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, )`
+* `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)`
+* `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)`
+* `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, )`
+* `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)`
+* `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)`
+* `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)`
+* `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)`
+* `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 ()`
+* `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)`
+* `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)`
+* `RV.LEVY(C, ɑ)`
Levy symmetric alpha-stable distribution with scale C and exponent
ɑ. Constraints: 0 < ɑ <= 2.
-* `RV.LVSKEW (C, ɑ, β)`
+* `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)`
+* `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)`
+* `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)`
+* `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)`
+ * `CDFNORM(X)`
Equivalent to `CDF.NORMAL(X, 0, 1)`.
- * `PROBIT (P)`
+ * `PROBIT(P)`
Equivalent to `IDF.NORMAL(P, 0, 1)`.
- * `NORMAL (σ)`
+ * `NORMAL(σ)`
Equivalent to `RV.NORMAL(0, σ)`.
-* `PDF.NTAIL (X, A, σ)`
- `RV.NTAIL (A, 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)`
+* `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)`
+* `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)`
+* `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)`
+* `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)`
+* `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)`
+* `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)`
+* `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)`
+ - `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)`
+* `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.
The following discrete distributions are available:
-* `PDF.BERNOULLI (X)`
- `CDF.BERNOULLI (X, P)`
- `RV.BERNOULLI (P)`
+* `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)`
+* `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)`
+* `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)`
+* `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)`
+* `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)`
+* `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)`
+* `PDF.POISSON(X, μ)`
+ `CDF.POISSON(X, μ)`
+ `RV.POISSON(μ)`
Poisson distribution with mean μ. Constraints: μ > 0, integer X >= 0.
# Mathematical Expressions
Expressions share a common syntax each place they appear in PSPP
-commands. Expressions are made up of "operands", which can be numbers,
-strings, or variable names, separated by "operators". There are five
-types of operators: grouping, arithmetic, logical, relational, and
-functions.
-
- Every operator takes one or more operands as input and yields exactly
-one result as output. Depending on the operator, operands accept
-strings or numbers as operands. With few exceptions, operands may be
-full-fledged expressions in themselves.
+commands. Expressions are made up of "operands", which can be
+numbers, strings, variable names, or invocations of functions,
+separated by "operators".
+
+## Boolean Values
+
+Some PSPP operators and expressions work with Boolean values, which
+represent true/false conditions. Booleans have only three possible
+values: 0 (false), 1 (true), and system-missing (unknown).
+System-missing is neither true nor false and indicates that the true
+value is unknown.
+
+ Boolean-typed operands or function arguments must take on one of
+these three values. Other values are considered false, but provoke a
+warning when the expression is evaluated.
+
+ Strings and Booleans are not compatible, and neither may be used in
+place of the other.
+
+## Missing Values
+
+Most numeric operators yield system-missing when given any
+system-missing operand. A string operator given any system-missing
+operand typically results in the empty string. Exceptions are listed
+under particular operator descriptions.
+
+ String user-missing values are not treated specially in expressions.
+
+ User-missing values for numeric variables are always transformed into
+the system-missing value, except inside the arguments to the `VALUE` and
+`SYSMIS` functions.
+
+ The [missing-value functions](functions/missing-value.md) can be
+used to precisely control how missing values are treated in
+expressions.
+
+## Order of Operations
+
+The following table describes operator precedence. Smaller-numbered
+levels in the table have higher precedence. Within a level,
+operations are always performed from left to right.
+
+1. `()`
+2. `**`
+3. Unary `+` and `-`
+4. `* /`
+5. Binary `+` and `-`
+6. `= >= > <= < <>`
+7. `NOT`
+8. `AND`
+9. `OR`
--- /dev/null
+# Operators
+
+Every operator takes one or more operands as input and yields exactly
+one result as output. Depending on the operator, operands accept
+strings or numbers as operands. With few exceptions, operands may be
+full-fledged expressions in themselves.
+
+## Grouping Operators
+
+Parentheses (`()`) are the grouping operators. Surround an expression
+with parentheses to force early evaluation.
+
+ Parentheses also surround the arguments to functions, but in that
+situation they act as punctuators, not as operators.
+
+## Arithmetic Operators
+
+The arithmetic operators take numeric operands and produce numeric
+results.
+
+* `A + B`
+ `A - B`
+ Addition and subtraction.
+
+* `A * B`
+ Multiplication. If either `A` or `B` is 0, then the result is 0,
+ even if the other operand is missing.
+
+* `A / B`
+ Division. If `A` is 0, then the result is 0, even if `B` is
+ missing. If `B` is zero, the result is system-missing.
+
+* `A ** B`
+ `A` raised to the power `B`. If `A` is negative and `B` is not an
+ integer, the result is system-missing. `0**0` is also
+ system-missing.
+
+* `-A`
+ Reverses the sign of `A`.
+
+## Logical Operators
+
+The logical operators take logical operands and produce logical
+results, meaning "true or false." Logical operators are not true
+Boolean operators because they may also result in a system-missing
+value. See [Boolean Values](#boolean-values), above, for more
+information.
+
+* `A AND B`
+ `A & B`
+ True if both `A` and `B` are true, false otherwise. If one operand
+ is false, the result is false even if the other is missing. If both
+ operands are missing, the result is missing.
+
+* `A OR B`
+ `A | B`
+ True if at least one of `A` and `B` is true. If one operand is
+ true, the result is true even if the other operand is missing. If
+ both operands are missing, the result is missing.
+
+* `NOT A`
+ `~A`
+ True if `A` is false. If the operand is missing, then the result is
+ missing.
+
+## Relational Operators
+
+The relational operators take numeric or string operands and produce
+Boolean results.
+
+ Strings cannot be compared to numbers. When strings of different
+lengths are compared, the shorter string is right-padded with spaces to
+match the length of the longer string.
+
+ The results of string comparisons, other than tests for equality or
+inequality, depend on the character set in use. String comparisons are
+case-sensitive.
+
+* `A EQ B`
+ `A = B`
+ True if `A` is equal to `B`.
+
+* `A LE B`
+ `A <= B`
+ True if `A` is less than or equal to `B`.
+
+* `A LT B`
+ `A < B`
+ True if `A` is less than `B`.
+
+* `A GE B`
+ `A >= B`
+ True if `A` is greater than or equal to `B`.
+
+* `A GT B`
+ `A > B`
+ True if `A` is greater than `B`.
+
+* `A NE B`
+ `A ~= B`
+ `A <> B`
+ True if `A` is not equal to `B`.
+
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