes the quantile function (inverse CDF) of the extreme_value distribution
Signature
dist_extreme_value_cdf_complement(
real: DOUBLE,
scale: DOUBLE,
x: DOUBLE
) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
real
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
scale
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Computes the complementary cumulative distribution function (1 - CDF) of the extreme_value distribution. Returns the probability that X > x, equivalent to the survival function.
1
Example 1
SELECT dist_extreme_value_cdf_complement(0, 1.0, 0.5);Output
| dist_extreme_value_cdf_complement(0, 1.0, 0.5) |
|---|
| 0.45476078810739495 |
Related functions
- dist_extreme_value_sample() — Generates random samples from the extreme_value distribution with specified parameters
- dist_extreme_value_pdf() — Computes the probability density function (PDF) of the extreme_value distribution
- dist_extreme_value_cdf() — Computes the cumulative distribution function (CDF) of the extreme_value distribution
- dist_extreme_value_quantile() — Computes the quantile function (inverse CDF) of the extreme_value distribution
Signature
dist_extreme_value_chf(
real: DOUBLE,
scale: DOUBLE,
x: DOUBLE
) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
real
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
scale
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Computes the cumulative hazard function of the extreme_value distribution.
1
Example 1
SELECT dist_extreme_value_chf(0, 1.0, 0.5);Output
| dist_extreme_value_chf(0, 1.0, 0.5) |
|---|
| 0.7879837387044486 |
Related functions
- dist_extreme_value_sample() — Generates random samples from the extreme_value distribution with specified parameters
- dist_extreme_value_pdf() — Computes the probability density function (PDF) of the extreme_value distribution
- dist_extreme_value_cdf() — Computes the cumulative distribution function (CDF) of the extreme_value distribution
- dist_extreme_value_quantile() — Computes the quantile function (inverse CDF) of the extreme_value distribution
Signature
dist_extreme_value_hazard(
real: DOUBLE,
scale: DOUBLE,
x: DOUBLE
) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
real
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
scale
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Computes the hazard function of the extreme_value distribution.
1
Example 1
SELECT dist_extreme_value_hazard(0, 1.0, 0.5);Output
| dist_extreme_value_hazard(0, 1.0, 0.5) |
|---|
| 0.7272049559653766 |
Related functions
- dist_extreme_value_sample() — Generates random samples from the extreme_value distribution with specified parameters
- dist_extreme_value_pdf() — Computes the probability density function (PDF) of the extreme_value distribution
- dist_extreme_value_cdf() — Computes the cumulative distribution function (CDF) of the extreme_value distribution
- dist_extreme_value_quantile() — Computes the quantile function (inverse CDF) of the extreme_value distribution
Signature
dist_extreme_value_kurtosis(real: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
real
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
scale
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Returns the kurtosis of the extreme_value distribution.
1
Example 1
SELECT dist_extreme_value_kurtosis(0.0, 1.0);Output
| dist_extreme_value_kurtosis(0.0, 1.0) |
|---|
| 5.4 |
Related functions
- dist_extreme_value_sample() — Generates random samples from the extreme_value distribution with specified parameters
- dist_extreme_value_pdf() — Computes the probability density function (PDF) of the extreme_value distribution
- dist_extreme_value_cdf() — Computes the cumulative distribution function (CDF) of the extreme_value distribution
- dist_extreme_value_quantile() — Computes the quantile function (inverse CDF) of the extreme_value distribution
Signature
dist_extreme_value_kurtosis_excess(real: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
real
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
scale
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Returns the excess kurtosis of the extreme_value distribution.
1
Example 1
SELECT dist_extreme_value_kurtosis_excess(0.0, 1.0);Output
| dist_extreme_value_kurtosis_excess(0.0, 1.0) |
|---|
| 2.4 |
Related functions
- dist_extreme_value_sample() — Generates random samples from the extreme_value distribution with specified parameters
- dist_extreme_value_pdf() — Computes the probability density function (PDF) of the extreme_value distribution
- dist_extreme_value_cdf() — Computes the cumulative distribution function (CDF) of the extreme_value distribution
- dist_extreme_value_quantile() — Computes the quantile function (inverse CDF) of the extreme_value distribution
Signature
dist_extreme_value_log_cdf(
real: DOUBLE,
scale: DOUBLE,
x: DOUBLE
) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
real
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
scale
|
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 extreme_value distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.
1
Example 1
SELECT dist_extreme_value_log_cdf(0, 1.0, 0.5);Output
| dist_extreme_value_log_cdf(0, 1.0, 0.5) |
|---|
| -0.6065306597126334 |
Related functions
- dist_extreme_value_sample() — Generates random samples from the extreme_value distribution with specified parameters
- dist_extreme_value_pdf() — Computes the probability density function (PDF) of the extreme_value distribution
- dist_extreme_value_cdf() — Computes the cumulative distribution function (CDF) of the extreme_value distribution
- dist_extreme_value_quantile() — Computes the quantile function (inverse CDF) of the extreme_value distribution
Signature
dist_extreme_value_log_cdf_complement(
real: DOUBLE,
scale: DOUBLE,
x: DOUBLE
) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
real
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
scale
|
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 extreme_value distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.
1
Example 1
SELECT dist_extreme_value_log_cdf_complement(0, 1.0, 0.5);Output
| dist_extreme_value_log_cdf_complement(0, 1.0, 0.5) |
|---|
| -0.7879837387044486 |
Related functions
- dist_extreme_value_sample() — Generates random samples from the extreme_value distribution with specified parameters
- dist_extreme_value_pdf() — Computes the probability density function (PDF) of the extreme_value distribution
- dist_extreme_value_cdf() — Computes the cumulative distribution function (CDF) of the extreme_value distribution
- dist_extreme_value_quantile() — Computes the quantile function (inverse CDF) of the extreme_value distribution
Signature
dist_extreme_value_log_pdf(
real: DOUBLE,
scale: DOUBLE,
x: DOUBLE
) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
real
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
scale
|
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 extreme_value distribution. Useful for numerical stability when dealing with very small probabilities.
1
Example 1
SELECT dist_extreme_value_log_pdf(0, 1.0, 0.5);Output
| dist_extreme_value_log_pdf(0, 1.0, 0.5) |
|---|
| -1.1065306597126334 |
Related functions
- dist_extreme_value_sample() — Generates random samples from the extreme_value distribution with specified parameters
- dist_extreme_value_pdf() — Computes the probability density function (PDF) of the extreme_value distribution
- dist_extreme_value_cdf() — Computes the cumulative distribution function (CDF) of the extreme_value distribution
- dist_extreme_value_quantile() — Computes the quantile function (inverse CDF) of the extreme_value distribution
Signature
dist_extreme_value_median(real: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
real
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
scale
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Returns the median (50th percentile) of the extreme_value distribution, which equals the mean.
1
Example 1
SELECT dist_extreme_value_median(0.0, 1.0);Output
| dist_extreme_value_median(0.0, 1.0) |
|---|
| 0.36651292058166435 |
Related functions
- dist_extreme_value_sample() — Generates random samples from the extreme_value distribution with specified parameters
- dist_extreme_value_pdf() — Computes the probability density function (PDF) of the extreme_value distribution
- dist_extreme_value_cdf() — Computes the cumulative distribution function (CDF) of the extreme_value distribution
- dist_extreme_value_quantile() — Computes the quantile function (inverse CDF) of the extreme_value distribution
Signature
dist_extreme_value_mode(real: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
real
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
scale
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Returns the mode (most likely value) of the extreme_value distribution, which equals the mean.
1
Example 1
SELECT dist_extreme_value_mode(0.0, 1.0);Output
| dist_extreme_value_mode(0.0, 1.0) |
|---|
| 0.0 |
Related functions
- dist_extreme_value_sample() — Generates random samples from the extreme_value distribution with specified parameters
- dist_extreme_value_pdf() — Computes the probability density function (PDF) of the extreme_value distribution
- dist_extreme_value_cdf() — Computes the cumulative distribution function (CDF) of the extreme_value distribution
- dist_extreme_value_quantile() — Computes the quantile function (inverse CDF) of the extreme_value distribution
Signature
dist_extreme_value_pdf(
real: DOUBLE,
scale: DOUBLE,
x: DOUBLE
) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
real
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
scale
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
x
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Computes the probability density function (PDF) of the extreme_value distribution. Returns the probability densityat point x for a extreme_value distribution with specified parameters.
1
Example 1
SELECT dist_extreme_value_pdf(0, 1.0, 0.5);Output
| dist_extreme_value_pdf(0, 1.0, 0.5) |
|---|
| 0.3307042988904181 |
Related functions
- dist_extreme_value_sample() — Generates random samples from the extreme_value distribution with specified parameters
- dist_extreme_value_cdf() — Computes the cumulative distribution function (CDF) of the extreme_value distribution
- dist_extreme_value_quantile() — Computes the quantile function (inverse CDF) of the extreme_value distribution
Signature
dist_extreme_value_quantile(
real: DOUBLE,
scale: DOUBLE,
p: DOUBLE
) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
real
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
scale
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
p
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Computes the quantile function (inverse CDF) of the extreme_value distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.
1
Example 1
SELECT dist_extreme_value_quantile(0, 1.0, 0.95);Output
| dist_extreme_value_quantile(0, 1.0, 0.95) |
|---|
| 2.9701952490421637 |
Related functions
- dist_extreme_value_sample() — Generates random samples from the extreme_value distribution with specified parameters
- dist_extreme_value_pdf() — Computes the probability density function (PDF) of the extreme_value distribution
- dist_extreme_value_cdf() — Computes the cumulative distribution function (CDF) of the extreme_value distribution
Signature
dist_extreme_value_quantile_complement(
real: DOUBLE,
scale: DOUBLE,
p: DOUBLE
) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
real
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
scale
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
p
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Computes the complementary quantile function of the extreme_value distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.
1
Example 1
SELECT dist_extreme_value_quantile_complement(0, 1.0, 0.95);Output
| dist_extreme_value_quantile_complement(0, 1.0, 0.95) |
|---|
| -1.0971887003649483 |
Related functions
- dist_extreme_value_sample() — Generates random samples from the extreme_value distribution with specified parameters
- dist_extreme_value_pdf() — Computes the probability density function (PDF) of the extreme_value distribution
- dist_extreme_value_cdf() — Computes the cumulative distribution function (CDF) of the extreme_value distribution
- dist_extreme_value_quantile() — Computes the quantile function (inverse CDF) of the extreme_value distribution
Signature
dist_extreme_value_range(real: DOUBLE, scale: DOUBLE) → DOUBLE[2]
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
real
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
scale
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Returns the range of the extreme_value distribution.
1
Example 1
SELECT dist_extreme_value_range(0.0, 1.0);Output
| dist_extreme_value_range(0.0, 1.0) |
|---|
| (-inf, inf) |
Related functions
- dist_extreme_value_sample() — Generates random samples from the extreme_value distribution with specified parameters
- dist_extreme_value_pdf() — Computes the probability density function (PDF) of the extreme_value distribution
- dist_extreme_value_cdf() — Computes the cumulative distribution function (CDF) of the extreme_value distribution
- dist_extreme_value_quantile() — Computes the quantile function (inverse CDF) of the extreme_value distribution
Signature
dist_extreme_value_sample(real: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
real
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
scale
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Generates random samples from the extreme_value distribution with specified parameters.
1
Example 1
SELECT dist_extreme_value_sample(0.0, 1.0);Output
| dist_extreme_value_sample(0.0, 1.0) |
|---|
| 1.02415581208542 |
Related functions
- dist_extreme_value_pdf() — Computes the probability density function (PDF) of the extreme_value distribution
- dist_extreme_value_cdf() — Computes the cumulative distribution function (CDF) of the extreme_value distribution
- dist_extreme_value_quantile() — Computes the quantile function (inverse CDF) of the extreme_value distribution
Signature
dist_extreme_value_skewness(real: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
real
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
scale
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Returns the skewness of the extreme_value distribution.
1
Example 1
SELECT dist_extreme_value_skewness(0.0, 1.0);Output
| dist_extreme_value_skewness(0.0, 1.0) |
|---|
| 1.1395470994046486 |
Related functions
- dist_extreme_value_sample() — Generates random samples from the extreme_value distribution with specified parameters
- dist_extreme_value_pdf() — Computes the probability density function (PDF) of the extreme_value distribution
- dist_extreme_value_cdf() — Computes the cumulative distribution function (CDF) of the extreme_value distribution
- dist_extreme_value_quantile() — Computes the quantile function (inverse CDF) of the extreme_value distribution
Signature
dist_extreme_value_support(real: DOUBLE, scale: DOUBLE) → DOUBLE[2]
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
real
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
scale
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Returns the support of the extreme_value distribution.
1
Example 1
SELECT dist_extreme_value_support(0.0, 1.0);Output
| dist_extreme_value_support(0.0, 1.0) |
|---|
| (-1.7976931348623157e+308, 1.7976931348623157e+308) |
Related functions
- dist_extreme_value_sample() — Generates random samples from the extreme_value distribution with specified parameters
- dist_extreme_value_pdf() — Computes the probability density function (PDF) of the extreme_value distribution
- dist_extreme_value_cdf() — Computes the cumulative distribution function (CDF) of the extreme_value distribution
- dist_extreme_value_quantile() — Computes the quantile function (inverse CDF) of the extreme_value distribution
Signature
dist_extreme_value_variance(real: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
| Argument | Type | Mode | Description |
|---|---|---|---|
Argument
real
|
Type
DOUBLE
|
Mode Positional | Description |
Argument
scale
|
Type
DOUBLE
|
Mode Positional | Description |
Description
Returns the variance (σ²) of the extreme_value distribution.
1
Example 1
SELECT dist_extreme_value_variance(0.0, 1.0);Output
| dist_extreme_value_variance(0.0, 1.0) |
|---|
| 1.6449340668482264 |
Related functions
- dist_extreme_value_sample() — Generates random samples from the extreme_value distribution with specified parameters
- dist_extreme_value_pdf() — Computes the probability density function (PDF) of the extreme_value distribution
- dist_extreme_value_cdf() — Computes the cumulative distribution function (CDF) of the extreme_value distribution
- dist_extreme_value_quantile() — Computes the quantile function (inverse CDF) of the extreme_value distribution