+@c PSPP - a program for statistical analysis.
+@c Copyright (C) 2017 Free Software Foundation, Inc.
+@c Permission is granted to copy, distribute and/or modify this document
+@c under the terms of the GNU Free Documentation License, Version 1.3
+@c or any later version published by the Free Software Foundation;
+@c with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
+@c A copy of the license is included in the section entitled "GNU
+@c Free Documentation License".
+@c
+@c Use @func when referring to a function.
+@c Use @deftypefn for their definitions
+@macro func{NAME}
+@code{\NAME\}
+@end macro
+
@node Expressions
@chapter Mathematical Expressions
@cindex expressions, mathematical
parenthesis, one or more arguments, and a right parenthesis.
Function names are not reserved. Their names are specially treated
-only when followed by a left parenthesis, so that @code{EXP(10)}
-refers to the constant value @code{e} raised to the 10th power, but
-@code{EXP} by itself refers to the value of variable EXP.
+only when followed by a left parenthesis, so that @samp{EXP(10)}
+refers to the constant value @math{e} raised to the 10th power, but
+@samp{EXP} by itself refers to the value of a variable called @code{EXP}.
The sections below describe each function in detail.
* Trigonometry:: ACOS ARCOS ARSIN ARTAN ASIN ATAN COS SIN TAN
* Missing Value Functions:: MISSING NMISS NVALID SYSMIS VALUE
* Set Membership:: ANY RANGE
-* Statistical Functions:: CFVAR MAX MEAN MIN SD SUM VARIANCE
+* Statistical Functions:: CFVAR MAX MEAN MEDIAN MIN SD SUM VARIANCE
* String Functions:: CONCAT INDEX LENGTH LOWER LPAD LTRIM NUMBER
- RINDEX RPAD RTRIM STRING SUBSTR UPCASE
+ REPLACE RINDEX RPAD RTRIM STRING STRUNC SUBSTR
+ UPCASE
* Time and Date:: CTIME.xxx DATE.xxx TIME.xxx XDATE.xxx
DATEDIFF DATESUM
* Miscellaneous Functions:: LAG YRMODA VALUELABEL
numeric results.
@deftypefn {Function} {} EXP (@var{exponent})
-Returns @i{e} (approximately 2.71828) raised to power @var{exponent}.
+Returns @math{e} (approximately 2.71828) raised to power @var{exponent}.
@end deftypefn
@cindex logarithms
@end deftypefn
@deftypefn {Function} {} LN (@var{number})
-Takes the base-@i{e} logarithm of @var{number}. If @var{number} is
+Takes the base-@math{e} logarithm of @var{number}. If @var{number} is
not positive, the result is system-missing.
@end deftypefn
@deftypefn {Function} {} LNGAMMA (@var{number})
-Yields the base-@i{e} logarithm of the complete gamma of @var{number}.
+Yields the base-@math{e} logarithm of the complete gamma of @var{number}.
If @var{number} is a negative integer, the result is system-missing.
@end deftypefn
@end deftypefn
@cindex rounding
-@deftypefn {Function} {} RND (@var{number})
-Takes the absolute value of @var{number} and rounds it to an integer.
-Then, if @var{number} was negative originally, negates the result.
+@deftypefn {Function} {} RND (@var{number} [, @var{mult}[, @var{fuzzbits}]])
+Rounds @var{number} and rounds it to a multiple of @var{mult} (by
+default 1). Halves are rounded away from zero, as are values that
+fall short of halves by less than @var{fuzzbits} of errors in the
+least-significant bits of @var{number}. If @var{fuzzbits} is not
+specified then the default is taken from SET FUZZBITS (@pxref{SET
+FUZZBITS}), which is 6 unless overridden.
@end deftypefn
@cindex truncation
-@deftypefn {Function} {} TRUNC (@var{number})
-Discards the fractional part of @var{number}; that is, rounds
-@var{number} towards zero.
+@deftypefn {Function} {} TRUNC (@var{number} [, @var{mult}[, @var{fuzzbits}]])
+Rounds @var{number} to a multiple of @var{mult}, toward zero. For the
+default @var{mult} of 1, this is equivalent to discarding the
+fractional part of @var{number}. Values that fall short of a multiple
+of @var{mult} by less than @var{fuzzbits} of errors in the
+least-significant bits of @var{number} are rounded away from zero. If
+@var{fuzzbits} is not specified then the default is taken from SET
+FUZZBITS (@pxref{SET FUZZBITS}), which is 6 unless overridden.
@end deftypefn
@node Trigonometry
@deftypefn {Function} {} TAN (@var{angle})
Takes the tangent of @var{angle} which should be in radians.
Results in system-missing at values
-of @var{angle} that are too close to odd multiples of pi/2.
+of @var{angle} that are too close to odd multiples of @math{\pi/2}.
Portability: none.
@end deftypefn
are converted to system-missing values.
@deftypefn {Function} {} MISSING (@var{expr})
-Returns 1 if @var{expr} has the system-missing value, 0 otherwise.
+When @var{expr} is simply the name of a numeric variable, returns 1 if
+the variable has the system-missing value or if it is user-missing.
+For any other value 0 is returned.
+If @var{expr} takes another form, the function returns 1 if the value is
+system-missing, 0 otherwise.
@end deftypefn
@deftypefn {Function} {} NMISS (@var{expr} [, @var{expr}]@dots{})
@end deftypefn
@deftypefn {Function} {} SYSMIS (@var{expr})
-When @var{expr} is simply the name of a numeric variable, returns 1 if
-the variable has the system-missing value, 0 if it is user-missing or
-not missing. If given @var{expr} takes another form, results in 1 if
-the value is system-missing, 0 otherwise.
+Returns 1 if @var{expr} has the system-missing value, 0 otherwise.
@end deftypefn
@deftypefn {Function} {} VALUE (@var{variable})
Results in true if @var{value} is equal to any of the @var{set}
values. Otherwise, results in false. If @var{value} is
system-missing, returns system-missing. System-missing values in
-@var{set} do not cause ANY to return system-missing.
+@var{set} do not cause @func{ANY} to return system-missing.
@end deftypefn
@deftypefn {Function} {} RANGE (@var{value}, @var{low}, @var{high} [, @var{low}, @var{high}]@dots{})
Each @var{low} must be less than or equal to its corresponding
@var{high} value. @var{low} and @var{high} must be given in pairs.
If @var{value} is system-missing, returns system-missing.
-System-missing values in @var{set} do not cause RANGE to return
+System-missing values in @var{set} do not cause @func{RANGE} to return
system-missing.
@end deftypefn
Unlike most functions, statistical functions can return non-missing
values even when some of their arguments are missing. Most
statistical functions, by default, require only 1 non-missing value to
-have a non-missing return, but CFVAR, SD, and VARIANCE require 2.
+have a non-missing return, but @func{CFVAR}, @func{SD}, and @func {VARIANCE} require 2.
These defaults can be increased (but not decreased) by appending a dot
and the minimum number of valid arguments to the function name. For
-example, @code{MEAN.3(X, Y, Z)} would only return non-missing if all
+example, @subcmd{MEAN.3(X, Y, Z)} would only return non-missing if all
of @samp{X}, @samp{Y}, and @samp{Z} were valid.
@cindex coefficient of variation
Results in the mean of the values of @var{number}.
@end deftypefn
+@cindex median
+@deftypefn {Function} {} MEDIAN (@var{number}, @var{number}[, @dots{}])
+Results in the median of the values of @var{number}. Given an even
+number of nonmissing arguments, yields the mean of the two middle
+values.
+@end deftypefn
+
@cindex minimum
@deftypefn {Function} {} MIN (@var{number}, @var{number}[, @dots{}])
Results in the value of the least @var{value}. The @var{value}s may
format for @var{format}, system-missing is returned.
@end deftypefn
+@cindex strings, replacing substrings
+@cindex replacing substrings
+@deftypefn {Function} {} REPLACE (@var{haystack}, @var{needle}, @var{replacement}[, @var{n}])
+Returns string @var{haystack} with instances of @var{needle} replaced
+by @var{replacement}. If nonnegative integer @var{n} is specified, it
+limits the maximum number of replacements; otherwise, all instances of
+@var{needle} are replaced.
+@end deftypefn
+
@cindex strings, searching backwards
-@deftypefn {Function} {} RINDEX (@var{string}, @var{format})
+@deftypefn {Function} {} RINDEX (@var{haystack}, @var{needle})
Returns a positive integer indicating the position of the last
occurrence of @var{needle} in @var{haystack}. Returns 0 if
@var{haystack} does not contain @var{needle}. Returns system-missing if
returns the largest value. Returns 0 if @var{haystack} does not contain
any part in @var{needle}. It is an error if @var{needle_len} does not
evenly divide the length of @var{needle}. Returns system-missing
-if @var{needle} is an empty string.
+if @var{needle} is an empty string or if needle_len is less than 1.
@end deftypefn
@cindex padding strings
has the value @code{"123.6"}.
@end deftypefn
+@cindex strings, trimming
+@cindex strings, truncating
+@cindex white space, trimming
+@deftypefn {Function} {} STRUNC (@var{string}, @var{n})
+Returns @var{string}, first trimming it to at most @var{n} bytes, then
+removing trailing spaces. Returns an empty string if @var{n} is
+missing or negative.
+@end deftypefn
+
@cindex substrings
@cindex strings, taking substrings of
@deftypefn {Function} {} SUBSTR (@var{string}, @var{start})
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.
+probability. Only a few distributions include an @func{SIG} function.
@item IDF.@var{dist} (@var{p}[, @var{param}@dots{}])
Inverse distribution function for @var{dist}, the value of @var{x} for
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.
+few distributions include an @func{NPDF} function.
@item NCDF.@var{dist} (@var{x}[, @var{param}@dots{}])
Noncentral cumulative distribution function for @var{dist}, that is,
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})
+@c @deftypefn {Function} {} PDF.CHISQ (@var{x}, @var{df})
+@deftypefn {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})
+@c @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}.
@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})
+@c @deftypefnx {Function} {} NPDF.F (@var{x}, @var{df1}, @var{df2}, @var{lambda})
+@c @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{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
+@c @deftypefn {Function} {} PDF.HALFNRM (@var{x}, @var{a}, @var{b})
+@c @deftypefnx {Function} {} CDF.HALFNRM (@var{x}, @var{a}, @var{b})
+@c @deftypefnx {Function} {} IDF.HALFNRM (@var{p}, @var{a}, @var{b})
+@c @deftypefnx {Function} {} RV.HALFNRM (@var{a}, @var{b})
+@c Half-normal distribution with location parameter @var{a} and shape
+@c parameter @var{b}. Constraints: @var{b} > 0, 0 < @var{p} < 1.
+@c @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
+@c @deftypefn {Function} {} PDF.IGAUSS (@var{x}, @var{a}, @var{b})
+@c @deftypefnx {Function} {} CDF.IGAUSS (@var{x}, @var{a}, @var{b})
+@c @deftypefnx {Function} {} IDF.IGAUSS (@var{p}, @var{a}, @var{b})
+@c @deftypefnx {Function} {} RV.IGAUSS (@var{a}, @var{b})
+@c Inverse Gaussian distribution with parameters @var{a} and @var{b}.
+@c Constraints: @var{a} > 0, @var{b} > 0, @var{x} > 0, 0 <= @var{p} < 1.
+@c @end deftypefn
@deftypefn {Function} {} PDF.LANDAU (@var{x})
@deftypefnx {Function} {} RV.LANDAU ()
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
+@c @deftypefn {Function} {} CDF.SMOD (@var{x}, @var{a}, @var{b})
+@c @deftypefnx {Function} {} IDF.SMOD (@var{p}, @var{a}, @var{b})
+@c Studentized maximum modulus distribution with parameters @var{a} and
+@c @var{b}. Constraints: @var{a} > 0, @var{b} > 0, @var{x} > 0, 0 <=
+@c @var{p} < 1.
+@c @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
+@c @deftypefn {Function} {} CDF.SRANGE (@var{x}, @var{a}, @var{b})
+@c @deftypefnx {Function} {} IDF.SRANGE (@var{p}, @var{a}, @var{b})
+@c Studentized range distribution with parameters @var{a} and @var{b}.
+@c Constraints: @var{a} >= 1, @var{b} >= 1, @var{x} > 0, 0 <= @var{p} <
+@c 1.
+@c @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})
+@c @deftypefnx {Function} {} NPDF.T (@var{x}, @var{df}, @var{lambda})
+@c @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.
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})
+@deftypefn {Function} {} PDF.BINOM (@var{x}, @var{n}, @var{p})
+@deftypefnx {Function} {} CDF.BINOM (@var{x}, @var{n}, @var{p})
+@deftypefnx {Function} {} RV.BINOM (@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}.
projects / pspp / blobdiff