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

# NAME¶

PDL::GSL::CDF - PDL interface to GSL Cumulative Distribution Functions

# DESCRIPTION¶

This is an interface to the Cumulative Distribution Function package present in the GNU Scientific Library.

Let us have a continuous random number distributions are 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 gives 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 defined by the integral of p(x), and gives the probability of a variate taking a value greater than "x". These functions are named cdf_NNNNNNN_Q().

The upper and lower cumulative distribution functions are related by "P(x) + Q(x) = 1" and satisfy "0 <= P(x) <= 1" and "0 <= Q(x) <= 1".

The inverse cumulative distributions, "x = Pinv(P)" and "x = Qinv(Q)" give the values of "x" which correspond to a specific value of "P" or "Q". They can be used to find confidence limits from probability values. These functions are named cdf_NNNNNNN_Pinv() and cdf_NNNNNNN_Qinv().

For 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, 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".

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)".

# SYNOPSIS¶

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

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

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

# 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();  [o]out())
```

gsl_cdf_beta_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_beta_Pinv¶

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

gsl_cdf_beta_Pinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_beta_Q¶

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

gsl_cdf_beta_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_beta_Qinv¶

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

gsl_cdf_beta_Qinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## 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.

## gsl_cdf_binomial_P¶

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

gsl_cdf_binomial_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_binomial_Q¶

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

gsl_cdf_binomial_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## 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();  [o]out())
```

gsl_cdf_cauchy_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_cauchy_Pinv¶

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

gsl_cdf_cauchy_Pinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_cauchy_Q¶

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

gsl_cdf_cauchy_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_cauchy_Qinv¶

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

gsl_cdf_cauchy_Qinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## 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();  [o]out())
```

gsl_cdf_chisq_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_chisq_Pinv¶

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

gsl_cdf_chisq_Pinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_chisq_Q¶

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

gsl_cdf_chisq_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_chisq_Qinv¶

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

gsl_cdf_chisq_Qinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## 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();  [o]out())
```

gsl_cdf_exponential_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_exponential_Pinv¶

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

gsl_cdf_exponential_Pinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_exponential_Q¶

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

gsl_cdf_exponential_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_exponential_Qinv¶

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

gsl_cdf_exponential_Qinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## 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.

## gsl_cdf_exppow_P¶

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

gsl_cdf_exppow_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_exppow_Q¶

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

gsl_cdf_exppow_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## 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();  [o]out())
```

gsl_cdf_fdist_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_fdist_Pinv¶

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

gsl_cdf_fdist_Pinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_fdist_Q¶

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

gsl_cdf_fdist_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_fdist_Qinv¶

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

gsl_cdf_fdist_Qinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## 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.

## gsl_cdf_flat_P¶

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

gsl_cdf_flat_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_flat_Pinv¶

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

gsl_cdf_flat_Pinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_flat_Q¶

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

gsl_cdf_flat_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_flat_Qinv¶

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

gsl_cdf_flat_Qinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## 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();  [o]out())
```

gsl_cdf_gamma_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_gamma_Pinv¶

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

gsl_cdf_gamma_Pinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_gamma_Q¶

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

gsl_cdf_gamma_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_gamma_Qinv¶

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

gsl_cdf_gamma_Qinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## The Gaussian Distribution (gsl_cdf_gaussian_*)¶

These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Gaussian distribution with standard deviation sigma.

## gsl_cdf_gaussian_P¶

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

gsl_cdf_gaussian_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_gaussian_Pinv¶

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

gsl_cdf_gaussian_Pinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_gaussian_Q¶

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

gsl_cdf_gaussian_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_gaussian_Qinv¶

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

gsl_cdf_gaussian_Qinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## The Geometric Distribution (gsl_cdf_geometric_*)¶

These functions 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();  [o]out())
```

gsl_cdf_geometric_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_geometric_Q¶

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

gsl_cdf_geometric_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## The Type-1 Gumbel Distribution (gsl_cdf_gumbel1_*)¶

These functions 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();  [o]out())
```

gsl_cdf_gumbel1_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_gumbel1_Pinv¶

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

gsl_cdf_gumbel1_Pinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_gumbel1_Q¶

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

gsl_cdf_gumbel1_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_gumbel1_Qinv¶

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

gsl_cdf_gumbel1_Qinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## The Type-2 Gumbel Distribution (gsl_cdf_gumbel2_*)¶

These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Type-2 Gumbel distribution with parameters a and b.

## gsl_cdf_gumbel2_P¶

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

gsl_cdf_gumbel2_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_gumbel2_Pinv¶

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

gsl_cdf_gumbel2_Pinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_gumbel2_Q¶

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

gsl_cdf_gumbel2_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_gumbel2_Qinv¶

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

gsl_cdf_gumbel2_Qinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## The Hypergeometric Distribution (gsl_cdf_hypergeometric_*)¶

These functions 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();  [o]out())
```

gsl_cdf_hypergeometric_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_hypergeometric_Q¶

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

gsl_cdf_hypergeometric_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## The Laplace Distribution (gsl_cdf_laplace_*)¶

These functions 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();  [o]out())
```

gsl_cdf_laplace_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_laplace_Pinv¶

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

gsl_cdf_laplace_Pinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_laplace_Q¶

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

gsl_cdf_laplace_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_laplace_Qinv¶

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

gsl_cdf_laplace_Qinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## The Logistic Distribution (gsl_cdf_logistic_*)¶

These functions 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();  [o]out())
```

gsl_cdf_logistic_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_logistic_Pinv¶

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

gsl_cdf_logistic_Pinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_logistic_Q¶

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

gsl_cdf_logistic_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_logistic_Qinv¶

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

gsl_cdf_logistic_Qinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## The Lognormal Distribution (gsl_cdf_lognormal_*)¶

These functions 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();  [o]out())
```

gsl_cdf_lognormal_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_lognormal_Pinv¶

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

gsl_cdf_lognormal_Pinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_lognormal_Q¶

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

gsl_cdf_lognormal_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_lognormal_Qinv¶

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

gsl_cdf_lognormal_Qinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_negative_binomial_P¶

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

gsl_cdf_negative_binomial_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_negative_binomial_Q¶

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

gsl_cdf_negative_binomial_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## The Pareto Distribution (gsl_cdf_pareto_*)¶

These functions 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();  [o]out())
```

gsl_cdf_pareto_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_pareto_Pinv¶

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

gsl_cdf_pareto_Pinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_pareto_Q¶

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

gsl_cdf_pareto_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_pareto_Qinv¶

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

gsl_cdf_pareto_Qinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## The Pascal Distribution (gsl_cdf_pascal_*)¶

These functions 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();  [o]out())
```

gsl_cdf_pascal_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_pascal_Q¶

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

gsl_cdf_pascal_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## The Poisson Distribution (gsl_cdf_poisson_*)¶

These functions compute the cumulative distribution functions P(k), Q(k) for the Poisson distribution with parameter mu.

## gsl_cdf_poisson_P¶

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

gsl_cdf_poisson_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_poisson_Q¶

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

gsl_cdf_poisson_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## The Rayleigh Distribution (gsl_cdf_rayleigh_*)¶

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

## gsl_cdf_rayleigh_P¶

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

gsl_cdf_rayleigh_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_rayleigh_Pinv¶

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

gsl_cdf_rayleigh_Pinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_rayleigh_Q¶

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

gsl_cdf_rayleigh_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_rayleigh_Qinv¶

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

gsl_cdf_rayleigh_Qinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## The t-distribution (gsl_cdf_tdist_*)¶

These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the t-distribution with nu degrees of freedom.

## gsl_cdf_tdist_P¶

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

gsl_cdf_tdist_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_tdist_Pinv¶

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

gsl_cdf_tdist_Pinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_tdist_Q¶

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

gsl_cdf_tdist_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_tdist_Qinv¶

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

gsl_cdf_tdist_Qinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## The Unit Gaussian Distribution (gsl_cdf_ugaussian_*)¶

These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the unit Gaussian distribution.

## gsl_cdf_ugaussian_P¶

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

gsl_cdf_ugaussian_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_ugaussian_Pinv¶

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

gsl_cdf_ugaussian_Pinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_ugaussian_Q¶

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

gsl_cdf_ugaussian_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_ugaussian_Qinv¶

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

gsl_cdf_ugaussian_Qinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## The Weibull Distribution (gsl_cdf_weibull_*)¶

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

## gsl_cdf_weibull_P¶

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

gsl_cdf_weibull_P processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_weibull_Pinv¶

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

gsl_cdf_weibull_Pinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_weibull_Q¶

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

gsl_cdf_weibull_Q processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

## gsl_cdf_weibull_Qinv¶

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

gsl_cdf_weibull_Qinv processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

# AUTHOR¶

Copyright (C) 2009 Maggie J. Xiong <maggiexyz users.sourceforge.net>

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.

 2018-11-02 perl v5.28.0