Stata 15 help for math_functions

[FN] Mathematical functions

Functions

abs(x) Description: the absolute value of x Domain: -8e+307 to 8e+307 Range: 0 to 8e+307

ceil(x) Description: the unique integer n such that n - 1 < x < n; x (not ".") if x is missing, meaning that ceil(.a) = .a

Also see floor(x), int(x), and round(x). Domain: -8e+307 to 8e+307 Range: integers in -8e+307 to 8e+307

cloglog(x) Description: the complementary log-log of x cloglog(x) = ln{-ln(1-x)} Domain: 0 to 1 Range: -8e+307 to 8e+307

comb(n,k) Description: the combinatorial function n!/{k!(n - k)!} Domain n: integers 1 to 1e+305 Domain k: integers 0 to n Range: 0 to 8e+307 or missing

digamma(x) Description: the digamma() function

This is the derivative of lngamma(x). The digamma(x) function is sometimes called the psi function. Domain: -1e+15 to 8e+307 Range: -8e+307 to 8e+307 or missing

exp(x) Description: the exponential function of e^x

This function is the inverse of ln(x). Domain: -8e+307 to 709 Range: 0 to 8e+307

expm1(x) Description: e^x - 1 with higher precision than exp(x)-1 for small values of |x| Domain: -8e+307 to 709 Range: -1 to 8e+307

floor(x) Description: the unique integer n such that n < x < n + 1; x (not ".") if x is missing, meaning that floor(.a) = .a

Also see ceil(x), int(x), and round(x). Domain: -8e+307 to 8e+307 Range: integers in -8e+307 to 8e+307

int(x) Description: the integer obtained by truncating x toward 0 (thus, int(5.2) = 5 and int(-5.8) = -5); 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). Domain: -8e+307 to 8e+307 Range: integers in -8e+307 to 8e+307

invcloglog(x) Description: the inverse of the complementary log-log function of x invcloglog(x) = 1 - exp{-exp(x)} Domain: -8e+307 to 8e+307 Range: 0 to 1 or missing

invlogit(x) Description: the inverse of the logit function of x invlogit(x) = exp(x)/{1 + exp(x)} Domain: -8e+307 to 8e+307 Range: 0 to 1 or missing

ln(x) Description: the natural logarithm, ln(x)

This function is the inverse of exp(x). Domain: 1e-323 to 8e+307 Range: -744 to 709

ln1m(x) Description: the natural logarithm of 1-x with higher precision than ln(1-x) for small values of |x| Domain: -8e+307 to 1-c(epsdouble) Range: -37 to 709

ln1p(x) Description: the natural logarithm of 1+x with higher precision than ln(1+x) for small values of |x| Domain: -1+c(epsdouble) to 8e+307 Range: -37 to 709

lnfactorial(n) Description: the natural log of n 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. Domain: integers 0 to 1e+305 Range: 0 to 8e+307

lngamma(x) Description: 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. Domain: -2,147,483,648 to 1e+305 (excluding negative integers) Range: -8e+307 to 8e+307

log(x) Description: the natural logarithm, ln(x); thus, a synonym for ln(x) Domain: 1e-323 to 8e+307 Range: -744 to 709

log10(x) Description: the base-10 logarithm of x Domain: 1e-323 to 8e+307 Range: -323 to 308

log1m(x) Description: a synonym for ln1m(x)

log1p(x) Description: a synonym for ln1p(x)

logit(x) Description: the log of the odds ratio of x, logit(x) = ln{x/(1-x)} Domain: 0 to 1 (exclusive) Range: -8e+307 to 8e+307 or missing

max(x1,x2,...,xn) Description: the maximum value of x1, x2, ..., xn

Unless all arguments are missing, missing values are ignored. max(2,10,.,7) = 10 max(.,.,.) = . Domain x1: -8e+307 to 8e+307 or missing Domain x2: -8e+307 to 8e+307 or missing ... Domain xn: -8e+307 to 8e+307 or missing Range: -8e+307 to 8e+307 or missing

min(x1,x2,...,xn) Description: the minimum value of x1, x2, ..., xn Unless all arguments are missing, missing values are ignored. min(2,10,.,7) = 2 min(.,.,.) = . Domain x1: -8e+307 to 8e+307 or missing Domain x2: -8e+307 to 8e+307 or missing ... Domain xn: -8e+307 to 8e+307 or missing Range: -8e+307 to 8e+307 or missing

mod(x,y) Description: the modulus of x with respect to y mod(x,y) = x - y*floor(x/y) mod(x,0) = . Domain x: -8e+307 to 8e+307 Domain y: 0 to 8e+307 Range: 0 to 8e+307

reldif(x,y) Description: the "relative" difference |x-y|/(|y|+1); 0 if both arguments are the same type of extended missing value; missing if only one argument is missing or if the two arguments are two different types of missing Domain x: -8e+307 to 8e+307 or missing Domain y: -8e+307 to 8e+307 or missing Range: -8e+307 to 8e+307 or missing

round(x,y) or round(x) Description: x rounded in units of y or x rounded to the nearest integer if the argument y is omitted; x (not ".") if x is missing (meaning that round(.a) = .a and that round(.a,y) = .a if y is not missing) and if y is missing, then "." 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 = 0.01, 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). Domain x: -8e+307 to 8e+307 Domain y: -8e+307 to 8e+307 Range: -8e+307 to 8e+307

sign(x) Description: the sign of x: -1 if x < 0, 0 if x = 0, 1 if x > 0, or missing if x is missing Domain: -8e+307 to 8e+307 or missing Range: -1, 0, 1 or missing

sqrt(x) Description: the square root of x Domain: 0 to 8e+307 Range: 0 to 1e+154

sum(x) Description: 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. Domain: all real numbers or missing Range: -8e+307 to 8e+307 (excluding missing)

trigamma(x) Description: the second derivative of lngamma(x)

The trigamma() function is the derivative of digamma(x). Domain: -1e+15 to 8e+307 Range: 0 to 8e+307 or missing

trunc(x) Description: a synonym for int(x)

Video example

How to round a continuous variable


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