+@c PSPP - a program for statistical analysis.
+@c Copyright (C) 2017, 2020 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
@cindex mathematical expressions
-Expressions share a common syntax each place they appear in PSPP
+Expressions share a common syntax each place they appear in @pspp{}
commands. Expressions are made up of @dfn{operands}, which can be
numbers, strings, or variable names, separated by @dfn{operators}.
There are five types of operators: grouping, arithmetic, logical,
@cindex Boolean
@cindex values, Boolean
-Some PSPP operators and expressions work with Boolean values, which
+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
@cindex @samp{-}
@cindex negation
@item - @var{a}
-Reverses the sign of @var{a}.
+Reverses the sign of @var{a}.
@end table
@node Logical Operators
@cindex @code{(}
@cindex @code{)}
@cindex names, of functions
-PSPP functions provide mathematical abilities above and beyond
+@pspp{} functions provide mathematical abilities above and beyond
those possible using simple operators. Functions have a common
syntax: each is composed of a function name followed by a left
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
-* String Functions:: CONCAT INDEX LENGTH LOWER LPAD LTRIM NUMBER
- RINDEX RPAD RTRIM STRING SUBSTR UPCASE
+* Statistical Functions:: CFVAR MAX MEAN MEDIAN MIN SD SUM VARIANCE
+* String Functions:: CONCAT INDEX LENGTH LOWER LPAD LTRIM NUMBER
+ 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
@deftypefnx {Function} {} ACOS (@var{number})
Takes the arccosine, in radians, of @var{number}. Results in
system-missing if @var{number} is not between -1 and 1 inclusive.
-This function is a PSPP extension.
+This function is a @pspp{} extension.
@end deftypefn
@cindex arcsine
@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})
-Prevents the user-missing values of @var{variable} from being
-transformed into system-missing values, and always results in the
-actual value of @var{variable}, whether it is valid, user-missing, or
+@deftypefnx {Function} {} VALUE (@var{vector}(@var{index}))
+Prevents the user-missing values of the variable or vector element
+from being transformed into system-missing values, and always results
+in its actual value, whether it is valid, user-missing, or
system-missing.
@end deftypefn
produce Boolean results.
String comparisons are performed according to the rules given in
-@ref{Relational Operators}.
+@ref{Relational Operators}. User-missing string values are treated as
+valid values.
@deftypefn {Function} {} ANY (@var{value}, @var{set} [, @var{set}]@dots{})
-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.
+Returns true if @var{value} is equal to any of the @var{set} values,
+and false otherwise. For numeric arguments, returns system-missing if
+@var{value} is system-missing or if all the values in @var{set} are
+system-missing. If @var{value}
@end deftypefn
@deftypefn {Function} {} RANGE (@var{value}, @var{low}, @var{high} [, @var{low}, @var{high}]@dots{})
-Results in true if @var{value} is in any of the intervals bounded by
-@var{low} and @var{high} inclusive. Otherwise, results in false.
-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.
+Returns true if @var{value} is in any of the intervals bounded by
+@var{low} and @var{high} inclusive, and false otherwise. @var{low}
+and @var{high} must be given in pairs. Returns system-missing if any
+@var{high} is less than its @var{low} or, for numeric arguments, if
+@var{value} is system-missing or if all the @var{low}-@var{high} pairs
+contain one (or two) system-missing values. A pair does not match
+@var{value} if either @var{low} or @var{high} is missing, even if
+@var{value} equals the non-missing endpoint.
@end deftypefn
@node Statistical Functions
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
@deftypefn {Function} {} CONCAT (@var{string}, @var{string}[, @dots{}])
Returns a string consisting of each @var{string} in sequence.
@code{CONCAT("abc", "def", "ghi")} has a value of @code{"abcdefghi"}.
-The resultant string is truncated to a maximum of 255 characters.
+The resultant string is truncated to a maximum of 32767 bytes.
@end deftypefn
@cindex searching strings
@deftypefn {Function} {} INDEX (@var{haystack}, @var{needle})
-Returns a positive integer indicating the position of the first
-occurrence of @var{needle} in @var{haystack}. Returns 0 if @var{haystack}
-does not contain @var{needle}. Returns system-missing if @var{needle}
-is an empty string.
+@deftypefnx {Function} {} RINDEX (@var{haystack}, @var{needle})
+Returns a positive integer indicating the position of the first (for
+@code{INDEX}) or last (for @code{RINDEX}) occurrence of @var{needle}
+in @var{haystack}. Returns 0 if @var{haystack} does not contain
+@var{needle}. Returns 1 if @var{needle} is the empty string.
@end deftypefn
@deftypefn {Function} {} INDEX (@var{haystack}, @var{needles}, @var{needle_len})
-Divides @var{needles} into one or more needles, each with length
-@var{needle_len}.
-Searches @var{haystack} for the first occurrence of each needle, and
-returns the smallest 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{needles}. Returns
-system-missing if @var{needles} is an empty string.
+@deftypefnx {Function} {} RINDEX (@var{haystack}, @var{needle}, @var{needle_len})
+Divides @var{needles} into multiple needles, each with length
+@var{needle_len}, which must be a positive integer that evenly divides
+the length of @var{needles}. Searches @var{haystack} for the
+occurrences of each needle and returns a positive integer indicating
+the byte index of the beginning of the first (for @code{INDEX}) or
+last (for @code{RINDEX}) needle it finds. Returns 0 if @var{haystack}
+does not contain any of the needles, or if @var{needles} is the empty
+string.
@end deftypefn
@cindex strings, finding length of
@deftypefn {Function} {} LENGTH (@var{string})
-Returns the number of characters in @var{string}.
+Returns the number of bytes in @var{string}.
@end deftypefn
@cindex strings, case of
@end deftypefn
@cindex strings, padding
-@deftypefn {Function} {} LPAD (@var{string}, @var{length})
-If @var{string} is at least @var{length} characters in length, returns
-@var{string} unchanged. Otherwise, returns @var{string} padded with
-spaces on the left side to length @var{length}. Returns an empty string
-if @var{length} is system-missing, negative, or greater than 255.
-@end deftypefn
+@deftypefn {Function} {} LPAD (@var{string}, @var{length}[, @var{padding}])
+@deftypefnx {Function} {} RPAD (@var{string}, @var{length}[, @var{padding}])
+If @var{string} is at least @var{length} bytes long, these functions
+return @var{string} unchanged. Otherwise, they return @var{string}
+padded with @var{padding} on the left side (for @code{LPAD}) or right
+side (for @code{RPAD}) to @var{length} bytes. These functions report
+an error and return @var{string} unchanged if @var{length} is missing
+or bigger than 32767.
-@deftypefn {Function} {} LPAD (@var{string}, @var{length}, @var{padding})
-If @var{string} is at least @var{length} characters in length, returns
-@var{string} unchanged. Otherwise, returns @var{string} padded with
-@var{padding} on the left side to length @var{length}. Returns an empty
-string if @var{length} is system-missing, negative, or greater than 255, or
-if @var{padding} does not contain exactly one character.
+The @var{padding} argument must not be an empty string and defaults to
+a space if not specified. If its length does not evenly fit the
+amount of space needed for padding, the returned string will be
+shorter than @var{length}.
@end deftypefn
@cindex strings, trimming
@cindex white space, trimming
-@deftypefn {Function} {} LTRIM (@var{string})
-Returns @var{string}, after removing leading spaces. Other white space,
-such as tabs, carriage returns, line feeds, and vertical tabs, is not
-removed.
-@end deftypefn
-
-@deftypefn {Function} {} LTRIM (@var{string}, @var{padding})
-Returns @var{string}, after removing leading @var{padding} characters.
-If @var{padding} does not contain exactly one character, returns an
-empty string.
+@deftypefn {Function} {} LTRIM (@var{string}[, @var{padding}])
+@deftypefnx {Function} {} RTRIM (@var{string}[, @var{padding}])
+These functions return @var{string}, after removing leading (for
+@code{LTRIM}) or trailing (for @code{RTRIM}) copies of @var{padding}.
+If @var{padding} is omitted, these functions remove spaces (but not
+tabs or other white space). These functions return @var{string}
+unchanged if @var{padding} is the empty string.
@end deftypefn
@cindex numbers, converting from strings
@deftypefn {Function} {} NUMBER (@var{string}, @var{format})
Returns the number produced when @var{string} is interpreted according
to format specifier @var{format}. If the format width @var{w} is less
-than the length of @var{string}, then only the first @var{w}
-characters in @var{string} are used, e.g.@: @code{NUMBER("123", F3.0)}
-and @code{NUMBER("1234", F3.0)} both have value 123. If @var{w} is
+than the length of @var{string}, then only the first @var{w} bytes in
+@var{string} are used, @i{e.g.}@: @code{NUMBER("123", F3.0)} and
+@code{NUMBER("1234", F3.0)} both have value 123. If @var{w} is
greater than @var{string}'s length, then it is treated as if it were
right-padded with spaces. If @var{string} is not in the correct
format for @var{format}, system-missing is returned.
@end deftypefn
-@cindex strings, searching backwards
-@deftypefn {Function} {} RINDEX (@var{string}, @var{format})
-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
-@var{needle} is an empty string.
-@end deftypefn
-
-@deftypefn {Function} {} RINDEX (@var{haystack}, @var{needle}, @var{needle_len})
-Divides @var{needle} into parts, each with length @var{needle_len}.
-Searches @var{haystack} for the last occurrence of each part, and
-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.
-@end deftypefn
-
-@cindex padding strings
-@cindex strings, padding
-@deftypefn {Function} {} RPAD (@var{string}, @var{length})
-If @var{string} is at least @var{length} characters in length, returns
-@var{string} unchanged. Otherwise, returns @var{string} padded with
-spaces on the right to length @var{length}. Returns an empty string if
-@var{length} is system-missing, negative, or greater than 255.
-@end deftypefn
-
-@deftypefn {Function} {} RPAD (@var{string}, @var{length}, @var{padding})
-If @var{string} is at least @var{length} characters in length, returns
-@var{string} unchanged. Otherwise, returns @var{string} padded with
-@var{padding} on the right to length @var{length}. Returns an empty
-string if @var{length} is system-missing, negative, or greater than 255,
-or if @var{padding} does not contain exactly one character.
-@end deftypefn
-
-@cindex strings, trimming
-@cindex white space, trimming
-@deftypefn {Function} {} RTRIM (@var{string})
-Returns @var{string}, after removing trailing spaces. Other types of
-white space are not removed.
-@end deftypefn
-
-@deftypefn {Function} {} RTRIM (@var{string}, @var{padding})
-Returns @var{string}, after removing trailing @var{padding} characters.
-If @var{padding} does not contain exactly one character, returns an
-empty string.
+@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, converting from numbers
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 (but not tabs or other white space). Returns
+an empty string if @var{n} is zero or negative, or @var{string}
+unchanged if @var{n} is missing.
+@end deftypefn
+
@cindex substrings
@cindex strings, taking substrings of
@deftypefn {Function} {} SUBSTR (@var{string}, @var{start})
@end deftypefn
@deftypefn {Function} {} SUBSTR (@var{string}, @var{start}, @var{count})
-Returns a string consisting of the first @var{count} characters from
-@var{string} beginning at position @var{start}. Returns an empty string
-if @var{start} or @var{count} is system-missing, if @var{start} is less
-than 1 or greater than the number of characters in @var{string}, or if
-@var{count} is less than 1. Returns a string shorter than @var{count}
-characters if @var{start} + @var{count} - 1 is greater than the number
-of characters in @var{string}. Examples: @code{SUBSTR("abcdefg", 3, 2)}
-has value @code{"cd"}; @code{SUBSTR("nonsense", 4, 10)} has the value
-@code{"sense"}.
+Returns a string consisting of the first @var{count} bytes from
+@var{string} beginning at position @var{start}. Returns an empty
+string if @var{start} or @var{count} is system-missing, if @var{start}
+is less than 1 or greater than the number of bytes in @var{string}, or
+if @var{count} is less than 1. Returns a string shorter than
+@var{count} bytes if @var{start} + @var{count} - 1 is greater than the
+number of bytes in @var{string}. Examples: @code{SUBSTR("abcdefg", 3,
+2)} has value @code{"cd"}; @code{SUBSTR("nonsense", 4, 10)} has the
+value @code{"sense"}.
@end deftypefn
@cindex case conversion
@cindex dates
@cindex dates, valid
-For compatibility, PSPP considers dates before 15 Oct 1582 invalid.
+For compatibility, @pspp{} considers dates before 15 Oct 1582 invalid.
Most time and date functions will not accept earlier dates.
@menu
@cindex time, concepts
@cindex time, intervals
-Times and dates are handled by PSPP as single numbers. A
-@dfn{time} is an interval. PSPP measures times in seconds.
+Times and dates are handled by @pspp{} as single numbers. A
+@dfn{time} is an interval. @pspp{} measures times in seconds.
Thus, the following intervals correspond with the numeric values given:
-
+
@example
10 minutes 600
1 hour 3,600
@cindex dates, concepts
@cindex time, instants of
A @dfn{date}, on the other hand, is a particular instant in the past
-or the future. PSPP represents a date as a number of seconds since
+or the future. @pspp{} represents a date as a number of seconds since
midnight preceding 14 Oct 1582. Because midnight preceding the dates
-given below correspond with the numeric PSPP dates given:
+given below correspond with the numeric @pspp{} dates given:
@example
15 Oct 1582 86,400
Returns a time corresponding to @var{nhours} hours, @var{nmins}
minutes, and @var{nsecs} seconds. The arguments may not have mixed
signs: if any of them are positive, then none may be negative, and
-vice versa.
+vice versa.
@end deftypefn
@node Time Extraction
@cindex examination, of times
@cindex time, lengths of
-These functions take numeric arguments in PSPP time format and
+These functions take numeric arguments in @pspp{} time format and
give numeric results.
@cindex days
@cindex date examination
@cindex arguments, of date extraction functions
-These functions take numeric arguments in PSPP date or time
+These functions take numeric arguments in @pspp{} date or time
format and give numeric results. These names are used for arguments:
@table @var
@item date
-A numeric value in PSPP date format.
+A numeric value in @pspp{} date format.
@item time
-A numeric value in PSPP time format.
+A numeric value in @pspp{} time format.
@item time-or-date
-A numeric value in PSPP time or date format.
+A numeric value in @pspp{} time or date format.
@end table
@cindex days
For a time, results in the number of whole hours beyond the number of
whole days represented by @var{date-or-time}. For a date, results in
the hour (as an integer between 0 and 23) corresponding to
-@var{date-or-time}.
+@var{date-or-time}.
@end deftypefn
@cindex day of the year
@cindex time, in minutes
@deftypefn {Function} {} XDATE.MINUTE (@var{time-or-date})
Results in the number of minutes (as an integer between 0 and 59) after
-the last hour in @var{time-or-date}.
+the last hour in @var{time-or-date}.
@end deftypefn
@cindex months
times or dates in seconds to some other unit, like days or years,
before performing analysis.
-PSPP supplies a few functions for date arithmetic:
+@pspp{} supplies a few functions for date arithmetic:
@deftypefn {Function} {} DATEDIFF (@var{date2}, @var{date1}, @var{unit})
Returns the span of time from @var{date1} to @var{date2} in terms of
current one. Results in system-missing (for numeric variables) or
blanks (for string variables) for the first @var{n} cases.
-@code{LAG} obtains values from the cases that become the new active file
+@code{LAG} obtains values from the cases that become the new active
+dataset
after a procedure executes. Thus, @code{LAG} will not return values
from cases dropped by transformations such as @cmd{SELECT IF}, and
transformations like @cmd{COMPUTE} that modify data will change the
@cindex Julian date
@deftypefn {Function} {} YRMODA (@var{year}, @var{month}, @var{day})
@var{year} is a year, either between 0 and 99 or at least 1582.
-Unlike other PSPP date functions, years between 0 and 99 always
+Unlike other @pspp{} date functions, years between 0 and 99 always
correspond to 1900 through 1999. @var{month} is a month between 1 and
13. @var{day} is a day between 0 and 31. A @var{day} of 0 refers to
the last day of the previous month, and a @var{month} of 13 refers to
@node Statistical Distribution Functions
@subsection Statistical Distribution Functions
-PSPP can calculate several functions of standard statistical
+@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:
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,
The individual distributions are described individually below.
@menu
-* Continuous Distributions::
-* Discrete Distributions::
+* Continuous Distributions::
+* Discrete Distributions::
@end menu
@node Continuous Distributions
@end deftypefn
@deftypefn {Function} {} PDF.BVNOR (@var{x0}, @var{x1}, @var{rho})
-@deftypefnx {Function} {} CDF.VBNOR (@var{x0}, @var{x1}, @var{rho})
+@deftypefnx {Function} {} CDF.BVNOR (@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.
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}.
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.
+@pspp{} extension.
@end deftypefn
@deftypefn {Function} {} PDF.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})
+@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 ()
@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.
+deviation @var{sigma}. This distribution is a @pspp{} extension.
Constraints: @var{a} > 0, @var{x} > @var{a}, 0 < @var{p} < 1.
@end deftypefn
@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,
+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.
+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
+@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.
@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.
+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 <
+distribution is a @pspp{} extension. Constraints: @var{x} > 0, 0 <
@var{p} < 1.
@end deftypefn
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}.
@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
+Negative binomial distribution with number of successes parameter
@var{n} and probability of success parameter @var{p}. Constraints:
integer @var{n} >= 0, 0 < @var{p} <= 1, integer @var{x} >= 1.
@end deftypefn
@enumerate
@item
-@code{( )}
+@code{()}
@item
@code{**}
@item
@item
@code{+ -}
@item
-@code{EQ GE GT LE LT NE}
+@code{= >= > <= < <>}
+@item
+@code{NOT}
+@item
+@code{AND}
@item
-@code{AND NOT OR}
+@code{OR}
@end enumerate
projects / pspp / blobdiff