Uniform (Integer) functions in the Stochastic DuckDB extension

P(X <= x) for the inclusive integer support [min, max]. For integers inside the support this is (x - min + 1) / (max - min + 1).

This describes the corrected v1.5 source dated October 7, 2026. Older community builds (including 234c881) have incorrect continuous-uniform analytics and truncated BIGINT moments. Bounds remain DOUBLE arguments but must be finite BIGINT-valued integers with min <= max.

P(X > x) for the inclusive integer support, computed directly for the upper tail.

This describes the corrected v1.5 source dated October 7, 2026. Older community builds (including 234c881) have incorrect continuous-uniform analytics and truncated BIGINT moments. Bounds remain DOUBLE arguments but must be finite BIGINT-valued integers with min <= max.

Cumulative hazard -ln(P(X > x)). Returns positive infinity at or above max.

This describes the corrected v1.5 source dated October 7, 2026. Older community builds (including 234c881) have incorrect continuous-uniform analytics and truncated BIGINT moments. Bounds remain DOUBLE arguments but must be finite BIGINT-valued integers with min <= max.

Discrete hazard P(X = x) / P(X >= x). Returns 0 below min and 1 at max; undefined above max (raises an error).

This describes the corrected v1.5 source dated October 7, 2026. Older community builds (including 234c881) have incorrect continuous-uniform analytics and truncated BIGINT moments. Bounds remain DOUBLE arguments but must be finite BIGINT-valued integers with min <= max.

Kurtosis of the inclusive discrete uniform distribution. Undefined for equal bounds (zero variance).

This describes the corrected v1.5 source dated October 7, 2026. Older community builds (including 234c881) have incorrect continuous-uniform analytics and truncated BIGINT moments. Bounds remain DOUBLE arguments but must be finite BIGINT-valued integers with min <= max.

Excess kurtosis of the inclusive discrete uniform distribution. Undefined for equal bounds (zero variance).

This describes the corrected v1.5 source dated October 7, 2026. Older community builds (including 234c881) have incorrect continuous-uniform analytics and truncated BIGINT moments. Bounds remain DOUBLE arguments but must be finite BIGINT-valued integers with min <= max.

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

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

Natural logarithm of the discrete probability mass. Outside the inclusive integer support, returns negative infinity.

This describes the corrected v1.5 source dated October 7, 2026. Older community builds (including 234c881) have incorrect continuous-uniform analytics and truncated BIGINT moments. Bounds remain DOUBLE arguments but must be finite BIGINT-valued integers with min <= max.

Mean of the inclusive discrete uniform distribution: (min + max) / 2, returned as DOUBLE.

This describes the corrected v1.5 source dated October 7, 2026. Older community builds (including 234c881) have incorrect continuous-uniform analytics and truncated BIGINT moments. Bounds remain DOUBLE arguments but must be finite BIGINT-valued integers with min <= max.

Midpoint (min + max) / 2, returned as DOUBLE. With an even number of outcomes this can be fractional; _quantile(..., 0.5) returns the lower central integer.

This describes the corrected v1.5 source dated October 7, 2026. Older community builds (including 234c881) have incorrect continuous-uniform analytics and truncated BIGINT moments. Bounds remain DOUBLE arguments but must be finite BIGINT-valued integers with min <= max.

Returns min as a representative mode. Every integer in the inclusive support has the same probability mass.

This describes the corrected v1.5 source dated October 7, 2026. Older community builds (including 234c881) have incorrect continuous-uniform analytics and truncated BIGINT moments. Bounds remain DOUBLE arguments but must be finite BIGINT-valued integers with min <= max.

Probability mass P(X = x) on the inclusive integer support [min, max]: 1 / (max - min + 1) inside the support and 0 outside.

This describes the corrected v1.5 source dated October 7, 2026. Older community builds (including 234c881) have incorrect continuous-uniform analytics and truncated BIGINT moments. Bounds remain DOUBLE arguments but must be finite BIGINT-valued integers with min <= max.

Smallest supported integer whose CDF is at least p. At p = 0 returns min; at p = 1 returns max. The probability must be finite and between 0 and 1.

This describes the corrected v1.5 source dated October 7, 2026. Older community builds (including 234c881) have incorrect continuous-uniform analytics and truncated BIGINT moments. Bounds remain DOUBLE arguments but must be finite BIGINT-valued integers with min <= max. The probability uses its exact binary DOUBLE value, without epsilon snapping at probability-mass boundaries.

Smallest supported integer whose upper-tail probability P(X > x) is at most p. At p = 0 returns max; at p = 1 returns min.

This describes the corrected v1.5 source dated October 7, 2026. Older community builds (including 234c881) have incorrect continuous-uniform analytics and truncated BIGINT moments. Bounds remain DOUBLE arguments but must be finite BIGINT-valued integers with min <= max. The probability uses its exact binary DOUBLE value, without epsilon snapping at probability-mass boundaries.

Returns the range of the uniform_int distribution.

Generates random samples from the uniform_int distribution with specified parameters.

Returns 0 for a nondegenerate discrete uniform distribution. Undefined for equal bounds (zero variance).

This describes the corrected v1.5 source dated October 7, 2026. Older community builds (including 234c881) have incorrect continuous-uniform analytics and truncated BIGINT moments. Bounds remain DOUBLE arguments but must be finite BIGINT-valued integers with min <= max.

Square root of the discrete uniform variance, returned as DOUBLE.

This describes the corrected v1.5 source dated October 7, 2026. Older community builds (including 234c881) have incorrect continuous-uniform analytics and truncated BIGINT moments. Bounds remain DOUBLE arguments but must be finite BIGINT-valued integers with min <= max.

Returns the support of the uniform_int distribution.

Variance of the inclusive discrete uniform distribution: ((max - min + 1)^2 - 1) / 12, returned as DOUBLE.

This describes the corrected v1.5 source dated October 7, 2026. Older community builds (including 234c881) have incorrect continuous-uniform analytics and truncated BIGINT moments. Bounds remain DOUBLE arguments but must be finite BIGINT-valued integers with min <= max.