+@c Use @func when refering 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.
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
@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
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
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