Differences between revisions 8 and 15 (spanning 7 versions)

Stata Numeric Functions

Stata supports these numeric functions in the global scope.

Contents

Stata Numeric Functions

General Purpose

Function Name	Meaning	Example
`abs(n)`	Absolute value function
`ceil(n)`	Round up to an integer
`comb(n,k)`	Combinatorial function
`exp(n)`	Exponential function: eⁿ
`expm1(n)`	High precision implementation of `exp(n)-1`
`floor(n)`	Round down to an integer
`int(n)`	Round towards 0 to an integer	`-5 = int(-5.8)`
`invlogit(n)`	Inverse logit function
`ln(n)`	Natural log function
`logit(n)`	Logit function
`ln1m(n)`	High precision implementation of `ln(n-1)`
`ln1p(n)`	High precision implementation of `ln(n+1)`
`max(n,...)`	Returns the value of the greatest argument	`5 = max(1,.,5)`
`mix(n,...)`	Returns the value of the least argument	`1 = min(1,.,5)`
`mod(x,y)`	x modulo y
`real(s)`	Convert string s into a real number
`round(n)`	Round to the nearest integer
`round(n,p)`	Round to the nearest value for a given precision
`sign(n)`	Returns -1 if n<0, 0 if n=0, and 1 if n>0
`sqrt(n)`	Square root function
`string(n)`	Convert numeric value n into a string
`strofreal(n)`	Convert numeric value n into a string
`sum(x)`	Running sum of variable x
`trunc(n)`	Round towards 0 to an integer	`-5 = trunc(-5.8)`

Date and Time Functions

These functions take numbers but return date and datetime formatted values.

Function Name	Meaning	Output Format
`dhms(d,h,m,s)`	Attach hour, minute, and second data to a date	`%tc`
`Cdhms(d,h,m,s)`	Attach hour, minute, and second data to a date	`%tC`
`dmy(d,m,y)`	Calculate a date from a day, month, and year	`%td`
`hms(h,m,s)`	Calculate a time from an hour, minute, and second	`%tc`
`Chms(h,m,s)`	Calculate a time from an hour, minute, and second	`%tC`
`mdy(m,d,y)`	Calculate a date from a month, day, and year	`%td`
`mdyhms(m,d,y,h,m,s)`	Calculate a datetime from a year, month, day, hour, minute, and second	`%tc`
`Cmdyhms(m,d,y,h,m,s)`	Calculate a datetime from a year, month, day, hour, minute, and second	`%tC`
`y(y)`	Convert a numeric year into the number of years since the epoch	`%ty`
`yh(y,h)`	Convert a year and halfyear into the number of half years since the epoch	`%th`
`ym(y,m)`	Convert a year and month into the number of months since the epoch	`%tm`
`yq(y,q)`	Convert a year and quarter into the number of quarters since the epoch	`%tq`
`yw(y,w)`	Convert a year and week into the number of weeks since the epoch	`%tw`

These functions take two arguments: a date and a number. The number is a weekday identifier and must be between 0 (representing Sunday) through 6 (representing Saturday). The return value must be between 1 and 7 (inclusive).

Function Name	Meaning
`dayssincedow(d,n)`	Days between reference date and last weekday `n`
`dayssinceweekday(d,n)`	Days between reference date and last weekday `n`
`daysuntildow(d,n)`	Days between reference date and next weekday `n`
`daysuntilweekday(d,n)`	Days between reference date and next weekday `n`

These functions also operate on date or datetime formatted values and return numbers.

Function Name	Meaning
`age(dob,d)`	Integer age calculated from `dob` and reference date
`age_frac(dob,d)`	Decimal age calculated from `dob` and reference date
`Clockdiff(a,b,u)`	Integer difference between two datetimes, assuming `%tC` format
`Clockdiff_frac(a,b,u)`	Decimal difference between two datetimes, assuming `%tC` format
`clockdiff(a,b,u)`	Integer difference between two datetimes, assuming `%tc` format
`clockdiff_frac(a,b,u)`	Decimal difference between two datetimes, assuming `%tc` format
`datediff(a,b,u)`	Integer difference between two dates
`datediff_frac(a,b,u)`	Decimal difference between two dates

Most of the above functions require a (case-insensitive) unit u argument, specifying what the return value should be encoded as. This then also determines whether there is a fractional element that can be returned by the _frac version of the function.

For date differences (e.g., datediff), u can be:
- "day" or "d" for days
- "month", "mon", or "m" for months
- "year" or "y" for years
For datetime differences (e.g., clockdiff), u can be:
- "day" or "d" for days
- "hour" or "h" for hours
- "minute", "min", or "m" for minutes
- "second", "sec", or "s" for seconds
- "millisecond" or "ms" for milliseconds

Additionally, the functions operating on dates (e.g., datediff) can take an (case-insensitive) optional argument, specifying what date should be considered the anniversary for February 29th outside of leap years. This argument can be:

"1mar", "01mar", "mar1", or "mar01" (the default)
"28feb" or "feb28"

Statistical Functions

Function Name	Meaning	Example
`invnormal(p)`	Inverse cumulative standard normal distribution	`1.959964 = invnormal(1-0.05/2)`
`normal(z)`	Cumulative standard normal distribution	`.9750021 = normal(1.96)`
`runiform()`	Random number from uniform distribution from 0 to 1
`runiform(a,b)`	Random number from uniform distribution from a to b

Of relevance to random values: see set rng and set seed.

-  ⇤ ← Revision 8 as of 2023-06-13 23:04:14 → 
  Size: 3634
  Editor: DominicRicottone
  Comment:
+   ← Revision 15 as of 2025-05-20 19:25:02 → ⇥
  Size: 7615
  Editor: DominicRicottone
  Comment: Date diff functions
-Deletions are marked like this.
+Additions are marked like this.
 Line 11:
-== Dhms ==
+== General Purpose ==
 Line 13:
-Convert an date value (formatted as `%td) plus an hour, minute, and second into the number of milliseconds since the Stata epoch (`01jan1960 00:00:00.000`) ''ignoring'' leap seconds.

{{{
generate double datetime = dhms(dmy(day, month, year), hour, minute, second)
format date %tc
}}}

See also `Cdhms`, which creates returns a number that should instead be formatted as `%tC` because it does ''not'' ignore leap seconds.
+||'''Function Name'''||'''Meaning'''                                     ||'''Example'''     ||
||`abs(n)`           ||Absolute value function                           || ||
||`ceil(n)`          ||Round up to an integer                            || ||
||`comb(n,k)`        ||[[Statistics/Combinations|Combinatorial function]]|| ||
||`exp(n)`           ||Exponential function: ''e^n^''                    || ||
||`expm1(n)`         ||High precision implementation of `exp(n)-1`       || ||
||`floor(n)`         ||Round down to an integer                          || ||
||`int(n)`           ||Round towards 0 to an integer                     ||`-5 = int(-5.8)`  ||
||`invlogit(n)`      ||Inverse [[Statistics/Logit|logit function]]       || ||
||`ln(n)`            ||Natural log function                              || ||
||`logit(n)`         ||[[Statistics/Logit|Logit function]]               || ||
||`ln1m(n)`          ||High precision implementation of `ln(n-1)`        || ||
||`ln1p(n)`          ||High precision implementation of `ln(n+1)`        || ||
||`max(n,...)`       ||Returns the value of the greatest argument        ||`5 = max(1,.,5)`  ||
||`mix(n,...)`       ||Returns the value of the least argument           ||`1 = min(1,.,5)`  ||
||`mod(x,y)`         ||x modulo y                                        || ||
||`real(s)`          ||Convert string s into a real number               || ||
||`round(n)`         ||Round to the nearest integer                      || ||
||`round(n,p)`       ||Round to the nearest value for a given precision  || ||
||`sign(n)`          ||Returns -1 if n<0, 0 if n=0, and 1 if n>0         || ||
||`sqrt(n)`          ||Square root function                              || ||
||`string(n)`        ||Convert numeric value n into a string             || ||
||`strofreal(n)`     ||Convert numeric value n into a string             || ||
||`sum(x)`           ||Running sum of variable x                         || ||
||`trunc(n)`         ||Round towards 0 to an integer                     ||`-5 = trunc(-5.8)`||
-Line 26:
+Line 43:
-== Dmy ==
-Line 28:
+Line 44:
-Convert a day, month, and year into the number of days since the Stata epoch (`01jan1960 00:00:00.000`).
+== Date and Time Functions ==
-Line 30:
+Line 46:
-{{{
generate long date = dmy(day, month, year)
format date %td
}}}
+These functions take numbers but return [[Stata/DataFormats#Date_and_Datetime_Formats|date and datetime formatted values]].

||'''Function Name'''   ||'''Meaning'''                                                            ||'''Output Format'''||
||`dhms(d,h,m,s)`       ||Attach hour, minute, and second data to a date                           ||`%tc`              ||
||`Cdhms(d,h,m,s)`      ||Attach hour, minute, and second data to a date                           ||`%tC`              ||
||`dmy(d,m,y)`          ||Calculate a date from a day, month, and year                             ||`%td`              ||
||`hms(h,m,s)`          ||Calculate a time from an hour, minute, and second                        ||`%tc`              ||
||`Chms(h,m,s)`         ||Calculate a time from an hour, minute, and second                        ||`%tC`              ||
||`mdy(m,d,y)`          ||Calculate a date from a month, day, and year                             ||`%td`              ||
||`mdyhms(m,d,y,h,m,s)` ||Calculate a datetime from a year, month, day, hour, minute, and second   ||`%tc`              ||
||`Cmdyhms(m,d,y,h,m,s)`||Calculate a datetime from a year, month, day, hour, minute, and second   ||`%tC`              ||
||`y(y)`                ||Convert a numeric year into the number of years since the epoch          ||`%ty`              ||
||`yh(y,h)`             ||Convert a year and halfyear into the number of half years since the epoch||`%th`              ||
||`ym(y,m)`             ||Convert a year and month into the number of months since the epoch       ||`%tm`              ||
||`yq(y,q)`             ||Convert a year and quarter into the number of quarters since the epoch   ||`%tq`              ||
||`yw(y,w)`             ||Convert a year and week into the number of weeks since the epoch         ||`%tw`              ||

These functions take two arguments: a date and a number. The number is a weekday identifier and must be between 0 (representing Sunday) through 6 (representing Saturday). The return value must be between 1 and 7 (inclusive).

||'''Function Name'''    ||'''Meaning'''                                   ||
||`dayssincedow(d,n)`    ||Days between reference date and last weekday `n`||
||`dayssinceweekday(d,n)`||Days between reference date and last weekday `n`||
||`daysuntildow(d,n)`    ||Days between reference date and next weekday `n`||
||`daysuntilweekday(d,n)`||Days between reference date and next weekday `n`||

These functions also operate on date or datetime formatted values and return numbers.

||'''Function Name'''    ||'''Meaning'''                                                  ||
||`age(dob,d)`           ||Integer age calculated from `dob` and reference date           ||
||`age_frac(dob,d)`      ||Decimal age calculated from `dob` and reference date           ||
||`Clockdiff(a,b,u)`     ||Integer difference between two datetimes, assuming `%tC` format||
||`Clockdiff_frac(a,b,u)`||Decimal difference between two datetimes, assuming `%tC` format||
||`clockdiff(a,b,u)`     ||Integer difference between two datetimes, assuming `%tc` format||
||`clockdiff_frac(a,b,u)`||Decimal difference between two datetimes, assuming `%tc` format||
||`datediff(a,b,u)`      ||Integer difference between two dates                           ||
||`datediff_frac(a,b,u)` ||Decimal difference between two dates                           ||

Most of the above functions require a (case-insensitive) unit `u` argument, specifying what the return value should be encoded as. This then also determines ''whether'' there is a fractional element that can be returned by the `_frac` version of the function.
 * For date differences (e.g., `datediff`), `u` can be:
   * `"day"` or `"d"` for days
   * `"month"`, `"mon"`, or `"m"` for months
   * `"year"` or `"y"` for years
 * For datetime differences (e.g., `clockdiff`), `u` can be:
   * `"day"` or `"d"` for days
   * `"hour"` or `"h"` for hours
   * `"minute"`, `"min"`, or `"m"` for minutes
   * `"second"`, `"sec"`, or `"s"` for seconds
   * `"millisecond"` or `"ms"` for milliseconds

Additionally, the functions operating on dates (e.g., `datediff`) can take an (case-insensitive) optional argument, specifying what date should be considered the anniversary for February 29th outside of leap years. This argument can be:
 * `"1mar"`, `"01mar"`, `"mar1"`, or `"mar01"` (the default)
 * `"28feb"` or `"feb28"`
-Line 39:
+Line 103:
-== Hms ==
+== Statistical Functions ==
-Line 41:
+Line 105:
-Convert an hour, minute, and second into the number of milliseconds since midnight ''ignoring'' leap seconds.
+||'''Function Name'''||'''Meaning'''                                      ||'''Example'''                   ||
||`invnormal(p)`     ||Inverse cumulative standard normal distribution    ||`1.959964 = invnormal(1-0.05/2)`||
||`normal(z)`        ||Cumulative standard normal distribution            ||`.9750021 = normal(1.96)`       ||
||`runiform()`       ||Random number from uniform distribution from 0 to 1|| ||
||`runiform(a,b)`    ||Random number from uniform distribution from a to b|| ||
-Line 43:
+Line 111:
-{{{
generate double datetime = hms(hour, minute, second)
format date %tc
}}}

See also `Chms`, which creates returns a number that should instead be formatted as `%tC` because it does ''not'' ignore leap seconds.
+Of relevance to random values: see [[Stata/Set#Rng|set rng]] and [[Stata/Set#Seed|set seed]].
-Line 54:
+Line 117:
-== Mdy ==
+== See also ==
-Line 56:
+Line 119:
-Convert a month, day, and year into the number of days since the Stata epoch (`01jan1960 00:00:00.000`).
+[[https://www.stata.com/manuals/fnmathematicalfunctions.pdf|Stata mathematical functions]]
-Line 58:
+Line 121:
-{{{
generate long date = mdy(month, day, year)
format date %td
}}}

----



== Mdyhms ==

Convert a day, month, year, hour, minute, and second into the number of milliseconds since the Stata epoch (`01jan1960 00:00:00.000`) ''ignoring'' leap seconds.

{{{
generate double datetime = mdyhms(month, day, year, hour, minute, second)
format date %tc
}}}

See also `Cmdyhms`, which creates returns a number that should instead be formatted as `%tC` because it does ''not'' ignore leap seconds.

----



== Real ==

----



== Runiform ==

'''`runiform(a,b)`''' returns a random number between `a` and `b`. If no parameters are specified, the defaults of `0` and `1` are used.

Below is a demonstration for how an [[SurveySamples#Sampling_Methods|SRS sample]] can be drawn.

{{{
set seed 123456
generate double r_sampled = runiform()
sort r_sampled
generate byte sampled = _n <= 100 
}}}

The return value is a [[Stata/DataTypes|double]]; it will be within `a + c(epsdouble)` and `b − c(epsdouble)`.

By default, `runiform` uses the 64-bit Mersenne Twister algorithm. Alternate algorithms are available; see [[Stata/Set#Rng|set rng]].

See also [[Stata/Set#Seed|set seed]] for designing deterministic programs.

----



== String ==

Alias for `strofreal`.

----



== StrOfReal ==

----



== Y ==

Convert a year into the number of years since the Stata epoch (`01jan1960 00:00:00.000`).

{{{
generate int year = y(year)
format year %ty
}}}

----



== Yh ==

Convert a year and half year into the number of half years since the Stata epoch (`01jan1960 00:00:00.000`).

{{{
generate int halfyears = yh(year, halfyear)
format halfyears %th
}}}

----



== Ym ==

Convert a year and month into the number of months since the Stata epoch (`01jan1960 00:00:00.000`).

{{{
generate int months = y(year, month)
format months %tm
}}}

----



== Yq ==

Convert a year and quarter into the number of years since the Stata epoch (`01jan1960 00:00:00.000`).

{{{
generate int quarters = yq(year, quarter)
format quarters %tq
}}}

----



== Yw ==

Convert a year and week into the number of weeks since the Stata epoch (`01jan1960 00:00:00.000`).

{{{
generate int weeks = yw(year, week)
format weeks %tw
}}}
+[[https://www.stata.com/manuals/ddatetime.pdf|Stata datetimes]]

Diff for "Stata/NumericFunctions"

Stata Numeric Functions

General Purpose

Date and Time Functions

Statistical Functions

See also