help math functions
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Title
[D] functions -- Functions
Description
This is a quick reference for the mathematical functions. For help on
all functions, see [D] functions.
Mathematical functions
abs(x)
Domain: -8e+307 to 8e+307
Range: 0 to 8e+307
Description: returns the absolute value of x.
acos(x)
Domain: -1 to 1
Range: 0 to pi
Description: returns the radian value of the arccosine of x.
acosh(x)
Domain: 1 to 8.9e+307
Range: 0 to 709.77
Description: returns the inverse hyperbolic cosine of x,
acosh(x) = ln{x+sqrt(x*x - 1)}.
asin(x)
Domain: -1 to 1
Range: -pi/2 to pi/2
Description: returns the radian value of the arcsine of x.
asinh(x)
Domain: -8.9e+307 to 8.9e+307
Range: -709.77 to 709.77
Description: returns the inverse hyperbolic sine of x,
asinh(x) = ln{x+sqrt(x*x + 1)}.
atan(x)
Domain: -8e+307 to 8e+307
Range: -pi/2 to pi/2
Description: returns the radian value of the arctangent of x.
atan2(y,x)
Domain y: -8e+307 to 8e+307
Domain x: -8e+307 to 8e+307
Range: -pi to pi
Description: returns the radian value of the arctangent of y/x where
the signs of the parameters y and x are used to
determine the quadrant of the answer.
atanh(x)
Domain: -1 to 1
Range: -8e+307 to 8e+307
Description: returns the inverse hyperbolic tangent of x, atanh(x) =
(1/2){ln(1+x) - ln(1-x)}.
ceil(x)
Domain: -8e+307 to 8e+307
Range: integers in -8e+307 to 8e+307
Description: returns the unique integer n such that n - 1 < x < n.
returns x (not ".") if x is missing, meaning that
ceil(.a) = .a.
Also see floor(x), int(x), and round(x).
cloglog(x)
Domain: 0 to 1
Range: -8e+307 to 8e+307
Description: returns the complementary log-log of x,
cloglog(x) = ln{-ln(1-x)}.
comb(n,k)
Domain n: integers 1 to 1e+305
Domain k: integers 0 to n
Range: 0 to 8e+307 and missing
Description: returns the combinatorial function n!/{k!(n - k)!}.
cos(x)
Domain: -1e+18 to 1e+18
Range: -1 to 1
Description: returns the cosine of x, where x is in radians.
cosh(x)
Domain: -709 to 709
Range: 1 to 4.11e+307
Description: returns the hyperbolic cosine of x,
cosh(x) = {exp(x) + exp(-x)}/2.
digamma(x)
Domain: -1e+15 to 8e+307
Range: -8e+307 to 8e+307 and missing
Description: returns the digamma() function. This is the derivative
of lngamma(x).
The digamma(x) function is sometimes called the psi
function.
exp(x)
Domain: -8e+307 to 709
Range: 0 to 8e+307
Description: returns the exponential function of e^x. This function
is the inverse of ln(x).
floor(x)
Domain: -8e+307 to 8e+307
Range: integers in -8e+307 to 8e+307
Description: returns the unique integer n such that n < x < n + 1.
returns x (not ".") if x is missing, meaning that
floor(.a) = .a.
Also see ceil(x), int(x), and round(x).
int(x)
Domain: -8e+307 to 8e+307
Range: integers -8e+307 to 8e+307
Description: returns the integer obtained by truncating x toward 0;
thus,
int(5.2) = 5
int(-5.2) = -5
returns x (not ".") if x is missing, meaning that
int(.a) = .a.
One way to obtain the closest integer to x is
int(x+sign(x)/2), which simplifies to int(x+0.5) for x >
0. However, use of the round() function is preferred.
Also see round(x), ceil(x), and floor(x).
invcloglog(x)
Domain: -8e+307 to 8e+307
Range: 0 to 1 and missing
Description: returns the inverse of the complementary log-log
function of x,
invcloglog(x) = 1 - exp{-exp(x)}.
invlogit(x)
Domain: -8e+307 to 8e+307
Range: 0 to 1 and missing
Description: returns the inverse of the logit function of x,
invlogit(x) = exp(x)/{1 + exp(x)}.
ln(x)
Domain: 1e-323 to 8e+307
Range: -744 to 709
Description: returns the natural logarithm of ln(x). This function
is the inverse of exp(x).
lnfactorial(n)
Domain: integers 0 to 1e+305
Range: 0 to 8e+307
Description: returns the natural log of factorial = ln(n!).
To calculate n!, use round(exp(lnfactorial(n)),1) to
ensure that the result is an integer. Logs of
factorials are generally more useful than the factorials
themselves because of overflow problems.
lngamma(x)
Domain: -2,147,483,648 to 1e+305 (excluding negative integers)
Range: -8e+307 to 8e+307
Description: returns the natural log of the gamma function of x. For
integer values of x > 0, this is ln((x-1)!).
lngamma(x) for x < 0 returns a number such that
exp(lngamma(x)) is equal to the absolute value of the
gamma function. That is, lngamma(x) always returns a
real (not complex) result.
log(x)
Domain: 1e-323 to 8e+307
Range: -744 to 709
Description: returns the natural logarithm of ln(x), which is a
synonym for ln(x). Also see ln(x) for more
information.
log10(x)
Domain: 1e-323 to 8e+307
Range: -323 to 308
Description: returns the base-10 logarithm of x.
logit(x)
Domain: 0 to 1
Range: -8e+307 to 8e+307 and missing
Description: returns the log of the odds ratio of x,
logit(x) = ln{x/(1-x)}.
max(x1,x2,...,xn)
Domain x1: -8e+307 to 8e+307 and missing
Domain x2: -8e+307 to 8e+307 and missing
...
Domain xn: -8e+307 to 8e+307 and missing
Range: -8e+307 to 8e+307 and missing
Description: returns the maximum value of x1, x2, ..., xn. Unless
all arguments are missing, missing values are
ignored.
max(2,10,.,7) = 10
max(.,.,.) = .
min(x1,x2,...,xn)
Domain x1: -8e+307 to 8e+307 and missing
Domain x2: -8e+307 to 8e+307 and missing
...
Domain xn: -8e+307 to 8e+307 and missing
Range: -8e+307 to 8e+307 and missing
Description: returns the minimum value of x1, x2, ..., xn. Unless
all arguments are missing, missing values are
ignored.
min(2,10,.,7) = 2
min(.,.,.) = .
mod(x,y)
Domain x: -8e+307 to 8e+307
Domain y: 0 to 8e+307
Range: 0 to 8e+307
Description: returns the modulus of x with respect to y.
mod(x,y) = x - y*int(x/y)
mod(x,0) = .
reldif(x,y)
Domain x: -8e+307 to 8e+307 and missing
Domain y: -8e+307 to 8e+307 and missing
Range: -8e+307 to 8e+307 and missing
Description: returns the "relative" difference |x-y|/(|y|+1).
returns 0 if both arguments are the same type of
extended missing value.
returns missing if only one argument is missing, or the
two arguments are two different types of missing.
round(x,y) or round(x)
Domain x: -8e+307 to 8e+307
Domain y: -8e+307 to 8e+307
Range: -8e+307 to 8e+307
Description: returns x rounded in units of y or x rounded to the
nearest integer if the argument y is omitted.
returns x (not ".") if x is missing, meaning that
round(.a) = .a and round(.a,y) = .a if y is not
missing; if y is missing, "." is returned.
For y = 1, or with y omitted, this amounts to the
closest integer to x; round(5.2,1) is 5, as is
round(4.8,1); round(-5.2,1) is -5, as is round(-4.8,1).
The rounding definition is generalized for y != 1. With
y = .01, for instance, x is rounded to two decimal
places; round(sqrt(2),.01) is 1.41. y may also be larger
than 1; round(28,5) is 30, which is 28 rounded to the
closest multiple of 5. For y = 0, the function is
defined as returning x unmodified. Also see int(x),
ceil(x), and floor(x).
sign(x)
Domain: -8e+307 to 8e+307 and missing
Range: -1, 0, 1 and missing
Description: returns the sign of x: -1 if x < 0, 0 if x = 0, 1 if x >
0, and missing if x is missing.
sin(x)
Domain: -1e+18 to 1e+18
Range: -1 to 1
Description: returns the sine of x, where x is in radians.
sinh(x)
Domain: -709 to 709
Range: -4.11e+307 to 4.11e+307
Description: returns the hyperbolic sine of x,
sinh(x) = {exp(x) - exp(-x)}/2.
sqrt(x)
Domain: 0 to 8e+307
Range: 0 to 1e+154
Description: returns the square root of x.
sum(x)
Domain: all real numbers and missing
Range: -8e+307 to 8e+307 (excluding missing)
Description: returns the running sum of x, treating missing values as
zero.
For example, following the command generate y=sum(x),
the jth observation on y contains the sum of the first
through jth observations on x. See [D] egen for an
alternative sum function, total(), that produces a
constant equal to the overall sum.
tan(x)
Domain: -1e+18 to 1e+18
Range: -1e+17 to 1e+17 and missing
Description: returns the tangent of x, where x is in radians.
tanh(x)
Domain: -8e+307 to 8e+307
Range: -1 to 1 and missing
Description: returns the hyperbolic tangent of x,
tanh(x) = {exp(x) - exp(-x)}/{exp(x) + exp(-x)}.
trigamma(x)
Domain: -1e+15 to 8e+307
Range: 0 to 8e+307 and missing
Description: returns the second derivative of lngamma(x). The
trigamma() function is the derivative of digamma(x).
trunc(x) is a synonym for int(x).
Also see
Manual: [D] functions
Help: [D] egen
