+@table @asis
+@item PDF.@var{dist} (@var{x}[, @var{param}@dots{}])
+Probability density function for @var{dist}. The domain of @var{x}
+depends on @var{dist}. For continuous distributions, the result is
+the density of the probability function at @var{x}, and the range is
+nonnegative real numbers. For discrete distributions, the result is
+the probability of @var{x}.
+
+@item CDF.@var{dist} (@var{x}[, @var{param}@dots{}])
+Cumulative distribution function for @var{dist}, that is, the
+probability that a random variate drawn from the distribution is less
+than @var{x}. The domain of @var{x} depends @var{dist}. The result is
+a probability.
+
+@item SIG.@var{dist} (@var{x}[, @var{param}@dots{})
+Tail probability function for @var{dist}, that is, the probability
+that a random variate drawn from the distribution is greater than
+@var{x}. The domain of @var{x} depends @var{dist}. The result is a
+probability. Only a few distributions include an SIG function.
+
+@item IDF.@var{dist} (@var{p}[, @var{param}@dots{}])
+Inverse distribution function for @var{dist}, the value of @var{x} for
+which the CDF would yield @var{p}. The value of @var{p} is a
+probability. The range depends on @var{dist} and is identical to the
+domain for the corresponding CDF.
+
+@item RV.@var{dist} ([@var{param}@dots{}])
+Random variate function for @var{dist}. The range depends on the
+distribution.
+
+@item NPDF.@var{dist} (@var{x}[, @var{param}@dots{}])
+Noncentral probability density function. The result is the density of
+the given noncentral distribution at @var{x}. The domain of @var{x}
+depends on @var{dist}. The range is nonnegative real numbers. Only a
+few distributions include an NPDF function.
+
+@item NCDF.@var{dist} (@var{x}[, @var{param}@dots{}])
+Noncentral cumulative distribution function for @var{dist}, that is,
+the probability that a random variate drawn from the given noncentral
+distribution is less than @var{x}. The domain of @var{x} depends
+@var{dist}. The result is a probability. Only a few distributions
+include an NCDF function.
+@end table
+
+The individual distributions are described individually below.
+
+@menu
+* Continuous Distributions::
+* Discrete Distributions::
+@end menu
+
+@node Continuous Distributions
+@subsubsection Continuous Distributions
+
+The following continuous distributions are available:
+
+@deftypefn {Function} {} PDF.BETA (@var{x})
+@deftypefnx {Function} {} CDF.BETA (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} IDF.BETA (@var{p}, @var{a}, @var{b})
+@deftypefnx {Function} {} RV.BETA (@var{a}, @var{b})
+@deftypefnx {Function} {} NPDF.BETA (@var{x}, @var{a}, @var{b}, @var{lambda})
+@deftypefnx {Function} {} NCDF.BETA (@var{x}, @var{a}, @var{b}, @var{lambda})
+Beta distribution with shape parameters @var{a} and @var{b}. The
+noncentral distribution takes an additional parameter @var{lambda}.
+Constraints: @var{a} > 0, @var{b} > 0, @var{lambda} >= 0, 0 <= @var{x}
+<= 1, 0 <= @var{p} <= 1.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.BVNOR (@var{x0}, @var{x1}, @var{rho})
+@deftypefnx {Function} {} CDF.VBNOR (@var{x0}, @var{x1}, @var{rho})
+Bivariate normal distribution of two standard normal variables with
+correlation coefficient @var{rho}. Two variates @var{x0} and @var{x1}
+must be provided. Constraints: 0 <= @var{rho} <= 1, 0 <= @var{p} <= 1.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.CAUCHY (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} CDF.CAUCHY (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} IDF.CAUCHY (@var{p}, @var{a}, @var{b})
+@deftypefnx {Function} {} RV.CAUCHY (@var{a}, @var{b})
+Cauchy distribution with location parameter @var{a} and scale
+parameter @var{b}. Constraints: @var{b} > 0, 0 < @var{p} < 1.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.CHISQ (@var{x}, @var{df})
+@deftypefnx {Function} {} CDF.CHISQ (@var{x}, @var{df})
+@deftypefnx {Function} {} SIG.CHISQ (@var{x}, @var{df})
+@deftypefnx {Function} {} IDF.CHISQ (@var{p}, @var{df})
+@deftypefnx {Function} {} RV.CHISQ (@var{df})
+@deftypefnx {Function} {} NPDF.CHISQ (@var{x}, @var{df}, @var{lambda})
+@deftypefnx {Function} {} NCDF.CHISQ (@var{x}, @var{df}, @var{lambda})
+Chi-squared distribution with @var{df} degrees of freedom. The
+noncentral distribution takes an additional parameter @var{lambda}.
+Constraints: @var{df} > 0, @var{lambda} > 0, @var{x} >= 0, 0 <=
+@var{p} < 1.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.EXP (@var{x}, @var{a})
+@deftypefnx {Function} {} CDF.EXP (@var{x}, @var{a})
+@deftypefnx {Function} {} IDF.EXP (@var{p}, @var{a})
+@deftypefnx {Function} {} RV.EXP (@var{a})
+Exponential distribution with scale parameter @var{a}. The inverse of
+@var{a} represents the rate of decay. Constraints: @var{a} > 0,
+@var{x} >= 0, 0 <= @var{p} < 1.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.XPOWER (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} RV.XPOWER (@var{a}, @var{b})
+Exponential power distribution with positive scale parameter @var{a}
+and nonnegative power parameter @var{b}. Constraints: @var{a} > 0,
+@var{b} >= 0, @var{x} >= 0, 0 <= @var{p} <= 1. This distribution is a
+PSPP extension.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.F (@var{x}, @var{df1}, @var{df2})
+@deftypefnx {Function} {} CDF.F (@var{x}, @var{df1}, @var{df2})
+@deftypefnx {Function} {} SIG.F (@var{x}, @var{df1}, @var{df2})
+@deftypefnx {Function} {} IDF.F (@var{p}, @var{df1}, @var{df2})
+@deftypefnx {Function} {} RV.F (@var{df1}, @var{df2})
+@deftypefnx {Function} {} NPDF.F (@var{x}, @var{df1}, @var{df2}, @var{lambda})
+@deftypefnx {Function} {} NCDF.F (@var{x}, @var{df1}, @var{df2}, @var{lambda})
+F-distribution of two chi-squared deviates with @var{df1} and
+@var{df2} degrees of freedom. The noncentral distribution takes an
+additional parameter @var{lambda}. Constraints: @var{df1} > 0,
+@var{df2} > 0, @var{lambda} >= 0, @var{x} >= 0, 0 <= @var{p} < 1.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.GAMMA (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} CDF.GAMMA (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} IDF.GAMMA (@var{p}, @var{a}, @var{b})
+@deftypefnx {Function} {} RV.GAMMA (@var{a}, @var{b})
+Gamma distribution with shape parameter @var{a} and scale parameter
+@var{b}. Constraints: @var{a} > 0, @var{b} > 0, @var{x} >= 0, 0 <=
+@var{p} < 1.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.HALFNRM (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} CDF.HALFNRM (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} IDF.HALFNRM (@var{p}, @var{a}, @var{b})
+@deftypefnx {Function} {} RV.HALFNRM (@var{a}, @var{b})
+Half-normal distribution with location parameter @var{a} and shape
+parameter @var{b}. Constraints: @var{b} > 0, 0 < @var{p} < 1.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.IGAUSS (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} CDF.IGAUSS (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} IDF.IGAUSS (@var{p}, @var{a}, @var{b})
+@deftypefnx {Function} {} RV.IGAUSS (@var{a}, @var{b})
+Inverse Gaussian distribution with parameters @var{a} and @var{b}.
+Constraints: @var{a} > 0, @var{b} > 0, @var{x} > 0, 0 <= @var{p} < 1.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.LANDAU (@var{x})
+@deftypefnx {Function} {} RV.LANDAU ()
+Landau distribution.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.LAPLACE (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} CDF.LAPLACE (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} IDF.LAPLACE (@var{p}, @var{a}, @var{b})
+@deftypefnx {Function} {} RV.LAPLACE (@var{a}, @var{b})
+Laplace distribution with location parameter @var{a} and scale
+parameter @var{b}. Constraints: @var{b} > 0, 0 < @var{p} < 1.
+@end deftypefn
+
+@deftypefn {Function} {} RV.LEVY (@var{c}, @var{alpha})
+Levy symmetric alpha-stable distribution with scale @var{c} and
+exponent @var{alpha}. Constraints: 0 < @var{alpha} <= 2.
+@end deftypefn
+
+@deftypefn {Function} {} RV.LVSKEW (@var{c}, @var{alpha}, @var{beta})
+Levy skew alpha-stable distribution with scale @var{c}, exponent
+@var{alpha}, and skewness parameter @var{beta}. Constraints: 0 <
+@var{alpha} <= 2, -1 <= @var{beta} <= 1.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.LOGISTIC (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} CDF.LOGISTIC (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} IDF.LOGISTIC (@var{p}, @var{a}, @var{b})
+@deftypefnx {Function} {} RV.LOGISTIC (@var{a}, @var{b})
+Logistic distribution with location parameter @var{a} and scale
+parameter @var{b}. Constraints: @var{b} > 0, 0 < @var{p} < 1.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.LNORMAL (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} CDF.LNORMAL (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} IDF.LNORMAL (@var{p}, @var{a}, @var{b})
+@deftypefnx {Function} {} RV.LNORMAL (@var{a}, @var{b})
+Lognormal distribution with parameters @var{a} and @var{b}.
+Constraints: @var{a} > 0, @var{b} > 0, @var{x} >= 0, 0 <= @var{p} < 1.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.NORMAL (@var{x}, @var{mu}, @var{sigma})
+@deftypefnx {Function} {} CDF.NORMAL (@var{x}, @var{mu}, @var{sigma})
+@deftypefnx {Function} {} IDF.NORMAL (@var{p}, @var{mu}, @var{sigma})
+@deftypefnx {Function} {} RV.NORMAL (@var{mu}, @var{sigma})
+Normal distribution with mean @var{mu} and standard deviation
+@var{sigma}. Constraints: @var{b} > 0, 0 < @var{p} < 1. Three
+additional functions are available as shorthand:
+
+@deftypefn {Function} {} CDFNORM (@var{x})
+Equivalent to CDF.NORMAL(@var{x}, 0, 1).
+@end deftypefn
+
+@deftypefn {Function} {} PROBIT (@var{p})
+Equivalent to IDF.NORMAL(@var{p}, 0, 1).
+@end deftypefn
+
+@deftypefn {Function} {} NORMAL (@var{sigma})
+Equivalent to RV.NORMAL(0, @var{sigma}).
+@end deftypefn
+@end deftypefn
+
+@deftypefn {Function} {} PDF.NTAIL (@var{x}, @var{a}, @var{sigma})
+@deftypefnx {Function} {} RV.NTAIL (@var{a}, @var{sigma})
+Normal tail distribution with lower limit @var{a} and standard
+deviation @var{sigma}. This distribution is a PSPP extension.
+Constraints: @var{a} > 0, @var{x} > @var{a}, 0 < @var{p} < 1.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.PARETO (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} CDF.PARETO (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} IDF.PARETO (@var{p}, @var{a}, @var{b})
+@deftypefnx {Function} {} RV.PARETO (@var{a}, @var{b})
+Pareto distribution with threshold parameter @var{a} and shape
+parameter @var{b}. Constraints: @var{a} > 0, @var{b} > 0, @var{x} >=
+@var{a}, 0 <= @var{p} < 1.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.RAYLEIGH (@var{x}, @var{sigma})
+@deftypefnx {Function} {} CDF.RAYLEIGH (@var{x}, @var{sigma})
+@deftypefnx {Function} {} IDF.RAYLEIGH (@var{p}, @var{sigma})
+@deftypefnx {Function} {} RV.RAYLEIGH (@var{sigma})
+Rayleigh distribution with scale parameter @var{sigma}. This
+distribution is a PSPP extension. Constraints: @var{sigma} > 0,
+@var{x} > 0.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.RTAIL (@var{x}, @var{a}, @var{sigma})
+@deftypefnx {Function} {} RV.RTAIL (@var{a}, @var{sigma})
+Rayleigh tail distribution with lower limit @var{a} and scale
+parameter @var{sigma}. This distribution is a PSPP extension.
+Constraints: @var{a} > 0, @var{sigma} > 0, @var{x} > @var{a}.
+@end deftypefn
+
+@deftypefn {Function} {} CDF.SMOD (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} IDF.SMOD (@var{p}, @var{a}, @var{b})
+Studentized maximum modulus distribution with parameters @var{a} and
+@var{b}. Constraints: @var{a} > 0, @var{b} > 0, @var{x} > 0, 0 <=
+@var{p} < 1.
+@end deftypefn
+
+@deftypefn {Function} {} CDF.SRANGE (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} IDF.SRANGE (@var{p}, @var{a}, @var{b})
+Studentized range distribution with parameters @var{a} and @var{b}.
+Constraints: @var{a} >= 1, @var{b} >= 1, @var{x} > 0, 0 <= @var{p} <
+1.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.T (@var{x}, @var{df})
+@deftypefnx {Function} {} CDF.T (@var{x}, @var{df})
+@deftypefnx {Function} {} IDF.T (@var{p}, @var{df})
+@deftypefnx {Function} {} RV.T (@var{df})
+@deftypefnx {Function} {} NPDF.T (@var{x}, @var{df}, @var{lambda})
+@deftypefnx {Function} {} NCDF.T (@var{x}, @var{df}, @var{lambda})
+T-distribution with @var{df} degrees of freedom. The noncentral
+distribution takes an additional parameter @var{lambda}. Constraints:
+@var{df} > 0, 0 < @var{p} < 1.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.T1G (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} CDF.T1G (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} IDF.T1G (@var{p}, @var{a}, @var{b})
+Type-1 Gumbel distribution with parameters @var{a} and @var{b}. This
+distribution is a PSPP extension. Constraints: 0 < @var{p} < 1.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.T2G (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} CDF.T2G (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} IDF.T2G (@var{p}, @var{a}, @var{b})
+Type-2 Gumbel distribution with parameters @var{a} and @var{b}. This
+distribution is a PSPP extension. Constraints: @var{x} > 0, 0 <
+@var{p} < 1.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.UNIFORM (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} CDF.UNIFORM (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} IDF.UNIFORM (@var{p}, @var{a}, @var{b})
+@deftypefnx {Function} {} RV.UNIFORM (@var{a}, @var{b})
+Uniform distribution with parameters @var{a} and @var{b}.
+Constraints: @var{a} <= @var{x} <= @var{b}, 0 <= @var{p} <= 1. An
+additional function is available as shorthand:
+
+@deftypefn {Function} {} UNIFORM (@var{b})
+Equivalent to RV.UNIFORM(0, @var{b}).
+@end deftypefn
+@end deftypefn
+
+@deftypefn {Function} {} PDF.WEIBULL (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} CDF.WEIBULL (@var{x}, @var{a}, @var{b})
+@deftypefnx {Function} {} IDF.WEIBULL (@var{p}, @var{a}, @var{b})
+@deftypefnx {Function} {} RV.WEIBULL (@var{a}, @var{b})
+Weibull distribution with parameters @var{a} and @var{b}.
+Constraints: @var{a} > 0, @var{b} > 0, @var{x} >= 0, 0 <= @var{p} < 1.
+@end deftypefn
+
+@node Discrete Distributions
+@subsubsection Discrete Distributions
+
+The following discrete distributions are available:
+
+@deftypefn {Function} {} PDF.BERNOULLI (@var{x})
+@deftypefnx {Function} {} CDF.BERNOULLI (@var{x}, @var{p})
+@deftypefnx {Function} {} RV.BERNOULLI (@var{p})
+Bernoulli distribution with probability of success @var{p}.
+Constraints: @var{x} = 0 or 1, 0 <= @var{p} <= 1.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.BINOMIAL (@var{x}, @var{n}, @var{p})
+@deftypefnx {Function} {} CDF.BINOMIAL (@var{x}, @var{n}, @var{p})
+@deftypefnx {Function} {} RV.BINOMIAL (@var{n}, @var{p})
+Binomial distribution with @var{n} trials and probability of success
+@var{p}. Constraints: integer @var{n} > 0, 0 <= @var{p} <= 1, integer
+@var{x} <= @var{n}.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.GEOM (@var{x}, @var{n}, @var{p})
+@deftypefnx {Function} {} CDF.GEOM (@var{x}, @var{n}, @var{p})
+@deftypefnx {Function} {} RV.GEOM (@var{n}, @var{p})
+Geometric distribution with probability of success @var{p}.
+Constraints: 0 <= @var{p} <= 1, integer @var{x} > 0.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.HYPER (@var{x}, @var{a}, @var{b}, @var{c})
+@deftypefnx {Function} {} CDF.HYPER (@var{x}, @var{a}, @var{b}, @var{c})
+@deftypefnx {Function} {} RV.HYPER (@var{a}, @var{b}, @var{c})
+Hypergeometric distribution when @var{b} objects out of @var{a} are
+drawn and @var{c} of the available objects are distinctive.
+Constraints: integer @var{a} > 0, integer @var{b} <= @var{a}, integer
+@var{c} <= @var{a}, integer @var{x} >= 0.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.LOG (@var{x}, @var{p})
+@deftypefnx {Function} {} RV.LOG (@var{p})
+Logarithmic distribution with probability parameter @var{p}.
+Constraints: 0 <= @var{p} < 1, @var{x} >= 1.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.NEGBIN (@var{x}, @var{n}, @var{p})
+@deftypefnx {Function} {} CDF.NEGBIN (@var{x}, @var{n}, @var{p})
+@deftypefnx {Function} {} RV.NEGBIN (@var{n}, @var{p})
+Negative binomial distribution with number of successes paramter
+@var{n} and probability of success parameter @var{p}. Constraints:
+integer @var{n} >= 0, 0 < @var{p} <= 1, integer @var{x} >= 1.
+@end deftypefn
+
+@deftypefn {Function} {} PDF.POISSON (@var{x}, @var{mu})
+@deftypefnx {Function} {} CDF.POISSON (@var{x}, @var{mu})
+@deftypefnx {Function} {} RV.POISSON (@var{mu})
+Poisson distribution with mean @var{mu}. Constraints: @var{mu} > 0,
+integer @var{x} >= 0.
+@end deftypefn