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DuckDB Extensions All extensions Stochastic

Laplace functions in the Stochastic DuckDB extension

Function category

Laplace

21 functions

Laplace (double exponential) — location/scale. Heavier tails than Normal; used in regularized regression and noise modeling.

dist_laplace_cdf

Scalar function Laplace
Signature
dist_laplace_cdf( location: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument location 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 laplace distribution. Returns the probability that a random variable X is less than or equal to x.

1 Example 1 
SELECT dist_laplace_cdf(0, 1.0, 0.5);

Output

dist_laplace_cdf(0, 1.0, 0.5)
0.6967346701436833
Related functions

dist_laplace_cdf_complement

Scalar function Laplace
Signature
dist_laplace_cdf_complement( location: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument location 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 laplace distribution. Returns the probability that X > x, equivalent to the survival function.

1 Example 1 
SELECT dist_laplace_cdf_complement(0, 1.0, 0.5);

Output

dist_laplace_cdf_complement(0, 1.0, 0.5)
0.3032653298563167
Related functions

dist_laplace_chf

Scalar function Laplace
Signature
dist_laplace_chf( location: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument location 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 laplace distribution.

1 Example 1 
SELECT dist_laplace_chf(0, 1.0, 0.5);

Output

dist_laplace_chf(0, 1.0, 0.5)
1.1931471805599454
Related functions

dist_laplace_hazard

Scalar function Laplace
Signature
dist_laplace_hazard( location: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument location 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 laplace distribution.

1 Example 1 
SELECT dist_laplace_hazard(0, 1.0, 0.5);

Output

dist_laplace_hazard(0, 1.0, 0.5)
1.0
Related functions

dist_laplace_kurtosis

Scalar function Laplace
Signature
dist_laplace_kurtosis(location: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument location Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the kurtosis of the laplace distribution.

1 Example 1 
SELECT dist_laplace_kurtosis(0.0, 1.0);

Output

dist_laplace_kurtosis(0.0, 1.0)
6.0
Related functions

dist_laplace_kurtosis_excess

Scalar function Laplace
Signature
dist_laplace_kurtosis_excess(location: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument location Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the excess kurtosis of the laplace distribution.

1 Example 1 
SELECT dist_laplace_kurtosis_excess(0.0, 1.0);

Output

dist_laplace_kurtosis_excess(0.0, 1.0)
3.0
Related functions

dist_laplace_log_cdf

Scalar function Laplace
Signature
dist_laplace_log_cdf( location: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument location 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 laplace distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.

1 Example 1 
SELECT dist_laplace_log_cdf(0, 1.0, 0.5);

Output

dist_laplace_log_cdf(0, 1.0, 0.5)
-0.3613506148087591
Related functions

dist_laplace_log_cdf_complement

Scalar function Laplace
Signature
dist_laplace_log_cdf_complement( location: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument location 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 laplace distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.

1 Example 1 
SELECT dist_laplace_log_cdf_complement(0, 1.0, 0.5);

Output

dist_laplace_log_cdf_complement(0, 1.0, 0.5)
-1.1931471805599454
Related functions

dist_laplace_log_pdf

Scalar function Laplace
Signature
dist_laplace_log_pdf( location: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument location 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 laplace distribution. Useful for numerical stability when dealing with very small probabilities.

1 Example 1 
SELECT dist_laplace_log_pdf(0, 1.0, 0.5);

Output

dist_laplace_log_pdf(0, 1.0, 0.5)
-1.1931471805599454
Related functions

dist_laplace_mean

Scalar function Laplace
Signature
dist_laplace_mean(location: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument location Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_laplace_mean(0.0, 1.0);

Output

dist_laplace_mean(0.0, 1.0)
0.0
Related functions

dist_laplace_median

Scalar function Laplace
Signature
dist_laplace_median(location: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument location Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_laplace_median(0.0, 1.0);

Output

dist_laplace_median(0.0, 1.0)
0.0
Related functions

dist_laplace_mode

Scalar function Laplace
Signature
dist_laplace_mode(location: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument location Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_laplace_mode(0.0, 1.0);

Output

dist_laplace_mode(0.0, 1.0)
0.0
Related functions

dist_laplace_pdf

Scalar function Laplace
Signature
dist_laplace_pdf( location: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument location 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 laplace distribution. Returns the probability densityat point x for a laplace distribution with specified parameters.

1 Example 1 
SELECT dist_laplace_pdf(0, 1.0, 0.5);

Output

dist_laplace_pdf(0, 1.0, 0.5)
0.3032653298563167
Related functions

dist_laplace_quantile

Scalar function Laplace
Signature
dist_laplace_quantile( location: DOUBLE, scale: DOUBLE, p: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument location 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 laplace distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.

1 Example 1 
SELECT dist_laplace_quantile(0, 1.0, 0.95);

Output

dist_laplace_quantile(0, 1.0, 0.95)
2.302585092994045
Related functions

dist_laplace_quantile_complement

Scalar function Laplace
Signature
dist_laplace_quantile_complement( location: DOUBLE, scale: DOUBLE, p: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument location 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 laplace distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.

1 Example 1 
SELECT dist_laplace_quantile_complement(0, 1.0, 0.95);

Output

dist_laplace_quantile_complement(0, 1.0, 0.95)
-2.302585092994045
Related functions

dist_laplace_range

Scalar function Laplace
Signature
dist_laplace_range(location: DOUBLE, scale: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument location Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the range of the laplace distribution.

1 Example 1 
SELECT dist_laplace_range(0.0, 1.0);

Output

dist_laplace_range(0.0, 1.0)
(-inf, inf)
Related functions

dist_laplace_sample

Scalar function Laplace
Signature
dist_laplace_sample(location: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument location Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

Generates random samples from the laplace distribution with specified parameters.

1 Example 1 
SELECT dist_laplace_sample(0.0, 1.0);

Output

dist_laplace_sample(0.0, 1.0)
-0.02158105116187718
Related functions

dist_laplace_skewness

Scalar function Laplace
Signature
dist_laplace_skewness(location: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument location Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the skewness of the laplace distribution.

1 Example 1 
SELECT dist_laplace_skewness(0.0, 1.0);

Output

dist_laplace_skewness(0.0, 1.0)
0.0
Related functions

dist_laplace_stddev

Scalar function Laplace
Signature
dist_laplace_stddev(location: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument location Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_laplace_stddev(0.0, 1.0);

Output

dist_laplace_stddev(0.0, 1.0)
1.4142135623730951
Related functions

dist_laplace_support

Scalar function Laplace
Signature
dist_laplace_support(location: DOUBLE, scale: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument location Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the support of the laplace distribution.

1 Example 1 
SELECT dist_laplace_support(0.0, 1.0);

Output

dist_laplace_support(0.0, 1.0)
(-inf, inf)
Related functions

dist_laplace_variance

Scalar function Laplace
Signature
dist_laplace_variance(location: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument location Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the variance (σ²) of the laplace distribution.

1 Example 1 
SELECT dist_laplace_variance(0.0, 1.0);

Output

dist_laplace_variance(0.0, 1.0)
2.0000000000000004
Related functions