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DuckDB Extensions All extensions Stochastic

Rayleigh functions in the Stochastic DuckDB extension

Function category

Rayleigh

21 functions

Rayleigh distribution — magnitude of a 2D vector with i.i.d. Normal components. Wind speed, signal envelopes.

dist_rayleigh_cdf

Scalar function Rayleigh
Signature
dist_rayleigh_cdf(scale: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument scale Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_rayleigh_cdf(1.0, 0.5);

Output

dist_rayleigh_cdf(1.0, 0.5)
0.1175030974154046
Related functions

dist_rayleigh_cdf_complement

Scalar function Rayleigh
Signature
dist_rayleigh_cdf_complement(scale: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
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 rayleigh distribution. Returns the probability that X > x, equivalent to the survival function.

1 Example 1 
SELECT dist_rayleigh_cdf_complement(1.0, 0.5);

Output

dist_rayleigh_cdf_complement(1.0, 0.5)
0.8824969025845955
Related functions

dist_rayleigh_chf

Scalar function Rayleigh
Signature
dist_rayleigh_chf(scale: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument scale Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the cumulative hazard function of the rayleigh distribution.

1 Example 1 
SELECT dist_rayleigh_chf(1.0, 0.5);

Output

dist_rayleigh_chf(1.0, 0.5)
0.12499999999999994
Related functions

dist_rayleigh_hazard

Scalar function Rayleigh
Signature
dist_rayleigh_hazard(scale: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument scale Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the hazard function of the rayleigh distribution.

1 Example 1 
SELECT dist_rayleigh_hazard(1.0, 0.5);

Output

dist_rayleigh_hazard(1.0, 0.5)
0.5
Related functions

dist_rayleigh_kurtosis

Scalar function Rayleigh
Signature
dist_rayleigh_kurtosis(scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the kurtosis of the rayleigh distribution.

1 Example 1 
SELECT dist_rayleigh_kurtosis(1.0);

Output

dist_rayleigh_kurtosis(1.0)
3.245089300687638
Related functions

dist_rayleigh_kurtosis_excess

Scalar function Rayleigh
Signature
dist_rayleigh_kurtosis_excess(scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the excess kurtosis of the rayleigh distribution.

1 Example 1 
SELECT dist_rayleigh_kurtosis_excess(1.0);

Output

dist_rayleigh_kurtosis_excess(1.0)
0.24508930068763807
Related functions

dist_rayleigh_log_cdf

Scalar function Rayleigh
Signature
dist_rayleigh_log_cdf(scale: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
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 rayleigh distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.

1 Example 1 
SELECT dist_rayleigh_log_cdf(1.0, 0.5);

Output

dist_rayleigh_log_cdf(1.0, 0.5)
-2.1412905847632016
Related functions

dist_rayleigh_log_cdf_complement

Scalar function Rayleigh
Signature
dist_rayleigh_log_cdf_complement(scale: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
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 rayleigh distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.

1 Example 1 
SELECT dist_rayleigh_log_cdf_complement(1.0, 0.5);

Output

dist_rayleigh_log_cdf_complement(1.0, 0.5)
-0.125
Related functions

dist_rayleigh_log_pdf

Scalar function Rayleigh
Signature
dist_rayleigh_log_pdf(scale: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
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 rayleigh distribution. Useful for numerical stability when dealing with very small probabilities.

1 Example 1 
SELECT dist_rayleigh_log_pdf(1.0, 0.5);

Output

dist_rayleigh_log_pdf(1.0, 0.5)
-0.8181471805599453
Related functions

dist_rayleigh_mean

Scalar function Rayleigh
Signature
dist_rayleigh_mean(scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument scale Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_rayleigh_mean(1.0);

Output

dist_rayleigh_mean(1.0)
1.2533141373155003
Related functions

dist_rayleigh_median

Scalar function Rayleigh
Signature
dist_rayleigh_median(scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument scale Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_rayleigh_median(1.0);

Output

dist_rayleigh_median(1.0)
1.1774100225154747
Related functions

dist_rayleigh_mode

Scalar function Rayleigh
Signature
dist_rayleigh_mode(scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument scale Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_rayleigh_mode(1.0);

Output

dist_rayleigh_mode(1.0)
1.0
Related functions

dist_rayleigh_pdf

Scalar function Rayleigh
Signature
dist_rayleigh_pdf(scale: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument scale Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_rayleigh_pdf(1.0, 0.5);

Output

dist_rayleigh_pdf(1.0, 0.5)
0.4412484512922977
Related functions

dist_rayleigh_quantile

Scalar function Rayleigh
Signature
dist_rayleigh_quantile(scale: DOUBLE, p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument scale Type DOUBLE Mode Positional Description
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_rayleigh_quantile(1.0, 0.95);

Output

dist_rayleigh_quantile(1.0, 0.95)
2.447746830680816
Related functions

dist_rayleigh_quantile_complement

Scalar function Rayleigh
Signature
dist_rayleigh_quantile_complement(scale: DOUBLE, p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument scale Type DOUBLE Mode Positional Description
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_rayleigh_quantile_complement(1.0, 0.05);

Output

dist_rayleigh_quantile_complement(1.0, 0.05)
2.4477468306808166
Related functions

dist_rayleigh_range

Scalar function Rayleigh
Signature
dist_rayleigh_range(scale: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the range of the rayleigh distribution.

1 Example 1 
SELECT dist_rayleigh_range(1.0);

Output

dist_rayleigh_range(1.0)
(0.0, inf)
Related functions

dist_rayleigh_sample

Scalar function Rayleigh
Signature
dist_rayleigh_sample(scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument scale Type DOUBLE Mode Positional Description
Description

Generates random samples from the rayleigh distribution with specified parameters.

1 Example 1 
SELECT dist_rayleigh_sample(1.0);

Output

dist_rayleigh_sample(1.0)
1.483969980665358
Related functions

dist_rayleigh_skewness

Scalar function Rayleigh
Signature
dist_rayleigh_skewness(scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the skewness of the rayleigh distribution.

1 Example 1 
SELECT dist_rayleigh_skewness(1.0);

Output

dist_rayleigh_skewness(1.0)
0.6311106578189372
Related functions

dist_rayleigh_stddev

Scalar function Rayleigh
Signature
dist_rayleigh_stddev(scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument scale Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_rayleigh_stddev(1.0);

Output

dist_rayleigh_stddev(1.0)
0.6551363775620336
Related functions

dist_rayleigh_support

Scalar function Rayleigh
Signature
dist_rayleigh_support(scale: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the support of the rayleigh distribution.

1 Example 1 
SELECT dist_rayleigh_support(1.0);

Output

dist_rayleigh_support(1.0)
(0.0, 1.7976931348623157e+308)
Related functions

dist_rayleigh_variance

Scalar function Rayleigh
Signature
dist_rayleigh_variance(scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the variance (σ²) of the rayleigh distribution.

1 Example 1 
SELECT dist_rayleigh_variance(1.0);

Output

dist_rayleigh_variance(1.0)
0.4292036732051034
Related functions