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I would like to generate a random sequence composed of 3000 points, which follows the normal distribution. The mean is c and the standard deviation is d. But I would like these 3000 points lies in the range of [a,b].
Can you tell me how to do it in R?
If I would like to plot this sequence, if Y-axis uses the generated 3000 points, then how should I generate the points corresponding to X-axis.
978
To generate random numbers from a uniform distribution you can use the runif() function. Alternatively, you can use sample() to take a random sample using with or without replacements.
To create a random vector for a range of values, we can use sample function. We just need to pass the range and the sample size inside the sample function.
The R software provides access to the t-distribution by the dt() , pt() , qt() and rt() functions. Apply the help() function on these functions for further information. The rt() function generates random deviates of the t-distribution and is written as rt(n, df) . We may easily generate n number of random samples.
The runif() function generates random deviates of the uniform distribution and is written as runif(n, min = 0, max = 1) .
You can do this using standard R functions like this:
c <- 1
d <- 2
a <- -2
b <- 3.5
ll <- pnorm(a, c, d)
ul <- pnorm(b, c, d)
x <- qnorm( runif(3000, ll, ul), c, d )
hist(x)
range(x)
mean(x)
sd(x)
plot(x, type='l')
The pnorm function is used to find the limits to use for the uniform distriution, data is then generated from a uniform and then transformed back to the normal.
This is even simpler using the distr package:
library(distr)
N <- Norm(c,d)
N2 <- Truncate(N, lower=a, upper=b)
plot(N2)
x <- r(N2)(3000)
hist(x)
range(x)
mean(x)
sd(x)
plot(x, type='l')
Note that in both cases the mean is not c and the sd is not d. If you want the mean and sd of the resulting truncated data to be c and d, then you need the parent distribution (before truncating) to have different values (higher sd, mean depends on the truncating values), finding those values would be a good homework problem for a math/stat theory course. If that is what you really need then add a comment or edit the question to say so specifically.
If you want to generate the data from the untruncated normal, but only plot the data within the range [a,b] then just use the ylim argument to plot:
plot( rnorm(3000, c, d), ylim=c(a,b) )
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