CDF(3pm)

📦

version 2.085 · 4 versions

🌸 CDF(3pm) — User Contributed Perl Documentation 🌸

ok so bestie, you've stumbled into CDF(3pm) and honestly? iconic. this is the whole PDL::GSL::CDF situation and i'm gonna walk you through it like we're texting at 2am 💖

✨ NAME ✨

PDL::GSL::CDF — the PDL interface to GSL Cumulative Distribution Functions. that's it. that's the name. we love a clear title 🎀

🦋 DESCRIPTION 🦋

okay so here's the vibe: this is an interface to the Cumulative Distribution Function package that lives inside the GNU Scientific Library. no cap, it's just a little bridge between PDL and GSL's CDF stuff 🫶

so picture this — we have continuous random number distributions, right? they're defined by a probability density function p(x).

the cumulative distribution function for the lower tail P(x) is defined by the integral of p(x), and it gives you the probability of a variate taking a value less than x. these functions are named cdf_NNNNNNN_P(). 💅

the cumulative distribution function for the upper tail Q(x) is also defined by the integral of p(x), and it gives you the probability of a variate taking a value greater than x. these ones are named cdf_NNNNNNN_Q(). ✨

and bestie, the upper and lower cumulative distribution functions are related by P(x) + Q(x) = 1 and they satisfy 0 <= P(x) <= 1 and 0 <= Q(x) <= 1. math said balance, and math meant it 😌

then we have the inverse cumulative distributions — x = Pinv(P) and x = Qinv(Q) — which give you the values of x that correspond to a specific value of P or Q. super useful for finding confidence limits from probability values. these functions are named cdf_NNNNNNN_Pinv() and cdf_NNNNNNN_Qinv(). 🔥

now for the discrete distributions, the probability of sampling the integer value k is given by p(k), where sum_k p(k) = 1. the cumulative distribution for the lower tail P(k) of a discrete distribution is defined as — and this is the key part — where the sum is over the allowed range of the distribution less than or equal to k. 👑

the cumulative distribution for the upper tail of a discrete distribution Q(k) is defined as giving the sum of probabilities for all values greater than k. these two definitions satisfy the identity P(k) + Q(k) = 1. the math is mathing fr fr 💜

and if the range of the distribution is 1 to n inclusive, then P(n) = 1, Q(n) = 0, while P(1) = p(1), Q(1) = 1 - p(1). write that down bestie 📝

🌈 SYNOPSIS 🌈

use PDL;
use PDL::GSL::CDF;

my $p = gsl_cdf_tdist_P( $t, $df );

my $t = gsl_cdf_tdist_Pinv( $p, $df );

look at that. two lines in, two lines out. main character energy 🎀

👑 FUNCTIONS 👑

🍓 The Beta Distribution (`gsl_cdf_beta_*`)

these functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the beta distribution with parameters a and b. 💖

`gsl_cdf_beta_P`

Signature: (double x(); double a(); double b(); double [o]out())

gsl_cdf_beta_P processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. so like, it's got your back 🫶

`gsl_cdf_beta_Pinv`

Signature: (double p(); double a(); double b(); double [o]out())

gsl_cdf_beta_Pinv processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ✨

`gsl_cdf_beta_Q`

Signature: (double x(); double a(); double b(); double [o]out())

gsl_cdf_beta_Q processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 💅

`gsl_cdf_beta_Qinv`

Signature: (double q(); double a(); double b(); double [o]out())

gsl_cdf_beta_Qinv processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 🌸

🦋 The Binomial Distribution (`gsl_cdf_binomial_*`)

these functions compute the cumulative distribution functions P(k), Q(k) for the binomial distribution with parameters p and n. note: no inverses here, bestie, just the two 💜

`gsl_cdf_binomial_P`

Signature: (ushort k(); double p(); ushort n(); double [o]out())

gsl_cdf_binomial_P processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 🔥

`gsl_cdf_binomial_Q`

Signature: (ushort k(); double p(); ushort n(); double [o]out())

gsl_cdf_binomial_Q processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 🎀

💜 The Cauchy Distribution (`gsl_cdf_cauchy_*`)

these functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Cauchy distribution with scale parameter a. 💖

`gsl_cdf_cauchy_P`

Signature: (double x(); double a(); double [o]out())

gsl_cdf_cauchy_P processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ✨

`gsl_cdf_cauchy_Pinv`

Signature: (double p(); double a(); double [o]out())

gsl_cdf_cauchy_Pinv processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 🫶

`gsl_cdf_cauchy_Q`

Signature: (double x(); double a(); double [o]out())

gsl_cdf_cauchy_Q processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 🌈

`gsl_cdf_cauchy_Qinv`

Signature: (double q(); double a(); double [o]out())

gsl_cdf_cauchy_Qinv processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 💅

🌸 The Chi-squared Distribution (`gsl_cdf_chisq_*`)

these functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the chi-squared distribution with nu degrees of freedom. 📊

`gsl_cdf_chisq_P`

Signature: (double x(); double nu(); double [o]out())

gsl_cdf_chisq_P processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 🔥

`gsl_cdf_chisq_Pinv`

Signature: (double p(); double nu(); double [o]out())

gsl_cdf_chisq_Pinv processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 👑

`gsl_cdf_chisq_Q`

Signature: (double x(); double nu(); double [o]out())

gsl_cdf_chisq_Q processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 💜

`gsl_cdf_chisq_Qinv`

Signature: (double q(); double nu(); double [o]out())

gsl_cdf_chisq_Qinv processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 🎀

🧚 The Exponential Distribution (`gsl_cdf_exponential_*`)

these functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the exponential distribution with mean mu. 💖

`gsl_cdf_exponential_P`

Signature: (double x(); double mu(); double [o]out())

gsl_cdf_exponential_P processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ✨

`gsl_cdf_exponential_Pinv`

Signature: (double p(); double mu(); double [o]out())

gsl_cdf_exponential_Pinv processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 🦋

`gsl_cdf_exponential_Q`

Signature: (double x(); double mu(); double [o]out())

gsl_cdf_exponential_Q processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 🌈

`gsl_cdf_exponential_Qinv`

Signature: (double q(); double mu(); double [o]out())

gsl_cdf_exponential_Qinv processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 💅

⭐ The Exponential Power Distribution (`gsl_cdf_exppow_*`)

these functions compute the cumulative distribution functions P(x), Q(x) for the exponential power distribution with parameters a and b. (again — no inverses, just the pair, iykyk) 💜

`gsl_cdf_exppow_P`

Signature: (double x(); double a(); double b(); double [o]out())

gsl_cdf_exppow_P processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 🔥

`gsl_cdf_exppow_Q`

Signature: (double x(); double a(); double b(); double [o]out())

gsl_cdf_exppow_Q processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 🎀

🔥 The F-distribution (`gsl_cdf_fdist_*`)

these functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the F-distribution with nu1 and nu2 degrees of freedom. 💖

`gsl_cdf_fdist_P`

Signature: (double x(); double nua(); double nub(); double [o]out())

gsl_cdf_fdist_P processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ✨

`gsl_cdf_fdist_Pinv`

Signature: (double p(); double nua(); double nub(); double [o]out())

gsl_cdf_fdist_Pinv processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 🫶

`gsl_cdf_fdist_Q`

Signature: (double x(); double nua(); double nub(); double [o]out())

gsl_cdf_fdist_Q processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 🌸

`gsl_cdf_fdist_Qinv`

Signature: (double q(); double nua(); double nub(); double [o]out())

gsl_cdf_fdist_Qinv processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 💅

🌈 The Flat (Uniform) Distribution (`gsl_cdf_flat_*`)

these functions compute the cumulative distribution functions P(x), Q(x) and their inverses for a uniform distribution from a to b. flat. even. no drama. we love her 💜

`gsl_cdf_flat_P`

Signature: (double x(); double a(); double b(); double [o]out())

gsl_cdf_flat_P processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 🔥

`gsl_cdf_flat_Pinv`

Signature: (double p(); double a(); double b(); double [o]out())

gsl_cdf_flat_Pinv processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 👑

`gsl_cdf_flat_Q`

Signature: (double x(); double a(); double b(); double [o]out())

gsl_cdf_flat_Q processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 🎀

`gsl_cdf_flat_Qinv`

Signature: (double q(); double a(); double b(); double [o]out())

gsl_cdf_flat_Qinv processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ✨

🎀 The Gamma Distribution (`gsl_cdf_gamma_*`)

these functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the gamma distribution with parameters a and b. 💖

`gsl_cdf_gamma_P`

Signature: (double x(); double a(); double b(); double [o]out())

gsl_cdf_gamma_P processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 🫶

`gsl_cdf_gamma_Pinv`

Signature: (double p(); double a(); double b(); double [o]out())

gsl_cdf_gamma_Pinv processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 🌈

`gsl_cdf_gamma_Q`

Signature: (double x(); double a(); double b(); double [o]out())

gsl_cdf_gamma_Q processes bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 💅

`gsl_cdf_gamma_Qinv`

Signature: (double q(); double a(); double b(); double [o]out())

okay so gsl_cdf_gamma_Qinv does the bad-value thing too 💅 it processes bad values, and if the bad-value flag is set on any of the input ndarrays, it will set the bad-value flag on all of the output ndarrays. that's just how it rolls, bestie.

✨ The Gaussian Distribution (`gsl_cdf_gaussian_*`) ✨

these ones compute the cumulative distribution functions P(x), Q(x) and their inverses for the Gaussian distribution, with standard deviation sigma. the bell curve!! the moment!! 🔔

`gsl_cdf_gaussian_P`

Signature: (double x(); double sigma(); double [o]out())

gsl_cdf_gaussian_P processes bad values — if the bad-value flag is set for any of the input ndarrays, it sets the bad-value flag of all the output ndarrays. every time. no exceptions. 💀

`gsl_cdf_gaussian_Pinv`

Signature: (double p(); double sigma(); double [o]out())

gsl_cdf_gaussian_Pinv processes bad values. bad-value flag set on any input ndarray → bad-value flag set on all output ndarrays. iconic behaviour, honestly.

`gsl_cdf_gaussian_Q`

Signature: (double x(); double sigma(); double [o]out())

gsl_cdf_gaussian_Q processes bad values, and yes, the bad-value flag of all output ndarrays gets set if the flag is set for any of the input ndarrays. 🦋

`gsl_cdf_gaussian_Qinv`

Signature: (double q(); double sigma(); double [o]out())

gsl_cdf_gaussian_Qinv processes bad values. any input ndarray flagged bad → all output ndarrays flagged bad. it's giving solidarity, fr fr. 🫶

✨ The Geometric Distribution (`gsl_cdf_geometric_*`) ✨

these compute the cumulative distribution functions P(k), Q(k) for the geometric distribution with parameter p. 🌸

`gsl_cdf_geometric_P`

Signature: (ushort k(); double p(); double [o]out())

gsl_cdf_geometric_P processes bad values — bad-value flag set for any input ndarray means it's set for all the output ndarrays too. periodt. 💅

`gsl_cdf_geometric_Q`

Signature: (ushort k(); double p(); double [o]out())

gsl_cdf_geometric_Q processes bad values. flag set on any input → flag set on all outputs. you know the drill, bestie. ✨

✨ The Type-1 Gumbel Distribution (`gsl_cdf_gumbel1_*`) ✨

these compute the cumulative distribution functions P(x), Q(x) and their inverses for the Type-1 Gumbel distribution, with parameters a and b. 🎀

`gsl_cdf_gumbel1_P`

Signature: (double x(); double a(); double b(); double [o]out())

gsl_cdf_gumbel1_P processes bad values: if the bad-value flag is set for any of the input ndarrays, the bad-value flag of all the output ndarrays gets set. 🔥

`gsl_cdf_gumbel1_Pinv`

Signature: (double p(); double a(); double b(); double [o]out())

gsl_cdf_gumbel1_Pinv processes bad values. any flagged input ndarray → every output ndarray flagged. 👑

`gsl_cdf_gumbel1_Q`

Signature: (double x(); double a(); double b(); double [o]out())

gsl_cdf_gumbel1_Q processes bad values, setting the bad-value flag of all output ndarrays whenever the flag is set for any of the input ndarrays. 🌈

`gsl_cdf_gumbel1_Qinv`

Signature: (double q(); double a(); double b(); double [o]out())

gsl_cdf_gumbel1_Qinv processes bad values. same deal — one bad input flag and all the outputs catch it. 💜

✨ The Type-2 Gumbel Distribution (`gsl_cdf_gumbel2_*`) ✨

these compute the cumulative distribution functions P(x), Q(x) and their inverses for the Type-2 Gumbel distribution, with parameters a and b. (yes, there's a type 2. the gumbel franchise is thriving. 🧚)

`gsl_cdf_gumbel2_P`

Signature: (double x(); double a(); double b(); double [o]out())

gsl_cdf_gumbel2_P processes bad values. bad-value flag set for any input ndarray → bad-value flag set for all output ndarrays. ✨

`gsl_cdf_gumbel2_Pinv`

Signature: (double p(); double a(); double b(); double [o]out())

gsl_cdf_gumbel2_Pinv processes bad values — all output ndarrays get the flag if any input ndarray has it. 💅

`gsl_cdf_gumbel2_Q`

Signature: (double x(); double a(); double b(); double [o]out())

gsl_cdf_gumbel2_Q processes bad values, and it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 🍓

`gsl_cdf_gumbel2_Qinv`

Signature: (double q(); double a(); double b(); double [o]out())

gsl_cdf_gumbel2_Qinv processes bad values. one flagged input, all outputs flagged. that's the rule. 😭

✨ The Hypergeometric Distribution (`gsl_cdf_hypergeometric_*`) ✨

these compute the cumulative distribution functions P(k), Q(k) for the hypergeometric distribution with parameters n1, n2 and t. 🎀

`gsl_cdf_hypergeometric_P`

Signature: (ushort k(); ushort na(); ushort nb(); ushort t(); double [o]out())

gsl_cdf_hypergeometric_P processes bad values: the bad-value flag of all output ndarrays is set if the flag is set for any of the input ndarrays. 🌸

`gsl_cdf_hypergeometric_Q`

Signature: (ushort k(); ushort na(); ushort nb(); ushort t(); double [o]out())

gsl_cdf_hypergeometric_Q processes bad values, and yep — any flagged input ndarray means every output ndarray gets flagged. 🦋

✨ The Laplace Distribution (`gsl_cdf_laplace_*`) ✨

these compute the cumulative distribution functions P(x), Q(x) and their inverses for the Laplace distribution with width a. 🌈

`gsl_cdf_laplace_P`

Signature: (double x(); double a(); double [o]out())

gsl_cdf_laplace_P processes bad values. bad-value flag set for any input ndarray → bad-value flag set for all output ndarrays. lowkey the most consistent thing in this whole page. 💀

`gsl_cdf_laplace_Pinv`

Signature: (double p(); double a(); double [o]out())

gsl_cdf_laplace_Pinv processes bad values — all output ndarrays get the bad-value flag if any of the input ndarrays has it. 👑

`gsl_cdf_laplace_Q`

Signature: (double x(); double a(); double [o]out())

gsl_cdf_laplace_Q processes bad values, setting the bad-value flag of all output ndarrays when the flag is set for any input ndarray. ✨

`gsl_cdf_laplace_Qinv`

Signature: (double q(); double a(); double [o]out())

gsl_cdf_laplace_Qinv processes bad values. any bad input flag → all the output flags. no cap. 🫶

✨ The Logistic Distribution (`gsl_cdf_logistic_*`) ✨

these compute the cumulative distribution functions P(x), Q(x) and their inverses for the logistic distribution with scale parameter a. 💜

`gsl_cdf_logistic_P`

Signature: (double x(); double a(); double [o]out())

gsl_cdf_logistic_P processes bad values. bad-value flag set on any input ndarray → bad-value flag set on all output ndarrays. 🧚

`gsl_cdf_logistic_Pinv`

Signature: (double p(); double a(); double [o]out())

gsl_cdf_logistic_Pinv processes bad values — every output ndarray gets the flag if any of the input ndarrays is flagged. 💅

`gsl_cdf_logistic_Q`

Signature: (double x(); double a(); double [o]out())

gsl_cdf_logistic_Q processes bad values, and it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 🍓

`gsl_cdf_logistic_Qinv`

Signature: (double q(); double a(); double [o]out())

gsl_cdf_logistic_Qinv processes bad values. flagged input → flagged outputs, always. 🌸

✨ The Lognormal Distribution (`gsl_cdf_lognormal_*`) ✨

these compute the cumulative distribution functions P(x), Q(x) and their inverses for the lognormal distribution, with parameters zeta and sigma. ⭐

`gsl_cdf_lognormal_P`

Signature: (double x(); double zeta(); double sigma(); double [o]out())

gsl_cdf_lognormal_P processes bad values. if the bad-value flag is set for any of the input ndarrays, it gets set for all of the output ndarrays. 🔥

`gsl_cdf_lognormal_Pinv`

Signature: (double p(); double zeta(); double sigma(); double [o]out())

gsl_cdf_lognormal_Pinv processes bad values — bad-value flag on any input ndarray means bad-value flag on all the output ndarrays. 🌈

`gsl_cdf_lognormal_Q`

Signature: (double x(); double zeta(); double sigma(); double [o]out())

gsl_cdf_lognormal_Q processes bad values, setting the bad-value flag of all output ndarrays whenever the flag is set for any of the input ndarrays. 💜

`gsl_cdf_lognormal_Qinv`

Signature: (double q(); double zeta(); double sigma(); double [o]out())

gsl_cdf_lognormal_Qinv processes bad values. one bad input flag and all the outputs match. it's giving hive mind. 🐝

`gsl_cdf_negative_binomial_P`

Signature: (ushort k(); double p(); double n(); double [o]out())

gsl_cdf_negative_binomial_P processes bad values: the bad-value flag of all output ndarrays is set if the flag is set for any of the input ndarrays. 👑

`gsl_cdf_negative_binomial_Q`

Signature: (ushort k(); double p(); double n(); double [o]out())

gsl_cdf_negative_binomial_Q processes bad values — any flagged input ndarray flags every output ndarray. ✨

✨ The Pareto Distribution (`gsl_cdf_pareto_*`) ✨

these compute the cumulative distribution functions P(x), Q(x) and their inverses for the Pareto distribution with exponent a and scale b. 💅

`gsl_cdf_pareto_P`

Signature: (double x(); double a(); double b(); double [o]out())

gsl_cdf_pareto_P processes bad values. bad-value flag set for any input ndarray → bad-value flag set for all output ndarrays. 🎀

`gsl_cdf_pareto_Pinv`

Signature: (double p(); double a(); double b(); double [o]out())

gsl_cdf_pareto_Pinv processes bad values — all output ndarrays get flagged if any of the input ndarrays is flagged. 🌸

`gsl_cdf_pareto_Q`

Signature: (double x(); double a(); double b(); double [o]out())

gsl_cdf_pareto_Q processes bad values, and yes bestie, the bad-value flag of all output ndarrays gets set if the flag is set for any of the input ndarrays. 🦋

`gsl_cdf_pareto_Qinv`

Signature: (double q(); double a(); double b(); double [o]out())

gsl_cdf_pareto_Qinv processes bad values. flagged input → flagged outputs. always. 😭

✨ The Pascal Distribution (`gsl_cdf_pascal_*`) ✨

these compute the cumulative distribution functions P(k), Q(k) for the Pascal distribution with parameters p and n. ⭐

`gsl_cdf_pascal_P`

Signature: (ushort k(); double p(); ushort n(); double [o]out())

gsl_cdf_pascal_P processes bad values: if the bad-value flag is set for any of the input ndarrays, it will be set for all of the output ndarrays. 🫶

`gsl_cdf_pascal_Q`

Signature: (ushort k(); double p(); ushort n(); double [o]out())

gsl_cdf_pascal_Q processes bad values — bad-value flag on any input ndarray means bad-value flag on every output ndarray. 💜

🍓 The Poisson Distribution (`gsl_cdf_poisson_*`) 🍓

Bestie these ones compute the cumulative distribution functions P(k) and Q(k) for the Poisson distribution, and the parameter is mu. That's it, that's the vibe.

`gsl_cdf_poisson_P`

Signature: (ushort k(); double mu(); double [o]out())

gsl_cdf_poisson_P handles bad values for you, no stress. If the bad-value flag is set on any of the input ndarrays, it sets the bad-value flag on all of the output ndarrays. Every single one. Periodt. 💅

`gsl_cdf_poisson_Q`

Signature: (ushort k(); double mu(); double [o]out())

Same energy, same rules: gsl_cdf_poisson_Q processes bad values, and if the flag is set for any input ndarray, it gets set on all the output ndarrays. 🫶

🦋 The Rayleigh Distribution (`gsl_cdf_rayleigh_*`) 🦋

These compute the cumulative distribution functions P(x), Q(x) and their inverses for the Rayleigh distribution — the scale parameter is sigma. Slay.

`gsl_cdf_rayleigh_P`

Signature: (double x(); double sigma(); double [o]out())

gsl_cdf_rayleigh_P processes bad values. Flag set on any input ndarray → flag set on every output ndarray. That's the deal. ✨

`gsl_cdf_rayleigh_Pinv`

Signature: (double p(); double sigma(); double [o]out())

gsl_cdf_rayleigh_Pinv processes bad values. Any input ndarray flagged → all output ndarrays flagged. Consistent king behavior. 👑

`gsl_cdf_rayleigh_Q`

Signature: (double x(); double sigma(); double [o]out())

gsl_cdf_rayleigh_Q processes bad values. You already know the rule: bad flag on any input, bad flag on all outputs. 💖

`gsl_cdf_rayleigh_Qinv`

Signature: (double q(); double sigma(); double [o]out())

gsl_cdf_rayleigh_Qinv processes bad values. Same exact energy — any input ndarray flagged means all output ndarrays get flagged. 😭

🌸 The t-distribution (`gsl_cdf_tdist_*`) 🌸

These compute the cumulative distribution functions P(x), Q(x) and their inverses for the t-distribution, with nu degrees of freedom. It's giving statistics main character energy, ngl.

`gsl_cdf_tdist_P`

Signature: (double x(); double nu(); double [o]out())

gsl_cdf_tdist_P processes bad values. If the bad-value flag is set for any of the input ndarrays, it sets it for all output ndarrays. Fr fr.

`gsl_cdf_tdist_Pinv`

Signature: (double p(); double nu(); double [o]out())

gsl_cdf_tdist_Pinv processes bad values. Any input ndarray flagged → all output ndarrays flagged. No cap. 🎀

`gsl_cdf_tdist_Q`

Signature: (double x(); double nu(); double [o]out())

gsl_cdf_tdist_Q processes bad values. Bad-value flag on any input ndarray? Then it's on all the output ndarrays too. 💜

`gsl_cdf_tdist_Qinv`

Signature: (double q(); double nu(); double [o]out())

gsl_cdf_tdist_Qinv processes bad values. Flag for any input → flag for all outputs. It's literally the same story every time and honestly? Iconic. 🌈

🧚 The Unit Gaussian Distribution (`gsl_cdf_ugaussian_*`) 🧚

These compute the cumulative distribution functions P(x), Q(x) and their inverses for the unit Gaussian distribution. The blueprint, the original, the moment. ⭐

`gsl_cdf_ugaussian_P`

Signature: (double x(); double [o]out())

gsl_cdf_ugaussian_P processes bad values. Bad-value flag set on any input ndarray → set on all output ndarrays. 🦋

`gsl_cdf_ugaussian_Pinv`

Signature: (double p(); double [o]out())

gsl_cdf_ugaussian_Pinv processes bad values. Any input flagged, all outputs flagged. That's the whole thing. 💅

`gsl_cdf_ugaussian_Q`

Signature: (double x(); double [o]out())

gsl_cdf_ugaussian_Q processes bad values. You know it, bestie — any input ndarray with the flag means every output ndarray gets the flag. 💖

`gsl_cdf_ugaussian_Qinv`

Signature: (double q(); double [o]out())

gsl_cdf_ugaussian_Qinv processes bad values. Flag on any input ndarray → flag on all output ndarrays. Periodt. 🫶

🌟 The Weibull Distribution (`gsl_cdf_weibull_*`) 🌟

These compute the cumulative distribution functions P(x), Q(x) and their inverses for the Weibull distribution — scale is a, exponent is b. Two params, twice the drama. 🔥

`gsl_cdf_weibull_P`

Signature: (double x(); double a(); double b(); double [o]out())

gsl_cdf_weibull_P processes bad values. If the flag is set for any of the input ndarrays, it will set the bad-value flag of all the output ndarrays. 🌸

`gsl_cdf_weibull_Pinv`

Signature: (double p(); double a(); double b(); double [o]out())

gsl_cdf_weibull_Pinv processes bad values. Any input ndarray flagged → all output ndarrays flagged. The consistency?? Obsessed. 😭

`gsl_cdf_weibull_Q`

Signature: (double x(); double a(); double b(); double [o]out())

gsl_cdf_weibull_Q processes bad values. Flag on any input ndarray means flag on all the output ndarrays, every single time. 🎀

`gsl_cdf_weibull_Qinv`

Signature: (double q(); double a(); double b(); double [o]out())

gsl_cdf_weibull_Qinv processes bad values. Same rules, same energy: any input ndarray with the bad-value flag set → all output ndarrays get it set. Go off. 💜

👑 AUTHOR 👑

The GSL CDF module was written by J. Stover.

All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation as described in the file COPYING in the PDL distribution. So like, read COPYING, it's right there, iykyk. 📄✨

And that's a wrap on part three, bestie!! 💖 This page ships as perl v5.38.2, dated 2024-04-10, and yes that footer is giving vintage but she still ate. 🌈🎀 Go compute some CDFs, you're gonna do amazing. 🦋💅

📦 where this page comes from

ubuntu noble: pdl 1:2.085-1ubuntu1 · Artistic-1.0-Perl OR GPL-1.0-or-later
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash on 2026-10-14: a language model's rewrite of the original, under its terms

CDF(3pm)

🌸 CDF(3pm) — User Contributed Perl Documentation 🌸

✨ NAME ✨

🦋 DESCRIPTION 🦋

🌈 SYNOPSIS 🌈

👑 FUNCTIONS 👑

🍓 The Beta Distribution (gsl_cdf_beta_*)

gsl_cdf_beta_P

gsl_cdf_beta_Pinv

gsl_cdf_beta_Q

gsl_cdf_beta_Qinv

🦋 The Binomial Distribution (gsl_cdf_binomial_*)

gsl_cdf_binomial_P

gsl_cdf_binomial_Q

💜 The Cauchy Distribution (gsl_cdf_cauchy_*)

gsl_cdf_cauchy_P

gsl_cdf_cauchy_Pinv

gsl_cdf_cauchy_Q

gsl_cdf_cauchy_Qinv

🌸 The Chi-squared Distribution (gsl_cdf_chisq_*)

gsl_cdf_chisq_P

gsl_cdf_chisq_Pinv

gsl_cdf_chisq_Q

gsl_cdf_chisq_Qinv

🧚 The Exponential Distribution (gsl_cdf_exponential_*)

gsl_cdf_exponential_P

gsl_cdf_exponential_Pinv

gsl_cdf_exponential_Q

gsl_cdf_exponential_Qinv

⭐ The Exponential Power Distribution (gsl_cdf_exppow_*)

gsl_cdf_exppow_P

gsl_cdf_exppow_Q

🔥 The F-distribution (gsl_cdf_fdist_*)

gsl_cdf_fdist_P

gsl_cdf_fdist_Pinv

gsl_cdf_fdist_Q

gsl_cdf_fdist_Qinv

🌈 The Flat (Uniform) Distribution (gsl_cdf_flat_*)

gsl_cdf_flat_P

gsl_cdf_flat_Pinv

gsl_cdf_flat_Q

gsl_cdf_flat_Qinv

🎀 The Gamma Distribution (gsl_cdf_gamma_*)

gsl_cdf_gamma_P

gsl_cdf_gamma_Pinv

gsl_cdf_gamma_Q

gsl_cdf_gamma_Qinv

✨ The Gaussian Distribution (gsl_cdf_gaussian_*) ✨

gsl_cdf_gaussian_P

gsl_cdf_gaussian_Pinv

gsl_cdf_gaussian_Q

gsl_cdf_gaussian_Qinv

✨ The Geometric Distribution (gsl_cdf_geometric_*) ✨

gsl_cdf_geometric_P

gsl_cdf_geometric_Q

✨ The Type-1 Gumbel Distribution (gsl_cdf_gumbel1_*) ✨

gsl_cdf_gumbel1_P

gsl_cdf_gumbel1_Pinv

gsl_cdf_gumbel1_Q

gsl_cdf_gumbel1_Qinv

✨ The Type-2 Gumbel Distribution (gsl_cdf_gumbel2_*) ✨

gsl_cdf_gumbel2_P

gsl_cdf_gumbel2_Pinv

gsl_cdf_gumbel2_Q

gsl_cdf_gumbel2_Qinv

✨ The Hypergeometric Distribution (gsl_cdf_hypergeometric_*) ✨

gsl_cdf_hypergeometric_P

gsl_cdf_hypergeometric_Q

✨ The Laplace Distribution (gsl_cdf_laplace_*) ✨

gsl_cdf_laplace_P

gsl_cdf_laplace_Pinv

gsl_cdf_laplace_Q

gsl_cdf_laplace_Qinv

✨ The Logistic Distribution (gsl_cdf_logistic_*) ✨

gsl_cdf_logistic_P

gsl_cdf_logistic_Pinv

gsl_cdf_logistic_Q

gsl_cdf_logistic_Qinv

✨ The Lognormal Distribution (gsl_cdf_lognormal_*) ✨

gsl_cdf_lognormal_P