X-Git-Url: https://pintos-os.org/cgi-bin/gitweb.cgi?a=blobdiff_plain;f=doc%2Fexpressions.texi;h=8e28ad5e24457e33c05161062f2ee546be707954;hb=b883ba798e5894de1bc246fe729c9a2fdb463d01;hp=32ace6c2dca2763ce716388c097d5e996f84650c;hpb=7fbfc32fc3c636959b0a25b3e76609f86519e84a;p=pspp diff --git a/doc/expressions.texi b/doc/expressions.texi index 32ace6c2dc..8e28ad5e24 100644 --- a/doc/expressions.texi +++ b/doc/expressions.texi @@ -1,9 +1,24 @@ +@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, @@ -15,14 +30,14 @@ strings or numbers as operands. With few exceptions, operands may be full-fledged expressions in themselves. @menu -* Boolean Values:: Boolean values. -* Missing Values in Expressions:: Using missing values in expressions. -* Grouping Operators:: parentheses -* Arithmetic Operators:: add sub mul div pow -* Logical Operators:: AND NOT OR -* Relational Operators:: EQ GE GT LE LT NE -* Functions:: More-sophisticated operators. -* Order of Operations:: Operator precedence. +* Boolean Values:: Boolean values +* Missing Values in Expressions:: Using missing values in expressions +* Grouping Operators:: parentheses +* Arithmetic Operators:: add sub mul div pow +* Logical Operators:: AND NOT OR +* Relational Operators:: EQ GE GT LE LT NE +* Functions:: More-sophisticated operators +* Order of Operations:: Operator precedence @end menu @node Boolean Values @@ -30,7 +45,7 @@ full-fledged expressions in themselves. @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 @@ -117,7 +132,7 @@ system-missing. The result of @code{0**0} is system-missing as well. @cindex @samp{-} @cindex negation @item - @var{a} -Reverses the sign of @var{a}. +Reverses the sign of @var{a}. @end table @node Logical Operators @@ -238,15 +253,15 @@ True if @var{a} is not equal to @var{b}. @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. @@ -256,10 +271,11 @@ 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 -* Time & Date:: CTIME.xxx DATE.xxx TIME.xxx XDATE.xxx +* 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 * Statistical Distribution Functions:: PDF CDF SIG IDF RV NPDF NCDF @@ -273,7 +289,7 @@ Advanced mathematical functions take numeric arguments and produce 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 @@ -283,12 +299,12 @@ not positive, the result is system-missing. @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 @@ -325,15 +341,24 @@ Returns the remainder when @var{number} is divided by 10. If @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 @@ -349,7 +374,7 @@ results. @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 @@ -381,7 +406,7 @@ Takes the sine of @var{angle} which should be in radians. @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 @@ -398,7 +423,11 @@ functions. In particular, user-missing values for numeric variables 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{}) @@ -414,10 +443,7 @@ variable ranges using the @code{@var{var1} TO @var{var2}} syntax. @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}) @@ -443,7 +469,7 @@ String comparisons are performed according to the rules given in 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{}) @@ -452,7 +478,7 @@ Results in true if @var{value} is in any of the intervals bounded by 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 @@ -475,10 +501,10 @@ using the @code{@var{var1} TO @var{var2}} syntax. 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 @@ -500,6 +526,13 @@ be numeric or string. 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 @@ -603,15 +636,24 @@ empty string. 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)} +characters 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, 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 @@ -624,7 +666,7 @@ 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. +if @var{needle} is an empty string or if needle_len is less than 1. @end deftypefn @cindex padding strings @@ -665,6 +707,15 @@ format specifier @var{format}. For example, @code{STRING(123.56, F5.1)} 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}) @@ -691,36 +742,36 @@ has value @code{"cd"}; @code{SUBSTR("nonsense", 4, 10)} has the value Returns @var{string}, changing lowercase letters to uppercase letters. @end deftypefn -@node Time & Date +@node Time and Date @subsection Time & Date Functions @cindex functions, time & date @cindex times @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 -* Time & Date Concepts:: How times & dates are defined and represented +* Time and Date Concepts:: How times & dates are defined and represented * Time Construction:: TIME.@{DAYS HMS@} * Time Extraction:: CTIME.@{DAYS HOURS MINUTES SECONDS@} * Date Construction:: DATE.@{DMY MDY MOYR QYR WKYR YRDAY@} * Date Extraction:: XDATE.@{DATE HOUR JDAY MDAY MINUTE MONTH QUARTER SECOND TDAY TIME WEEK WKDAY YEAR@} -* Time & Date Arithmetic:: DATEDIFF DATESUM +* Time and Date Arithmetic:: DATEDIFF DATESUM @end menu -@node Time & Date Concepts +@node Time and Date Concepts @subsubsection How times & dates are defined and represented @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 @@ -731,9 +782,9 @@ Thus, the following intervals correspond with the numeric values given: @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 @@ -763,7 +814,7 @@ Returns a time corresponding to @var{ndays} days. 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 @@ -773,7 +824,7 @@ vice versa. @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 @@ -886,18 +937,18 @@ Results in a date value corresponding to the day @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 @@ -917,7 +968,7 @@ that is, gives the date that @var{date-or-time} is in. 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 @@ -939,7 +990,7 @@ corresponding to @var{date}. @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 @@ -1001,7 +1052,7 @@ Returns the year (as an integer 1582 or greater) corresponding to @var{date}. @end deftypefn -@node Time & Date Arithmetic +@node Time and Date Arithmetic @subsubsection Time and Date Arithmetic @cindex time, mathematical properties of @@ -1025,7 +1076,7 @@ accuracy of some procedures may be affected. If necessary, convert 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 @@ -1077,7 +1128,8 @@ yields the value of that variable for the case @var{n} before the 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 @@ -1097,7 +1149,7 @@ use of a large value will increase memory consumption. @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 @@ -1120,7 +1172,7 @@ associated label, then this function returns the empty string. @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: @@ -1143,7 +1195,7 @@ a probability. 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 @@ -1159,7 +1211,7 @@ distribution. 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, @@ -1172,8 +1224,8 @@ include an NCDF function. The individual distributions are described individually below. @menu -* Continuous Distributions:: -* Discrete Distributions:: +* Continuous Distributions:: +* Discrete Distributions:: @end menu @node Continuous Distributions @@ -1194,7 +1246,7 @@ Constraints: @var{a} > 0, @var{b} > 0, @var{lambda} >= 0, 0 <= @var{x} @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. @@ -1208,12 +1260,12 @@ 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}) +@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}. @@ -1235,7 +1287,7 @@ Exponential distribution with scale parameter @var{a}. The inverse of 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}) @@ -1243,8 +1295,8 @@ PSPP extension. @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, @@ -1260,21 +1312,21 @@ Gamma distribution with shape parameter @var{a} and scale parameter @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 () @@ -1340,7 +1392,7 @@ Equivalent to RV.NORMAL(0, @var{sigma}). @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 @@ -1358,37 +1410,37 @@ parameter @var{b}. Constraints: @var{a} > 0, @var{b} > 0, @var{x} >= @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. @@ -1398,14 +1450,14 @@ distribution takes an additional parameter @var{lambda}. Constraints: @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 @@ -1442,9 +1494,9 @@ 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}) +@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}. @@ -1475,7 +1527,7 @@ Constraints: 0 <= @var{p} < 1, @var{x} >= 1. @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 @@ -1502,7 +1554,7 @@ subtraction. @enumerate @item -@code{( )} +@code{()} @item @code{**} @item @@ -1512,7 +1564,11 @@ subtraction. @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