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DuckDB Extensions All extensions Stochastic

Logistic functions in the Stochastic DuckDB extension

Function category

Logistic

19 functions

Logistic distribution — symmetric S-curve via location/scale. Backbone of logistic regression and Elo-style ratings.

dist_logistic_cdf

Scalar function Logistic
Signature
dist_logistic_cdf( loc: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument loc 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 logistic distribution. Returns the probability that a random variable X is less than or equal to x.

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

Output

dist_logistic_cdf(0, 1.0, 0.5)
0.6224593312018546
Related functions

dist_logistic_cdf_complement

Scalar function Logistic
Signature
dist_logistic_cdf_complement( loc: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument loc 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 logistic distribution. Returns the probability that X > x, equivalent to the survival function.

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

Output

dist_logistic_cdf_complement(0, 1.0, 0.5)
0.3775406687981454
Related functions

dist_logistic_chf

Scalar function Logistic
Signature
dist_logistic_chf( loc: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument loc 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 logistic distribution.

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

Output

dist_logistic_chf(0, 1.0, 0.5)
0.9740769841801068
Related functions

dist_logistic_hazard

Scalar function Logistic
Signature
dist_logistic_hazard( loc: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument loc 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 logistic distribution.

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

Output

dist_logistic_hazard(0, 1.0, 0.5)
0.6224593312018546
Related functions

dist_logistic_kurtosis

Scalar function Logistic
Signature
dist_logistic_kurtosis(loc: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument loc Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the kurtosis of the logistic distribution.

1 Example 1 
SELECT dist_logistic_kurtosis(0.0, 1.0);

Output

dist_logistic_kurtosis(0.0, 1.0)
4.2
Related functions

dist_logistic_kurtosis_excess

Scalar function Logistic
Signature
dist_logistic_kurtosis_excess(loc: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument loc Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the excess kurtosis of the logistic distribution.

1 Example 1 
SELECT dist_logistic_kurtosis_excess(0.0, 1.0);

Output

dist_logistic_kurtosis_excess(0.0, 1.0)
1.2
Related functions

dist_logistic_log_cdf

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

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

Output

dist_logistic_log_cdf(0, 1.0, 0.5)
-0.4740769841801067
Related functions

dist_logistic_log_cdf_complement

Scalar function Logistic
Signature
dist_logistic_log_cdf_complement( loc: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument loc 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 logistic distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.

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

Output

dist_logistic_log_cdf_complement(0, 1.0, 0.5)
-0.9740769841801067
Related functions

dist_logistic_log_pdf

Scalar function Logistic
Signature
dist_logistic_log_pdf( loc: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument loc 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 logistic distribution. Useful for numerical stability when dealing with very small probabilities.

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

Output

dist_logistic_log_pdf(0, 1.0, 0.5)
-1.4481539683602134
Related functions

dist_logistic_median

Scalar function Logistic
Signature
dist_logistic_median(loc: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument loc Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_logistic_median(0.0, 1.0);

Output

dist_logistic_median(0.0, 1.0)
0.0
Related functions

dist_logistic_mode

Scalar function Logistic
Signature
dist_logistic_mode(loc: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument loc Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_logistic_mode(0.0, 1.0);

Output

dist_logistic_mode(0.0, 1.0)
0.0
Related functions

dist_logistic_pdf

Scalar function Logistic
Signature
dist_logistic_pdf( loc: DOUBLE, scale: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument loc 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 logistic distribution. Returns the probability densityat point x for a logistic distribution with specified parameters.

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

Output

dist_logistic_pdf(0, 1.0, 0.5)
0.2350037122015945
Related functions

dist_logistic_quantile

Scalar function Logistic
Signature
dist_logistic_quantile( loc: DOUBLE, scale: DOUBLE, p: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument loc 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 logistic distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.

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

Output

dist_logistic_quantile(0, 1.0, 0.95)
2.9444389791664394
Related functions

dist_logistic_quantile_complement

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

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

Output

dist_logistic_quantile_complement(0, 1.0, 0.95)
-2.9444389791664394
Related functions

dist_logistic_range

Scalar function Logistic
Signature
dist_logistic_range(loc: DOUBLE, scale: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument loc Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the range of the logistic distribution.

1 Example 1 
SELECT dist_logistic_range(0.0, 1.0);

Output

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

dist_logistic_sample

Scalar function Logistic
Signature
dist_logistic_sample(loc: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument loc Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

Generates random samples from the logistic distribution with specified parameters.

1 Example 1 
SELECT dist_logistic_sample(0.0, 1.0);

Output

dist_logistic_sample(0.0, 1.0)
-0.17993445860265622
Related functions

dist_logistic_skewness

Scalar function Logistic
Signature
dist_logistic_skewness(loc: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument loc Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the skewness of the logistic distribution.

1 Example 1 
SELECT dist_logistic_skewness(0.0, 1.0);

Output

dist_logistic_skewness(0.0, 1.0)
0.0
Related functions

dist_logistic_support

Scalar function Logistic
Signature
dist_logistic_support(loc: DOUBLE, scale: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument loc Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the support of the logistic distribution.

1 Example 1 
SELECT dist_logistic_support(0.0, 1.0);

Output

dist_logistic_support(0.0, 1.0)
(-1.7976931348623157e+308, 1.7976931348623157e+308)
Related functions

dist_logistic_variance

Scalar function Logistic
Signature
dist_logistic_variance(loc: DOUBLE, scale: DOUBLE) → DOUBLE
Arguments (Positional)
Argument loc Type DOUBLE Mode Positional Description
Argument scale Type DOUBLE Mode Positional Description
Description

Returns the variance (σ²) of the logistic distribution.

1 Example 1 
SELECT dist_logistic_variance(0.0, 1.0);

Output

dist_logistic_variance(0.0, 1.0)
3.289868133696453
Related functions