Statistical functions

Beta and noncentral beta distributions

Cumulative beta distribution

Probability density of the beta distribution

Right-tailed beta distribution

Inverse cumulative beta distribution

Inverse of the upper-tailed distribution

Cumulative noncentral beta distribution

Probability density of the noncentral beta distribution

Inverse cumulative noncentral beta distribution

Binomial distribution

Cumulative binomial distribution

Probability mass of the binomial distribution

Right-tailed binomial distribution

Inverse cumulative binomial distribution

Inverse of the upper-tailed binomial distribution

Cauchy distribution New

Cumulative Cauchy distribution

Probability density of the Cauchy distribution

Reverse cumulative Cauchy distribution

Inverse cumulative Cauchy distribution

Inverse upper-tailed Cauchy distribution

Natural log of the Cauchy density

Chi-squared distribution

Cumulative chi-squared distribution

Probability density of chi-squared distribution

Right-tailed chi-squared distribution

Inverse cumulative chi-squared distribution

Inverse of the upper-tailed chi-squared distribution

Noncentral chi-squared distribution

Cumulative noncentral chi-squared distribution

Inverse cumulative noncentral chi-squared distribution

Noncentrality parameter of the noncentral chi-squared distribution

Probability density of noncentral chi-squared distribution

Reverse cumulative noncentral chi-squared distribution

Inverse of upper-tailed noncentral chi-squared distribution

Dunnett’s multiple range

Cumulative Dunnett’s multiple range distribution

Inverse cumulative Dunnett’s multiple range distribution

Exponential distribution*

Probability density of the exponential distribution

Cumulative exponential distribution

Reverse cumulative exponential distribution

Inverse cumulative exponential distribution

Inverse upper-tailed exponential distribution

F and noncentral F distributions

Cumulative F distribution

Probability density of the F distribution

Right-tailed F distribution

Inverse cumulative noncentral F distribution New

Inverse cumulative F distribution

Inverse of the upper-tailed distribution

Cumulative noncentral F distribution

Probability density of the noncentral F

Right-tailed noncentral F distribution

Inverse upper-tailed noncentral F distribution

Noncentrality parameter of the noncentral F distribution

Gamma distribution

Cumulative gamma distribution

Probability density of the gamma distribution

Right-tailed gamma distribution

Inverse cumulative gamma distribution

Inverse of the upper-tailed distribution

Partial derivatives of the cumulative gamma distribution

Second partial derivatives of the cumulative gamma distribution

Natural log of the inverse gamma density*

Hypergeometric distribution

Cumulative hypergeometric distribution

Probability mass of the hypergeometric distribution

Inverse Gaussian distribution

Cumulative inverse Gaussian distribution

Probability density of the inverse Gaussian distribution

Reverse cumulative inverse Gaussian distribution

Inverse cumulative inverse Gaussian distribution

Inverse upper-tailed inverse Gaussian distribution

Natural log of the inverse Gaussian density

Laplace distribution New

Cumulative Laplace distribution

Probability density of the Laplace distribution

Reverse cumulative Laplace distribution

Inverse cumulative Laplace distribution

Inverse upper-tailed Laplace distribution

Natural log of the Laplace density

Logistic distribution*

Probability density of the logistic distribution

Cumulative logistic distribution

Reverse cumulative logistic distribution

Inverse cumulative logistic distribution

Inverse upper-tailed logistic distribution

Negative binomial distribution

Cumulative negative binomial distribution

Probability mass function of the negative binomial distribution

Right-tailed negative binomial distribution

Inverse cumulative negative binomial distribution

Inverse of the upper-tailed negative binomial distribution

Normal, log of the normal, and binormal distributions

Cumulative bivariate normal distribution

Cumulative standard normal distribution

Probability density of the normal distribution

Inverse cumulative standard normal distribution

Log of the cumulative standard normal distribution

Log of the probability density of the normal distribution

Natural log of the multivariate normal density*

Poisson distribution

Cumulative Poisson distribution

Probability mass of the Poisson distribution

Right-tailed Poisson distribution

Inverse cumulative Poisson distribution

Inverse of the upper-tailed Poisson distribution

Student’s t and noncentral Student’s t distributions

Cumulative Student’s t distribution

Robability density of the Student’s t distribution

Right-tailed Student’s t distribution

Inverse cumulative Student’s t distribution

Inverse of the upper-tailed Student’s t distribution*

Cumulative noncentral Student’s t distribution

Probability density of the noncentral Student’s t distribution

Right-tailed noncentral Student’s t distribution

Inverse cumulative noncentral Student’s t distribution New

Inverse of the upper-tailed noncentral Student’s t distribution

Noncentrality parameter of the noncentral Student’s t distribution

Tukey’s Studentized range

Cumulative Tukey’s Studentized range distribution

Inverse cumulative Tukey’s Studentized range distribution

Weibull distribution*

Probability density of the Weibull distribution

Cumulative Weibull distribution

Upper-tailed Weibull distribution

Inverse cumulative Weibull distribution

Inverse upper-tailed Weibull distribution

Weibull (proportional hazards) distribution

Probability density of the Weibull (proportional hazards) distribution

Cumulative Weibull (proportional hazards) distribution

Reverse cumulative Weibull (proportional hazards) distribution

Inverse cumulative Weibull (proportional hazards) distribution

Inverse upper-tailed Weibull (proportional hazards) distribution

Wishart and inverse Wishart distributions*

Natural log of the density of the Wishart distribution

Natural log of the density of the inverse Wishart distribution

 

Date and time functions

Complete suite of functions for manipulating dates and datetimes, including support for business calendars and leap seconds

Convert dates and datetimes in string form to numeric form with great flexibility, including support for any order of year, month, day, hour, minute, second, and millisecond

Extract day, day of week, week of year, month, quarter, half-year, or year from specified date

Extract hour, minute, second, or millisecond from specified time or datetime, including optional adjustments for leap seconds

Convert between units of date and time

Convert between business dates and regular dates

 

Matrix functions

Stata has a powerful matrix language called Mata that contains hundreds of functions.

Below, we list some basic matrix functions that are provided within Stata. All of the same functionality, and more, is provided in Mata too. Mata is included with Stata.

Determinant of matrix

Trace of matrix

Number of rows of matrix

Number of columns of matrix

Number of zeros on diagonal of matrix

Floor of matrix element

Check if matrix is symmetric

Check for missing elements in matrix

Relative difference of two matrices

Column number associated with specified column name

Row number associated with specified row name

Identity matrix

Inverse of matrix

Cholesky decomposition

Hadamard matrix

Sweep matrix

Correlation matrix of variance matrix

Diagonal matrix from vector

r x c matrix with each element equal to z

r x c matrix with elements containing uniformly distributed pseudorandom numbers in [0,1]

Column vector from matrix

Random-number functions

Uniform over interval (0,1)

Uniform over interval (a,b)*

Uniform integers over interval [a,b]*

Standard normal

Normal, mean m and std. deviation 1

Normal, mean m and std. deviation s

Beta

Binomial

Cauchy New

Chi-squared

Exponential*

Gamma

Hypergeometric

Inverse Gaussian

Laplace New

Logistic, mean 0 and std. deviation π/√3*

Logistic, mean 0, scale s, std. deviation sπ/√3*

Logistic, mean m, scale s, std. deviation sπ/√3*

Negative binomial

Poisson

Student’s t

Weibull, shape a, scale b*

Weibull, shape a, scale b, location g*

Weibull (proportional hazards), shape a, scale b*

Weibull (proportional hazards), shape a, scale b, location g*

 

Random-number generators

64-bit Mersenne Twister generator*

Stream version of 64-bit Mersenne Twister  

Allow random numbers to be drawn correctly on multiple machines or in multiple processes

Each stream is independent of other streams

When the stream generator is used, all random-number functions automatically become stream enabled.

32-bit KISS generator

 

Mathematical functions

Programming functions

Absolute value

Ceiling

Combinatorial

Floor

Maximum

Minimum

Modulus

Relative difference

Round of x in units of y

Running sum

Sign

Truncation

Common transcendental functions

Natural logarithm

Base-10 logarithm

Exponential

Natural log of n factorial

Complementary log-log

Inverse of the complementary log-log

Logit

Inverse of the logit

Square root

Natural log of gamma

digamma

trigamma

 

Trigonometric functions

Sine of radians

Cosine of radians

Tangent of radians

Arcsine returning radians

Arccosine returning radians

Arctangent returning radians

Two-argument arctangent

Inverse hyperbolic sine

Inverse hyperbolic cosine

Inverse hyperbolic tangent

Hyperbolic sine

Hyperbolic cosine

Hyperbolic tangent

 

Time-series functions

Return whether time is within a specified range, excluding the range’s endpoints

Return whether time is within a specified range, including the range’s endpoints

 

String functions

Full Unicode (UTF-8) support*

Abbreviation

Concatenation

Duplication

Reduce multiple, consecutive internal blanks to one blank

Remove leading blanks

Remove trailing blanks

Remove both leading and trailing blanks

Lowercase string

Convert string to “proper” case

Uppercase string

Locale-aware “titlecase” string*

Pluralize string

Reversed string

Substitution of characters for pattern found in string

Substitution of characters for word found in string

Extract substring

Length of string

Position of first character in string in list of match characters

Position of first character in string not in list of match characters

Position of string in another string

nth word of string

Number of words in string

Convert string to numeric

Convert numeric to string

Sort and compare Unicode strings based on locale*

Regular expression pattern matching

Regular expression pattern replacement

Regular expression pattern subexpressions

Convert string to valid Stata name

Wildcard pattern matching

Convert strings to/from Unicode (UTF-8) and extended ASCII*

Escape and unescape Unicode (UTF-8) strings*

Unicode character for code point*

Code point for Unicode character*

ASCII character for decimal number

Soundex code for string

U.S. Census soundex code for string

Watch Unicode in Stata.

 

Low-level programming functions

Partition interval into n equal-length intervals

Recode number into one of several specified categories

Byte order of computer architecture on which Stata is currently running

Version of caller of currently running program to assist with backward compatibility version control

Round if rounding does not exceed specified tolerance

Convert number to single-precision floating-point value

Restrict returned value to a range

Conditional function to return one value if argument is true and another value if argument is false

Check for any missing value in set or arguments

Access to system parameters, system constants, and current setting values

Access to results of Stata commands

Return whether observation is in estimation subsample

Check whether value is in a list of arguments, string or numeric

Check whether value lies within a specified range of numbers or strings

Return maximum output width for value displayed with specified display format

Access to machine precision of double- and single-precision floating-point numbers

Access to cutoff value for normalized/denormalized IEEE double-precision floating point numbers

Access to largest and smallest possible values of each numeric Stata variable storage type

Read contents of file into string

Write string to file

Check whether file exists

Normalize Unicode strings*

Search for invalid UTF-8 sequences*