--- /dev/null
+# Statistical Distribution Functions
+
+PSPP can calculate several functions of standard statistical
+distributions. These functions are named systematically based on the
+function and the distribution. The table below describes the
+statistical distribution functions in general:
+
+* `PDF.DIST(X[, PARAM...])`
+ Probability density function for `DIST`. The domain of `X` depends on
+ `DIST`. For continuous distributions, the result is the density of
+ the probability function at X, and the range is nonnegative real
+ numbers. For discrete distributions, the result is the probability
+ of `X`.
+
+* `CDF.DIST(X[, PARAM...])`
+ Cumulative distribution function for `DIST`, that is, the probability
+ that a random variate drawn from the distribution is less than `X`.
+ The domain of `X` depends `DIST`. The result is a probability.
+
+* `SIG.DIST(X[, PARAM...)`
+ Tail probability function for `DIST`, that is, the probability that a
+ random variate drawn from the distribution is greater than `X`. The
+ domain of `X` depends `DIST`. The result is a probability. Only a few
+ distributions include an `SIG` function.
+
+* `IDF.DIST(P[, PARAM...])`
+ Inverse distribution function for `DIST`, the value of `X` for which
+ the CDF would yield P. The value of P is a probability. The range
+ depends on `DIST` and is identical to the domain for the
+ corresponding CDF.
+
+* `RV.DIST([PARAM...])`
+ Random variate function for `DIST`. The range depends on the
+ distribution.
+
+* `NPDF.DIST(X[, PARAM...])`
+ Noncentral probability density function. The result is the density
+ of the given noncentral distribution at `X`. The domain of `X` depends
+ on `DIST`. The range is nonnegative real numbers. Only a few
+ distributions include an `NPDF` function.
+
+* `NCDF.DIST(X[, PARAM...])`
+ Noncentral cumulative distribution function for `DIST`, that is, the
+ probability that a random variate drawn from the given noncentral
+ distribution is less than `X`. The domain of `X` depends `DIST`. The
+ result is a probability. Only a few distributions include an NCDF
+ function.
+
+## Continuous Distributions
+
+The following continuous distributions are available:
+
+* `PDF.BETA (X)`
+ `CDF.BETA (X, A, B)`
+ `IDF.BETA (P, A, B)`
+ `RV.BETA (A, B)`
+ `NPDF.BETA (X, A, B, )`
+ `NCDF.BETA (X, A, B, )`
+ Beta distribution with shape parameters `A` and `B`. The noncentral
+ distribution takes an additional parameter . Constraints: `A > 0, B > 0, >= 0, 0 <= X <= 1, 0 <= P <= 1`.
+
+* `PDF.BVNOR (X0, X1, ρ)`
+ `CDF.BVNOR (X0, X1, ρ)`
+ Bivariate normal distribution of two standard normal variables with
+ correlation coefficient ρ. Two variates X0 and X1 must be
+ provided. Constraints: 0 <= ρ <= 1, 0 <= P <= 1.
+
+* `PDF.CAUCHY (X, A, B)`
+ `CDF.CAUCHY (X, A, B)`
+ `IDF.CAUCHY (P, A, B)`
+ `RV.CAUCHY (A, B)`
+ Cauchy distribution with location parameter `A` and scale parameter
+ `B`. Constraints: B > 0, 0 < P < 1.
+
+* `CDF.CHISQ (X, DF)`
+ `SIG.CHISQ (X, DF)`
+ `IDF.CHISQ (P, DF)`
+ `RV.CHISQ (DF)`
+ `NCDF.CHISQ (X, DF, )`
+ Chi-squared distribution with DF degrees of freedom. The
+ noncentral distribution takes an additional parameter .
+ Constraints: DF > 0, > 0, X >= 0, 0 <= P < 1.
+
+* `PDF.EXP (X, A)`
+ `CDF.EXP (X, A)`
+ `IDF.EXP (P, A)`
+ `RV.EXP (A)`
+ Exponential distribution with scale parameter `A`. The inverse of `A`
+ represents the rate of decay. Constraints: A > 0, X >= 0, 0 <= P <
+ 1.
+
+* `PDF.XPOWER (X, A, B)`
+ `RV.XPOWER (A, B)`
+ Exponential power distribution with positive scale parameter `A` and
+ nonnegative power parameter `B`. Constraints: A > 0, B >= 0, X >= 0,
+ 0 <= P <= 1. This distribution is a PSPP extension.
+
+* `PDF.F (X, DF1, DF2)`
+ `CDF.F (X, DF1, DF2)`
+ `SIG.F (X, DF1, DF2)`
+ `IDF.F (P, DF1, DF2)`
+ `RV.F (DF1, DF2)`
+ F-distribution of two chi-squared deviates with DF1 and DF2 degrees
+ of freedom. The noncentral distribution takes an additional
+ parameter . Constraints: DF1 > 0, DF2 > 0, >= 0, X >=
+ 0, 0 <= P < 1.
+
+* `PDF.GAMMA (X, A, B)`
+ `CDF.GAMMA (X, A, B)`
+ `IDF.GAMMA (P, A, B)`
+ `RV.GAMMA (A, B)`
+ Gamma distribution with shape parameter `A` and scale parameter `B`.
+ Constraints: A > 0, B > 0, X >= 0, 0 <= P < 1.
+
+* `PDF.LANDAU (X)`
+ `RV.LANDAU ()`
+ Landau distribution.
+
+* `PDF.LAPLACE (X, A, B)`
+ `CDF.LAPLACE (X, A, B)`
+ `IDF.LAPLACE (P, A, B)`
+ `RV.LAPLACE (A, B)`
+ Laplace distribution with location parameter `A` and scale parameter
+ `B`. Constraints: B > 0, 0 < P < 1.
+
+* `RV.LEVY (C, ɑ)`
+ Levy symmetric alpha-stable distribution with scale C and exponent
+ ɑ. Constraints: 0 < ɑ <= 2.
+
+* `RV.LVSKEW (C, ɑ, β)`
+ Levy skew alpha-stable distribution with scale C, exponent ɑ, and
+ skewness parameter β. Constraints: 0 < ɑ <= 2, -1 <= β <= 1.
+
+* `PDF.LOGISTIC (X, A, B)`
+ `CDF.LOGISTIC (X, A, B)`
+ `IDF.LOGISTIC (P, A, B)`
+ `RV.LOGISTIC (A, B)`
+ Logistic distribution with location parameter `A` and scale parameter
+ `B`. Constraints: B > 0, 0 < P < 1.
+
+* `PDF.LNORMAL (X, A, B)`
+ `CDF.LNORMAL (X, A, B)`
+ `IDF.LNORMAL (P, A, B)`
+ `RV.LNORMAL (A, B)`
+ Lognormal distribution with parameters `A` and `B`. Constraints: A >
+ 0, B > 0, X >= 0, 0 <= P < 1.
+
+* `PDF.NORMAL (X, μ, σ)`
+ `CDF.NORMAL (X, μ, σ)`
+ `IDF.NORMAL (P, μ, σ)`
+ `RV.NORMAL (μ, σ)`
+ Normal distribution with mean μ and standard deviation σ.
+ Constraints: B > 0, 0 < P < 1. Three additional functions are
+ available as shorthand:
+
+ * `CDFNORM (X)`
+ Equivalent to `CDF.NORMAL(X, 0, 1)`.
+
+ * `PROBIT (P)`
+ Equivalent to `IDF.NORMAL(P, 0, 1)`.
+
+ * `NORMAL (σ)`
+ Equivalent to `RV.NORMAL(0, σ)`.
+
+* `PDF.NTAIL (X, A, σ)`
+ `RV.NTAIL (A, σ)`
+ Normal tail distribution with lower limit `A` and standard deviation
+ `σ`. This distribution is a PSPP extension. Constraints: A >
+ 0, X > A, 0 < P < 1.
+
+* `PDF.PARETO (X, A, B)`
+ `CDF.PARETO (X, A, B)`
+ `IDF.PARETO (P, A, B)`
+ `RV.PARETO (A, B)`
+ Pareto distribution with threshold parameter `A` and shape parameter
+ `B`. Constraints: A > 0, B > 0, X >= A, 0 <= P < 1.
+
+* `PDF.RAYLEIGH (X, σ)`
+ `CDF.RAYLEIGH (X, σ)`
+ `IDF.RAYLEIGH (P, σ)`
+ `RV.RAYLEIGH (σ)`
+ Rayleigh distribution with scale parameter σ. This
+ distribution is a PSPP extension. Constraints: σ > 0, X > 0.
+
+* `PDF.RTAIL (X, A, σ)`
+ `RV.RTAIL (A, σ)`
+ Rayleigh tail distribution with lower limit `A` and scale parameter
+ `σ`. This distribution is a PSPP extension. Constraints: A > 0,
+ σ > 0, X > A.
+
+* `PDF.T (X, DF)`
+ `CDF.T (X, DF)`
+ `IDF.T (P, DF)`
+ `RV.T (DF)`
+ T-distribution with DF degrees of freedom. The noncentral
+ distribution takes an additional parameter . Constraints: DF > 0,
+ 0 < P < 1.
+
+* `PDF.T1G (X, A, B)`
+ `CDF.T1G (X, A, B)`
+ `IDF.T1G (P, A, B)`
+ Type-1 Gumbel distribution with parameters `A` and `B`. This
+ distribution is a PSPP extension. Constraints: 0 < P < 1.
+
+* `PDF.T2G (X, A, B)`
+ `CDF.T2G (X, A, B)`
+ `IDF.T2G (P, A, B)`
+ Type-2 Gumbel distribution with parameters `A` and `B`. This
+ distribution is a PSPP extension. Constraints: X > 0, 0 < P < 1.
+
+* `PDF.UNIFORM (X, A, B)`
+ `CDF.UNIFORM (X, A, B)`
+ `IDF.UNIFORM (P, A, B)`
+ `RV.UNIFORM (A, B)`
+ Uniform distribution with parameters `A` and `B`. Constraints: A <= X
+ <= B, 0 <= P <= 1. An additional function is available as
+ shorthand:
+
+ - `UNIFORM (B)`
+ Equivalent to `RV.UNIFORM(0, B)`.
+
+* `PDF.WEIBULL (X, A, B)`
+ `CDF.WEIBULL (X, A, B)`
+ `IDF.WEIBULL (P, A, B)`
+ `RV.WEIBULL (A, B)`
+ Weibull distribution with parameters `A` and `B`. Constraints: A > 0,
+ B > 0, X >= 0, 0 <= P < 1.
+
+## Discrete Distributions
+
+The following discrete distributions are available:
+
+* `PDF.BERNOULLI (X)`
+ `CDF.BERNOULLI (X, P)`
+ `RV.BERNOULLI (P)`
+ Bernoulli distribution with probability of success P. Constraints:
+ X = 0 or 1, 0 <= P <= 1.
+
+* `PDF.BINOM (X, N, P)`
+ `CDF.BINOM (X, N, P)`
+ `RV.BINOM (N, P)`
+ Binomial distribution with N trials and probability of success P.
+ Constraints: integer N > 0, 0 <= P <= 1, integer X <= N.
+
+* `PDF.GEOM (X, N, P)`
+ `CDF.GEOM (X, N, P)`
+ `RV.GEOM (N, P)`
+ Geometric distribution with probability of success P. Constraints:
+ 0 <= P <= 1, integer X > 0.
+
+* `PDF.HYPER (X, A, B, C)`
+ `CDF.HYPER (X, A, B, C)`
+ `RV.HYPER (A, B, C)`
+ Hypergeometric distribution when `B` objects out of `A` are drawn and `C`
+ of the available objects are distinctive. Constraints: integer A >
+ 0, integer B <= A, integer C <= A, integer X >= 0.
+
+* `PDF.LOG (X, P)`
+ `RV.LOG (P)`
+ Logarithmic distribution with probability parameter P.
+ Constraints: 0 <= P < 1, X >= 1.
+
+* `PDF.NEGBIN (X, N, P)`
+ `CDF.NEGBIN (X, N, P)`
+ `RV.NEGBIN (N, P)`
+ Negative binomial distribution with number of successes parameter N
+ and probability of success parameter P. Constraints: integer N >=
+ 0, 0 < P <= 1, integer X >= 1.
+
+* `PDF.POISSON (X, μ)`
+ `CDF.POISSON (X, μ)`
+ `RV.POISSON (μ)`
+ Poisson distribution with mean μ. Constraints: μ > 0, integer X >= 0.
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