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DuckDB Extensions All extensions Stochastic

Weibull functions in the Stochastic DuckDB extension

Function category

Weibull

19 functions

Weibull distribution — flexible shape/scale. Reliability engineering, time-to-failure, wind-speed modeling.

dist_weibull_cdf

Scalar function Weibull
Signature
dist_weibull_cdf( shape: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument shape 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 weibull distribution. Returns the probability that a random variable X is less than or equal to x.

1 Example 1 
SELECT dist_weibull_cdf(1.5, 1.0, 0.5);

Output

dist_weibull_cdf(1.5, 1.0, 0.5)
0.2978114986734404
Related functions

dist_weibull_cdf_complement

Scalar function Weibull
Signature
dist_weibull_cdf_complement( shape: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument shape 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 weibull distribution. Returns the probability that X > x, equivalent to the survival function.

1 Example 1 
SELECT dist_weibull_cdf_complement(1.5, 1.0, 0.5);

Output

dist_weibull_cdf_complement(1.5, 1.0, 0.5)
0.7021885013265596
Related functions

dist_weibull_chf

Scalar function Weibull
Signature
dist_weibull_chf( shape: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument shape 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 weibull distribution.

1 Example 1 
SELECT dist_weibull_chf(1.5, 1.0, 0.5);

Output

dist_weibull_chf(1.5, 1.0, 0.5)
0.35355339059327373
Related functions

dist_weibull_hazard

Scalar function Weibull
Signature
dist_weibull_hazard( shape: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument shape 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 weibull distribution.

1 Example 1 
SELECT dist_weibull_hazard(1.5, 1.0, 0.5);

Output

dist_weibull_hazard(1.5, 1.0, 0.5)
1.0606601717798214
Related functions

dist_weibull_kurtosis

Scalar function Weibull
Signature
dist_weibull_kurtosis(shape: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the kurtosis of the weibull distribution.

1 Example 1 
SELECT dist_weibull_kurtosis(1.5, 1.0);

Output

dist_weibull_kurtosis(1.5, 1.0)
4.3904035615957975
Related functions

dist_weibull_kurtosis_excess

Scalar function Weibull
Signature
dist_weibull_kurtosis_excess(shape: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the excess kurtosis of the weibull distribution.

1 Example 1 
SELECT dist_weibull_kurtosis_excess(1.5, 1.0);

Output

dist_weibull_kurtosis_excess(1.5, 1.0)
1.3904035615957977
Related functions

dist_weibull_log_cdf

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

1 Example 1 
SELECT dist_weibull_log_cdf(1.5, 1.0, 0.5);

Output

dist_weibull_log_cdf(1.5, 1.0, 0.5)
-1.211294547411032
Related functions

dist_weibull_log_cdf_complement

Scalar function Weibull
Signature
dist_weibull_log_cdf_complement( shape: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument shape 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 weibull distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.

1 Example 1 
SELECT dist_weibull_log_cdf_complement(1.5, 1.0, 0.5);

Output

dist_weibull_log_cdf_complement(1.5, 1.0, 0.5)
-0.3535533905932738
Related functions

dist_weibull_log_pdf

Scalar function Weibull
Signature
dist_weibull_log_pdf( shape: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument shape 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 weibull distribution. Useful for numerical stability when dealing with very small probabilities.

1 Example 1 
SELECT dist_weibull_log_pdf(1.5, 1.0, 0.5);

Output

dist_weibull_log_pdf(1.5, 1.0, 0.5)
-0.29466187276508204
Related functions

dist_weibull_median

Scalar function Weibull
Signature
dist_weibull_median(shape: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_weibull_median(1.5, 1.0);

Output

dist_weibull_median(1.5, 1.0)
0.7832197687746514
Related functions

dist_weibull_mode

Scalar function Weibull
Signature
dist_weibull_mode(shape: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_weibull_mode(1.5, 1.0);

Output

dist_weibull_mode(1.5, 1.0)
0.4807498567691361
Related functions

dist_weibull_pdf

Scalar function Weibull
Signature
dist_weibull_pdf( shape: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument shape 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 weibull distribution. Returns the probability densityat point x for a weibull distribution with specified parameters.

1 Example 1 
SELECT dist_weibull_pdf(1.5, 1.0, 0.5);

Output

dist_weibull_pdf(1.5, 1.0, 0.5)
0.7447833764388441
Related functions

dist_weibull_quantile

Scalar function Weibull
Signature
dist_weibull_quantile( shape: DOUBLE, scale: DOUBLE, p: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument shape 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 weibull distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.

1 Example 1 
SELECT dist_weibull_quantile(1.5, 1.0, 0.95);

Output

dist_weibull_quantile(1.5, 1.0, 0.95)
2.0781106375345564
Related functions

dist_weibull_quantile_complement

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

1 Example 1 
SELECT dist_weibull_quantile_complement(1.5, 1.0, 0.05);

Output

dist_weibull_quantile_complement(1.5, 1.0, 0.05)
2.078110637534557
Related functions

dist_weibull_range

Scalar function Weibull
Signature
dist_weibull_range(shape: DOUBLE, scale: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the range of the weibull distribution.

1 Example 1 
SELECT dist_weibull_range(1.5, 1.0);

Output

dist_weibull_range(1.5, 1.0)
(0.0, 1.7976931348623157e+308)
Related functions

dist_weibull_sample

Scalar function Weibull
Signature
dist_weibull_sample(shape: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

Generates random samples from the weibull distribution with specified parameters.

1 Example 1 
SELECT dist_weibull_sample(1.5, 1.0);

Output

dist_weibull_sample(1.5, 1.0)
1.1238833819731295
Related functions

dist_weibull_skewness

Scalar function Weibull
Signature
dist_weibull_skewness(shape: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the skewness of the weibull distribution.

1 Example 1 
SELECT dist_weibull_skewness(1.5, 1.0);

Output

dist_weibull_skewness(1.5, 1.0)
1.0719865728909461
Related functions

dist_weibull_support

Scalar function Weibull
Signature
dist_weibull_support(shape: DOUBLE, scale: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the support of the weibull distribution.

1 Example 1 
SELECT dist_weibull_support(1.5, 1.0);

Output

dist_weibull_support(1.5, 1.0)
(2.2250738585072014e-308, 1.7976931348623157e+308)
Related functions

dist_weibull_variance

Scalar function Weibull
Signature
dist_weibull_variance(shape: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the variance (σ²) of the weibull distribution.

1 Example 1 
SELECT dist_weibull_variance(1.5, 1.0);

Output

dist_weibull_variance(1.5, 1.0)
0.3756902848139321
Related functions