# Linear Congruential Generator (LCG)

The building block of a simulation study is the ability to generate random numbers where a random number represents the value of a random variable uniformly distributed on (0,1).

The generator is defined by the recurrence relation:

Xi+1=(aXi + C) Modulo m

$a$ and $m$ are given positive integers, $X_n$ is either $0,1, \dots, m-1$ and quantity $\frac{X_n}{m}$ is pseudo random number.

Some conditions are:

1. m>0m is usually large
2. 0<a<m;  (a is the multiplier)
3. 0≤<c<m (c is the increment)
4. 0≤X0<m  (X0is seed or starting value)
5. c and m are relatively prime numbers (there is no common factor between c and m).
6. a−1 is a multiple of every prime factor m
7. a−1 is multiple of 4 if m is multiple of 4

If  c=0, the generator is often called a multiplicative congruential method, or Lehmer RNG. If $c\neq0$ the generator is called a mixed congruential generator.

Read more about Pseudo Random Process and Random number Generation

Updated: Dec 1, 2014 — 12:04 am

#### Muhammad Imdadullah

Student and Instructor of Statistics and business mathematics. Currently Ph.D. Scholar (Statistics), Bahauddin Zakariya University Multan. Like Applied Statistics and Mathematics and Statistical Computing. Statistical and Mathematical software used are: SAS, STATA, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis etc.