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.\" ========================================================================
.\"
.IX Title "CDF 3pm"
.TH CDF 3pm "2020-12-20" "perl v5.32.0" "User Contributed Perl Documentation"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
.if n .ad l
.nh
.SH "NAME"
PDL::GSL::CDF \- PDL interface to GSL Cumulative Distribution Functions
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
This is an interface to the Cumulative Distribution Function package present in the \s-1GNU\s0 Scientific Library.
.PP
Let us have a continuous random number distributions are defined by a probability density function \f(CWp(x)\fR.
.PP
The cumulative distribution function for the lower tail \f(CWP(x)\fR is defined by the integral of \f(CWp(x)\fR, and
gives the probability of a variate taking a value less than \f(CW\*(C`x\*(C'\fR. These functions are named \fB\fBcdf_NNNNNNN_P()\fB\fR.
.PP
The cumulative distribution function for the upper tail \f(CWQ(x)\fR is defined by the integral of \f(CWp(x)\fR, and
gives the probability of a variate taking a value greater than \f(CW\*(C`x\*(C'\fR. These functions are named \fB\fBcdf_NNNNNNN_Q()\fB\fR.
.PP
The upper and lower cumulative distribution functions are related by \f(CW\*(C`P(x) + Q(x) = 1\*(C'\fR and
satisfy \f(CW\*(C`0 <= P(x) <= 1\*(C'\fR and \f(CW\*(C`0 <= Q(x) <= 1\*(C'\fR.
.PP
The inverse cumulative distributions, \f(CW\*(C`x = Pinv(P)\*(C'\fR and \f(CW\*(C`x = Qinv(Q)\*(C'\fR give the values of \f(CW\*(C`x\*(C'\fR which correspond
to a specific value of \f(CW\*(C`P\*(C'\fR or \f(CW\*(C`Q\*(C'\fR. They can be used to find confidence limits from probability values.
These functions are named \fB\fBcdf_NNNNNNN_Pinv()\fB\fR and \fB\fBcdf_NNNNNNN_Qinv()\fB\fR.
.PP
For discrete distributions the probability of sampling the integer value \f(CW\*(C`k\*(C'\fR is given by \f(CWp(k)\fR, where
\&\f(CW\*(C`sum_k p(k) = 1\*(C'\fR. The cumulative distribution for the lower tail \f(CWP(k)\fR of a discrete distribution is
defined as, where the sum is over the allowed range of the distribution less than or equal to \f(CW\*(C`k\*(C'\fR.
.PP
The cumulative distribution for the upper tail of a discrete distribution \f(CWQ(k)\fR is defined as giving the sum
of probabilities for all values greater than \f(CW\*(C`k\*(C'\fR. These two definitions satisfy the identity \f(CW\*(C`P(k) + Q(k) = 1\*(C'\fR.
.PP
If the range of the distribution is \f(CW1\fR to \f(CW\*(C`n\*(C'\fR inclusive then \f(CW\*(C`P(n) = 1\*(C'\fR, \f(CW\*(C`Q(n) = 0\*(C'\fR
while \f(CW\*(C`P(1) = p(1)\*(C'\fR, \f(CW\*(C`Q(1) = 1 \- p(1)\*(C'\fR.
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 2
\&    use PDL;
\&    use PDL::GSL::CDF;
\&
\&    my $p = gsl_cdf_tdist_P( $t, $df );
\&
\&    my $t = gsl_cdf_tdist_Pinv( $p, $df );
.Ve
.SH "FUNCTIONS"
.IX Header "FUNCTIONS"
.SS "The Beta Distribution (gsl_cdf_beta_*)"
.IX Subsection "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 \fIa\fR and \fIb\fR.
.SS "gsl_cdf_beta_P"
.IX Subsection "gsl_cdf_beta_P"
.Vb 1
\&  Signature: (double x(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_beta_Pinv"
.IX Subsection "gsl_cdf_beta_Pinv"
.Vb 1
\&  Signature: (double p(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_beta_Q"
.IX Subsection "gsl_cdf_beta_Q"
.Vb 1
\&  Signature: (double x(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_beta_Qinv"
.IX Subsection "gsl_cdf_beta_Qinv"
.Vb 1
\&  Signature: (double q(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "The Binomial Distribution (gsl_cdf_binomial_*)"
.IX Subsection "The Binomial Distribution (gsl_cdf_binomial_*)"
These functions compute the cumulative distribution functions P(k), Q(k) for the binomial distribution with parameters \fIp\fR and \fIn\fR.
.SS "gsl_cdf_binomial_P"
.IX Subsection "gsl_cdf_binomial_P"
.Vb 1
\&  Signature: (ushort k(); double p(); ushort n();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_binomial_Q"
.IX Subsection "gsl_cdf_binomial_Q"
.Vb 1
\&  Signature: (ushort k(); double p(); ushort n();  [o]out())
.Ve
.PP
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.
.SS "The Cauchy Distribution (gsl_cdf_cauchy_*)"
.IX Subsection "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 \fIa\fR.
.SS "gsl_cdf_cauchy_P"
.IX Subsection "gsl_cdf_cauchy_P"
.Vb 1
\&  Signature: (double x(); double a();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_cauchy_Pinv"
.IX Subsection "gsl_cdf_cauchy_Pinv"
.Vb 1
\&  Signature: (double p(); double a();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_cauchy_Q"
.IX Subsection "gsl_cdf_cauchy_Q"
.Vb 1
\&  Signature: (double x(); double a();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_cauchy_Qinv"
.IX Subsection "gsl_cdf_cauchy_Qinv"
.Vb 1
\&  Signature: (double q(); double a();  [o]out())
.Ve
.PP
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.
.SS "The Chi-squared Distribution (gsl_cdf_chisq_*)"
.IX Subsection "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 \fInu\fR degrees of freedom.
.SS "gsl_cdf_chisq_P"
.IX Subsection "gsl_cdf_chisq_P"
.Vb 1
\&  Signature: (double x(); double nu();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_chisq_Pinv"
.IX Subsection "gsl_cdf_chisq_Pinv"
.Vb 1
\&  Signature: (double p(); double nu();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_chisq_Q"
.IX Subsection "gsl_cdf_chisq_Q"
.Vb 1
\&  Signature: (double x(); double nu();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_chisq_Qinv"
.IX Subsection "gsl_cdf_chisq_Qinv"
.Vb 1
\&  Signature: (double q(); double nu();  [o]out())
.Ve
.PP
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.
.SS "The Exponential Distribution (gsl_cdf_exponential_*)"
.IX Subsection "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 \fImu\fR.
.SS "gsl_cdf_exponential_P"
.IX Subsection "gsl_cdf_exponential_P"
.Vb 1
\&  Signature: (double x(); double mu();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_exponential_Pinv"
.IX Subsection "gsl_cdf_exponential_Pinv"
.Vb 1
\&  Signature: (double p(); double mu();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_exponential_Q"
.IX Subsection "gsl_cdf_exponential_Q"
.Vb 1
\&  Signature: (double x(); double mu();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_exponential_Qinv"
.IX Subsection "gsl_cdf_exponential_Qinv"
.Vb 1
\&  Signature: (double q(); double mu();  [o]out())
.Ve
.PP
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.
.SS "The Exponential Power Distribution (gsl_cdf_exppow_*)"
.IX Subsection "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 \fIa\fR and \fIb\fR.
.SS "gsl_cdf_exppow_P"
.IX Subsection "gsl_cdf_exppow_P"
.Vb 1
\&  Signature: (double x(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_exppow_Q"
.IX Subsection "gsl_cdf_exppow_Q"
.Vb 1
\&  Signature: (double x(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "The F\-distribution (gsl_cdf_fdist_*)"
.IX Subsection "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 \fInu1\fR and \fInu2\fR degrees of freedom.
.SS "gsl_cdf_fdist_P"
.IX Subsection "gsl_cdf_fdist_P"
.Vb 1
\&  Signature: (double x(); double nua(); double nub();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_fdist_Pinv"
.IX Subsection "gsl_cdf_fdist_Pinv"
.Vb 1
\&  Signature: (double p(); double nua(); double nub();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_fdist_Q"
.IX Subsection "gsl_cdf_fdist_Q"
.Vb 1
\&  Signature: (double x(); double nua(); double nub();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_fdist_Qinv"
.IX Subsection "gsl_cdf_fdist_Qinv"
.Vb 1
\&  Signature: (double q(); double nua(); double nub();  [o]out())
.Ve
.PP
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.
.SS "The Flat (Uniform) Distribution (gsl_cdf_flat_*)"
.IX Subsection "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 \fIa\fR to \fIb\fR.
.SS "gsl_cdf_flat_P"
.IX Subsection "gsl_cdf_flat_P"
.Vb 1
\&  Signature: (double x(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_flat_Pinv"
.IX Subsection "gsl_cdf_flat_Pinv"
.Vb 1
\&  Signature: (double p(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_flat_Q"
.IX Subsection "gsl_cdf_flat_Q"
.Vb 1
\&  Signature: (double x(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_flat_Qinv"
.IX Subsection "gsl_cdf_flat_Qinv"
.Vb 1
\&  Signature: (double q(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "The Gamma Distribution (gsl_cdf_gamma_*)"
.IX Subsection "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 \fIa\fR and \fIb\fR.
.SS "gsl_cdf_gamma_P"
.IX Subsection "gsl_cdf_gamma_P"
.Vb 1
\&  Signature: (double x(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_gamma_Pinv"
.IX Subsection "gsl_cdf_gamma_Pinv"
.Vb 1
\&  Signature: (double p(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_gamma_Q"
.IX Subsection "gsl_cdf_gamma_Q"
.Vb 1
\&  Signature: (double x(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_gamma_Qinv"
.IX Subsection "gsl_cdf_gamma_Qinv"
.Vb 1
\&  Signature: (double q(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "The Gaussian Distribution (gsl_cdf_gaussian_*)"
.IX Subsection "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 \fIsigma\fR.
.SS "gsl_cdf_gaussian_P"
.IX Subsection "gsl_cdf_gaussian_P"
.Vb 1
\&  Signature: (double x(); double sigma();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_gaussian_Pinv"
.IX Subsection "gsl_cdf_gaussian_Pinv"
.Vb 1
\&  Signature: (double p(); double sigma();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_gaussian_Q"
.IX Subsection "gsl_cdf_gaussian_Q"
.Vb 1
\&  Signature: (double x(); double sigma();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_gaussian_Qinv"
.IX Subsection "gsl_cdf_gaussian_Qinv"
.Vb 1
\&  Signature: (double q(); double sigma();  [o]out())
.Ve
.PP
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.
.SS "The Geometric Distribution (gsl_cdf_geometric_*)"
.IX Subsection "The Geometric Distribution (gsl_cdf_geometric_*)"
These functions compute the cumulative distribution functions P(k), Q(k) for the geometric distribution with parameter \fIp\fR.
.SS "gsl_cdf_geometric_P"
.IX Subsection "gsl_cdf_geometric_P"
.Vb 1
\&  Signature: (ushort k(); double p();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_geometric_Q"
.IX Subsection "gsl_cdf_geometric_Q"
.Vb 1
\&  Signature: (ushort k(); double p();  [o]out())
.Ve
.PP
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.
.SS "The Type\-1 Gumbel Distribution (gsl_cdf_gumbel1_*)"
.IX Subsection "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 \fIa\fR and \fIb\fR.
.SS "gsl_cdf_gumbel1_P"
.IX Subsection "gsl_cdf_gumbel1_P"
.Vb 1
\&  Signature: (double x(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_gumbel1_Pinv"
.IX Subsection "gsl_cdf_gumbel1_Pinv"
.Vb 1
\&  Signature: (double p(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_gumbel1_Q"
.IX Subsection "gsl_cdf_gumbel1_Q"
.Vb 1
\&  Signature: (double x(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_gumbel1_Qinv"
.IX Subsection "gsl_cdf_gumbel1_Qinv"
.Vb 1
\&  Signature: (double q(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "The Type\-2 Gumbel Distribution (gsl_cdf_gumbel2_*)"
.IX Subsection "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 \fIa\fR and \fIb\fR.
.SS "gsl_cdf_gumbel2_P"
.IX Subsection "gsl_cdf_gumbel2_P"
.Vb 1
\&  Signature: (double x(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_gumbel2_Pinv"
.IX Subsection "gsl_cdf_gumbel2_Pinv"
.Vb 1
\&  Signature: (double p(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_gumbel2_Q"
.IX Subsection "gsl_cdf_gumbel2_Q"
.Vb 1
\&  Signature: (double x(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_gumbel2_Qinv"
.IX Subsection "gsl_cdf_gumbel2_Qinv"
.Vb 1
\&  Signature: (double q(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "The Hypergeometric Distribution (gsl_cdf_hypergeometric_*)"
.IX Subsection "The Hypergeometric Distribution (gsl_cdf_hypergeometric_*)"
These functions compute the cumulative distribution functions P(k), Q(k) for the hypergeometric distribution with parameters \fIn1\fR, \fIn2\fR and \fIt\fR.
.SS "gsl_cdf_hypergeometric_P"
.IX Subsection "gsl_cdf_hypergeometric_P"
.Vb 1
\&  Signature: (ushort k(); ushort na(); ushort nb(); ushort t();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_hypergeometric_Q"
.IX Subsection "gsl_cdf_hypergeometric_Q"
.Vb 1
\&  Signature: (ushort k(); ushort na(); ushort nb(); ushort t();  [o]out())
.Ve
.PP
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.
.SS "The Laplace Distribution (gsl_cdf_laplace_*)"
.IX Subsection "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 \fIa\fR.
.SS "gsl_cdf_laplace_P"
.IX Subsection "gsl_cdf_laplace_P"
.Vb 1
\&  Signature: (double x(); double a();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_laplace_Pinv"
.IX Subsection "gsl_cdf_laplace_Pinv"
.Vb 1
\&  Signature: (double p(); double a();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_laplace_Q"
.IX Subsection "gsl_cdf_laplace_Q"
.Vb 1
\&  Signature: (double x(); double a();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_laplace_Qinv"
.IX Subsection "gsl_cdf_laplace_Qinv"
.Vb 1
\&  Signature: (double q(); double a();  [o]out())
.Ve
.PP
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.
.SS "The Logistic Distribution (gsl_cdf_logistic_*)"
.IX Subsection "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 \fIa\fR.
.SS "gsl_cdf_logistic_P"
.IX Subsection "gsl_cdf_logistic_P"
.Vb 1
\&  Signature: (double x(); double a();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_logistic_Pinv"
.IX Subsection "gsl_cdf_logistic_Pinv"
.Vb 1
\&  Signature: (double p(); double a();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_logistic_Q"
.IX Subsection "gsl_cdf_logistic_Q"
.Vb 1
\&  Signature: (double x(); double a();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_logistic_Qinv"
.IX Subsection "gsl_cdf_logistic_Qinv"
.Vb 1
\&  Signature: (double q(); double a();  [o]out())
.Ve
.PP
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.
.SS "The Lognormal Distribution (gsl_cdf_lognormal_*)"
.IX Subsection "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 \fIzeta\fR and \fIsigma\fR.
.SS "gsl_cdf_lognormal_P"
.IX Subsection "gsl_cdf_lognormal_P"
.Vb 1
\&  Signature: (double x(); double zeta(); double sigma();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_lognormal_Pinv"
.IX Subsection "gsl_cdf_lognormal_Pinv"
.Vb 1
\&  Signature: (double p(); double zeta(); double sigma();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_lognormal_Q"
.IX Subsection "gsl_cdf_lognormal_Q"
.Vb 1
\&  Signature: (double x(); double zeta(); double sigma();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_lognormal_Qinv"
.IX Subsection "gsl_cdf_lognormal_Qinv"
.Vb 1
\&  Signature: (double q(); double zeta(); double sigma();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_negative_binomial_P"
.IX Subsection "gsl_cdf_negative_binomial_P"
.Vb 1
\&  Signature: (ushort k(); double p(); double n();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_negative_binomial_Q"
.IX Subsection "gsl_cdf_negative_binomial_Q"
.Vb 1
\&  Signature: (ushort k(); double p(); double n();  [o]out())
.Ve
.PP
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.
.SS "The Pareto Distribution (gsl_cdf_pareto_*)"
.IX Subsection "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 \fIa\fR and scale \fIb\fR.
.SS "gsl_cdf_pareto_P"
.IX Subsection "gsl_cdf_pareto_P"
.Vb 1
\&  Signature: (double x(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_pareto_Pinv"
.IX Subsection "gsl_cdf_pareto_Pinv"
.Vb 1
\&  Signature: (double p(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_pareto_Q"
.IX Subsection "gsl_cdf_pareto_Q"
.Vb 1
\&  Signature: (double x(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_pareto_Qinv"
.IX Subsection "gsl_cdf_pareto_Qinv"
.Vb 1
\&  Signature: (double q(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "The Pascal Distribution (gsl_cdf_pascal_*)"
.IX Subsection "The Pascal Distribution (gsl_cdf_pascal_*)"
These functions compute the cumulative distribution functions P(k), Q(k) for the Pascal distribution with parameters \fIp\fR and \fIn\fR.
.SS "gsl_cdf_pascal_P"
.IX Subsection "gsl_cdf_pascal_P"
.Vb 1
\&  Signature: (ushort k(); double p(); ushort n();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_pascal_Q"
.IX Subsection "gsl_cdf_pascal_Q"
.Vb 1
\&  Signature: (ushort k(); double p(); ushort n();  [o]out())
.Ve
.PP
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.
.SS "The Poisson Distribution (gsl_cdf_poisson_*)"
.IX Subsection "The Poisson Distribution (gsl_cdf_poisson_*)"
These functions compute the cumulative distribution functions P(k), Q(k) for the Poisson distribution with parameter \fImu\fR.
.SS "gsl_cdf_poisson_P"
.IX Subsection "gsl_cdf_poisson_P"
.Vb 1
\&  Signature: (ushort k(); double mu();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_poisson_Q"
.IX Subsection "gsl_cdf_poisson_Q"
.Vb 1
\&  Signature: (ushort k(); double mu();  [o]out())
.Ve
.PP
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.
.SS "The Rayleigh Distribution (gsl_cdf_rayleigh_*)"
.IX Subsection "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 \fIsigma\fR.
.SS "gsl_cdf_rayleigh_P"
.IX Subsection "gsl_cdf_rayleigh_P"
.Vb 1
\&  Signature: (double x(); double sigma();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_rayleigh_Pinv"
.IX Subsection "gsl_cdf_rayleigh_Pinv"
.Vb 1
\&  Signature: (double p(); double sigma();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_rayleigh_Q"
.IX Subsection "gsl_cdf_rayleigh_Q"
.Vb 1
\&  Signature: (double x(); double sigma();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_rayleigh_Qinv"
.IX Subsection "gsl_cdf_rayleigh_Qinv"
.Vb 1
\&  Signature: (double q(); double sigma();  [o]out())
.Ve
.PP
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.
.SS "The t\-distribution (gsl_cdf_tdist_*)"
.IX Subsection "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 \fInu\fR degrees of freedom.
.SS "gsl_cdf_tdist_P"
.IX Subsection "gsl_cdf_tdist_P"
.Vb 1
\&  Signature: (double x(); double nu();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_tdist_Pinv"
.IX Subsection "gsl_cdf_tdist_Pinv"
.Vb 1
\&  Signature: (double p(); double nu();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_tdist_Q"
.IX Subsection "gsl_cdf_tdist_Q"
.Vb 1
\&  Signature: (double x(); double nu();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_tdist_Qinv"
.IX Subsection "gsl_cdf_tdist_Qinv"
.Vb 1
\&  Signature: (double q(); double nu();  [o]out())
.Ve
.PP
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.
.SS "The Unit Gaussian Distribution (gsl_cdf_ugaussian_*)"
.IX Subsection "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.
.SS "gsl_cdf_ugaussian_P"
.IX Subsection "gsl_cdf_ugaussian_P"
.Vb 1
\&  Signature: (double x();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_ugaussian_Pinv"
.IX Subsection "gsl_cdf_ugaussian_Pinv"
.Vb 1
\&  Signature: (double p();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_ugaussian_Q"
.IX Subsection "gsl_cdf_ugaussian_Q"
.Vb 1
\&  Signature: (double x();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_ugaussian_Qinv"
.IX Subsection "gsl_cdf_ugaussian_Qinv"
.Vb 1
\&  Signature: (double q();  [o]out())
.Ve
.PP
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.
.SS "The Weibull Distribution (gsl_cdf_weibull_*)"
.IX Subsection "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 \fIa\fR and exponent \fIb\fR.
.SS "gsl_cdf_weibull_P"
.IX Subsection "gsl_cdf_weibull_P"
.Vb 1
\&  Signature: (double x(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_weibull_Pinv"
.IX Subsection "gsl_cdf_weibull_Pinv"
.Vb 1
\&  Signature: (double p(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_weibull_Q"
.IX Subsection "gsl_cdf_weibull_Q"
.Vb 1
\&  Signature: (double x(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SS "gsl_cdf_weibull_Qinv"
.IX Subsection "gsl_cdf_weibull_Qinv"
.Vb 1
\&  Signature: (double q(); double a(); double b();  [o]out())
.Ve
.PP
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.
.SH "AUTHOR"
.IX Header "AUTHOR"
Copyright (C) 2009 Maggie J. Xiong <maggiexyz users.sourceforge.net>
.PP
The \s-1GSL CDF\s0 module was written by J. Stover.
.PP
All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation as described in the file \s-1COPYING\s0 in the \s-1PDL\s0 distribution.