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DuckDB Extensions All extensions Stochastic

Exponential functions in the Stochastic DuckDB extension

Function category

Exponential

21 functions

Exponential distribution — memoryless waiting time between events at rate λ. Survival analysis and reliability.

dist_exponential_cdf

Scalar function Exponential
Signature
dist_exponential_cdf(rate: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_exponential_cdf(1.0, 0.5);

Output

dist_exponential_cdf(1.0, 0.5)
0.3934693402873666
Related functions

dist_exponential_cdf_complement

Scalar function Exponential
Signature
dist_exponential_cdf_complement(rate: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the complementary cumulative distribution function (1 - CDF) of the exponential distribution. Returns the probability that X > x, equivalent to the survival function.

1 Example 1 
SELECT dist_exponential_cdf_complement(1.0, 0.5);

Output

dist_exponential_cdf_complement(1.0, 0.5)
0.6065306597126334
Related functions

dist_exponential_chf

Scalar function Exponential
Signature
dist_exponential_chf(rate: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the cumulative hazard function of the exponential distribution.

1 Example 1 
SELECT dist_exponential_chf(1.0, 0.5);

Output

dist_exponential_chf(1.0, 0.5)
0.5
Related functions

dist_exponential_hazard

Scalar function Exponential
Signature
dist_exponential_hazard(rate: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the hazard function of the exponential distribution.

1 Example 1 
SELECT dist_exponential_hazard(1.0, 0.5);

Output

dist_exponential_hazard(1.0, 0.5)
1.0
Related functions

dist_exponential_kurtosis

Scalar function Exponential
Signature
dist_exponential_kurtosis(rate: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

Returns the kurtosis of the exponential distribution.

1 Example 1 
SELECT dist_exponential_kurtosis(1.0);

Output

dist_exponential_kurtosis(1.0)
9.0
Related functions

dist_exponential_kurtosis_excess

Scalar function Exponential
Signature
dist_exponential_kurtosis_excess(rate: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

Returns the excess kurtosis of the exponential distribution.

1 Example 1 
SELECT dist_exponential_kurtosis_excess(1.0);

Output

dist_exponential_kurtosis_excess(1.0)
6.0
Related functions

dist_exponential_log_cdf

Scalar function Exponential
Signature
dist_exponential_log_cdf(rate: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate 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 exponential distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.

1 Example 1 
SELECT dist_exponential_log_cdf(1.0, 0.5);

Output

dist_exponential_log_cdf(1.0, 0.5)
-0.9327521295671886
Related functions

dist_exponential_log_cdf_complement

Scalar function Exponential
Signature
dist_exponential_log_cdf_complement(rate: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate 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 exponential distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.

1 Example 1 
SELECT dist_exponential_log_cdf_complement(1.0, 0.5);

Output

dist_exponential_log_cdf_complement(1.0, 0.5)
-0.5
Related functions

dist_exponential_log_pdf

Scalar function Exponential
Signature
dist_exponential_log_pdf(rate: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate 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 exponential distribution. Useful for numerical stability when dealing with very small probabilities.

1 Example 1 
SELECT dist_exponential_log_pdf(1.0, 0.5);

Output

dist_exponential_log_pdf(1.0, 0.5)
-0.5
Related functions

dist_exponential_mean

Scalar function Exponential
Signature
dist_exponential_mean(rate: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_exponential_mean(1.0);

Output

dist_exponential_mean(1.0)
1.0
Related functions

dist_exponential_median

Scalar function Exponential
Signature
dist_exponential_median(rate: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_exponential_median(1.0);

Output

dist_exponential_median(1.0)
0.6931471805599453
Related functions

dist_exponential_mode

Scalar function Exponential
Signature
dist_exponential_mode(rate: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_exponential_mode(1.0);

Output

dist_exponential_mode(1.0)
0.0
Related functions

dist_exponential_pdf

Scalar function Exponential
Signature
dist_exponential_pdf(rate: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_exponential_pdf(1.0, 0.5);

Output

dist_exponential_pdf(1.0, 0.5)
0.6065306597126334
Related functions

dist_exponential_quantile

Scalar function Exponential
Signature
dist_exponential_quantile(rate: DOUBLE, p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_exponential_quantile(1.0, 0.95);

Output

dist_exponential_quantile(1.0, 0.95)
2.99573227355399
Related functions

dist_exponential_quantile_complement

Scalar function Exponential
Signature
dist_exponential_quantile_complement(rate: DOUBLE, p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_exponential_quantile_complement(1.0, 0.05);

Output

dist_exponential_quantile_complement(1.0, 0.05)
2.995732273553991
Related functions

dist_exponential_range

Scalar function Exponential
Signature
dist_exponential_range(rate: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

Returns the range of the exponential distribution.

1 Example 1 
SELECT dist_exponential_range(1.0);

Output

dist_exponential_range(1.0)
(0.0, inf)
Related functions

dist_exponential_sample

Scalar function Exponential
Signature
dist_exponential_sample(rate: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

Generates random samples from the exponential distribution with specified parameters.

1 Example 1 
SELECT dist_exponential_sample(1.0);

Output

dist_exponential_sample(1.0)
1.0694970905789465
Related functions

dist_exponential_skewness

Scalar function Exponential
Signature
dist_exponential_skewness(rate: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

Returns the skewness of the exponential distribution.

1 Example 1 
SELECT dist_exponential_skewness(1.0);

Output

dist_exponential_skewness(1.0)
2.0
Related functions

dist_exponential_stddev

Scalar function Exponential
Signature
dist_exponential_stddev(rate: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_exponential_stddev(1.0);

Output

dist_exponential_stddev(1.0)
1.0
Related functions

dist_exponential_support

Scalar function Exponential
Signature
dist_exponential_support(rate: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

Returns the support of the exponential distribution.

1 Example 1 
SELECT dist_exponential_support(1.0);

Output

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

dist_exponential_variance

Scalar function Exponential
Signature
dist_exponential_variance(rate: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

Returns the variance (σ²) of the exponential distribution.

1 Example 1 
SELECT dist_exponential_variance(1.0);

Output

dist_exponential_variance(1.0)
1.0
Related functions