Generating sequence of random numbers - r

Question

I need to create a function of five variables,
a (multiplier)
n (sample size)
c (increment with default 0)
m (modulus)
x0 (Initial seed value)
I need to generate a sequence of random numbers with the equation
xi = (a*xi-1 + c) (mod m), i = 1, 2, ..., n
As in the vector x = (x1, ..., xn).
My attempt:
my.unif1 <- function(n, a,c = 0, m, x = x[0]) {
while(n > 0) {
x[n] <- (a*x[n-1]+c)%%m
}
}

Answer 1

It sounds like you want to learn more about Linear Congruential Generators. Here's a resource that will probably help you solve your code problem: https://qualityandinnovation.com/2015/03/03/a-linear-congruential-generator-lcg-in-r/
lcg <- function(a,c,m,run.length,seed) {
x <- rep(0,run.length)
x[1] <- seed
for (i in 1:(run.length-1)) {
x[i+1] <- (a * x[i] + c) %% m
}
U <- x/m # scale all of the x's to
# produce uniformly distributed
# random numbers between [0,1)
return(list(x=x,U=U))
}
> z <- lcg(6,7,23,20,5)
> z
$x
[1] 5 14 22 1 13 16 11 4 8 9 15 5 14 22 1 13 16 11
[19] 4 8
$U
[1] 0.21739130 0.60869565 0.95652174 0.04347826 0.56521739
[6] 0.69565217 0.47826087 0.17391304 0.34782609 0.39130435
[11] 0.65217391 0.21739130 0.60869565 0.95652174 0.04347826
[16] 0.56521739 0.69565217 0.47826087 0.17391304 0.34782609

Answer 2

That could help:
my.fct.1 <- function(x, multiplier, increment, modulus){
increment <- ifelse(missing(increment), 0, increment) # setting the default increment to 0
newval <- (multiplier*x + increment) %% modulus
return(newval)
}
my.fct.2 <- function(x0, n, multiplier, increment, modulus){
if(n == 1){
val <- my.fct.1(x = x0, multiplier = multiplier, increment = increment, modulus = modulus)
vec <- c(x0, val)
return(vec)
}
if(n > 1){
vec <- my.fct.2(x = x0, n = n-1, multiplier = multiplier, increment = increment, modulus = modulus)
val <- vec[length(vec)]
newval <- my.fct.1(x = val, multiplier = multiplier, increment = increment, modulus = modulus)
newvec <- c(vec, newval)
return(newvec)
}
}
my.fct.2 does the required, the arguments are pretty much self explanatory. Watch out though, because it is a recursive function (which can affect speed among other things).
And here are some examples of such generated sequences:
> my.fct.2(3, 9, 7, -1, 4)
[1] 3 0 3 0 3 0 3 0 3 0
> my.fct.2(1, 9, 2, 1, 13)
[1] 1 3 7 2 5 11 10 8 4 9
> my.fct.2(0, 17, 5, 3, 7)
[1] 0 3 4 2 6 5 0 3 4 2 6 5 0 3 4 2 6 5
# and here the arguments set to cross check it against #mysteRious's answer
> my.fct.2(5, 20, 6, 7, 23)
[1] 5 14 22 1 13 16 11 4 8 9 15 5 14 22 1 13 16 11 4 8 9
U <- my.fct.2(5, 20, 6, 7, 23)/23
> U
[1] 0.21739130 0.60869565 0.95652174 0.04347826 0.56521739 0.69565217 0.47826087 0.17391304
[9] 0.34782609 0.39130435 0.65217391 0.21739130 0.60869565 0.95652174 0.04347826 0.56521739
[17] 0.69565217 0.47826087 0.17391304 0.34782609 0.39130435