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DuckDB Extensions All extensions Stochastic

Student's t functions in the Stochastic DuckDB extension

Function category

Student's t

21 functions

Student's t — heavier-tailed alternative to Normal, parameterized by degrees of freedom. Small-sample inference.

dist_students_t_cdf

Scalar function Student's t
Signature
dist_students_t_cdf(degrees_of_freedom: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_students_t_cdf(10, 1.5);

Output

dist_students_t_cdf(10, 1.5)
0.9177463367772799
Related functions

dist_students_t_cdf_complement

Scalar function Student's t
Signature
dist_students_t_cdf_complement(degrees_of_freedom: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_students_t_cdf_complement(10, 1.5);

Output

dist_students_t_cdf_complement(10, 1.5)
0.08225366322272007
Related functions

dist_students_t_chf

Scalar function Student's t
Signature
dist_students_t_chf(degrees_of_freedom: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the cumulative hazard function of the students_t distribution.

1 Example 1 
SELECT dist_students_t_chf(10, 1.5);

Output

dist_students_t_chf(10, 1.5)
2.497947352666178
Related functions

dist_students_t_hazard

Scalar function Student's t
Signature
dist_students_t_hazard(degrees_of_freedom: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the hazard function of the students_t distribution.

1 Example 1 
SELECT dist_students_t_hazard(10, 1.5);

Output

dist_students_t_hazard(10, 1.5)
1.5494117744276812
Related functions

dist_students_t_kurtosis

Scalar function Student's t
Signature
dist_students_t_kurtosis(degrees_of_freedom: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

Returns the kurtosis of the students_t distribution.

1 Example 1 
SELECT dist_students_t_kurtosis(10);

Output

dist_students_t_kurtosis(10)
4.0
Related functions

dist_students_t_kurtosis_excess

Scalar function Student's t
Signature
dist_students_t_kurtosis_excess(degrees_of_freedom: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

Returns the excess kurtosis of the students_t distribution.

1 Example 1 
SELECT dist_students_t_kurtosis_excess(10);

Output

dist_students_t_kurtosis_excess(10)
1.0
Related functions

dist_students_t_log_cdf

Scalar function Student's t
Signature
dist_students_t_log_cdf(degrees_of_freedom: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom 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 students_t distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.

1 Example 1 
SELECT dist_students_t_log_cdf(10, 1.5);

Output

dist_students_t_log_cdf(10, 1.5)
-0.08583424813886927
Related functions

dist_students_t_log_cdf_complement

Scalar function Student's t
Signature
dist_students_t_log_cdf_complement(degrees_of_freedom: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom 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 students_t distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.

1 Example 1 
SELECT dist_students_t_log_cdf_complement(10, 1.5);

Output

dist_students_t_log_cdf_complement(10, 1.5)
-2.497947352666178
Related functions

dist_students_t_log_pdf

Scalar function Student's t
Signature
dist_students_t_log_pdf(degrees_of_freedom: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom 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 students_t distribution. Useful for numerical stability when dealing with very small probabilities.

1 Example 1 
SELECT dist_students_t_log_pdf(10, 1.5);

Output

dist_students_t_log_pdf(10, 1.5)
-2.0600719941327497
Related functions

dist_students_t_mean

Scalar function Student's t
Signature
dist_students_t_mean(degrees_of_freedom: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_students_t_mean(10);

Output

dist_students_t_mean(10)
0.0
Related functions

dist_students_t_median

Scalar function Student's t
Signature
dist_students_t_median(degrees_of_freedom: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_students_t_median(10);

Output

dist_students_t_median(10)
0.0
Related functions

dist_students_t_mode

Scalar function Student's t
Signature
dist_students_t_mode(degrees_of_freedom: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_students_t_mode(10);

Output

dist_students_t_mode(10)
0.0
Related functions

dist_students_t_pdf

Scalar function Student's t
Signature
dist_students_t_pdf(degrees_of_freedom: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_students_t_pdf(10, 1.5);

Output

dist_students_t_pdf(10, 1.5)
0.1274447942870916
Related functions

dist_students_t_quantile

Scalar function Student's t
Signature
dist_students_t_quantile(degrees_of_freedom: DOUBLE, p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_students_t_quantile(10, 0.95);

Output

dist_students_t_quantile(10, 0.95)
1.812461122811676
Related functions

dist_students_t_quantile_complement

Scalar function Student's t
Signature
dist_students_t_quantile_complement(degrees_of_freedom: DOUBLE, p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_students_t_quantile_complement(10, 0.05);

Output

dist_students_t_quantile_complement(10, 0.05)
1.8124611228116767
Related functions

dist_students_t_range

Scalar function Student's t
Signature
dist_students_t_range(degrees_of_freedom: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

Returns the range of the students_t distribution.

1 Example 1 
SELECT dist_students_t_range(10);

Output

dist_students_t_range(10)
(-inf, inf)
Related functions

dist_students_t_sample

Scalar function Student's t
Signature
dist_students_t_sample(degrees_of_freedom: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

Generates random samples from the students_t distribution with specified parameters.

1 Example 1 
SELECT dist_students_t_sample(10);

Output

dist_students_t_sample(10)
-0.5258729282048364
Related functions

dist_students_t_skewness

Scalar function Student's t
Signature
dist_students_t_skewness(degrees_of_freedom: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

Returns the skewness of the students_t distribution.

1 Example 1 
SELECT dist_students_t_skewness(10);

Output

dist_students_t_skewness(10)
0.0
Related functions

dist_students_t_stddev

Scalar function Student's t
Signature
dist_students_t_stddev(degrees_of_freedom: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_students_t_stddev(10);

Output

dist_students_t_stddev(10)
1.118033988749895
Related functions

dist_students_t_support

Scalar function Student's t
Signature
dist_students_t_support(degrees_of_freedom: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

Returns the support of the students_t distribution.

1 Example 1 
SELECT dist_students_t_support(10);

Output

dist_students_t_support(10)
(-inf, inf)
Related functions

dist_students_t_variance

Scalar function Student's t
Signature
dist_students_t_variance(degrees_of_freedom: DOUBLE) → DOUBLE
Arguments (Positional)
Argument degrees_of_freedom Type DOUBLE Mode Positional Description
Description

Returns the variance (σ²) of the students_t distribution.

1 Example 1 
SELECT dist_students_t_variance(10);

Output

dist_students_t_variance(10)
1.25
Related functions