# [R] density plot of simulated exponential distributed data

Dennis Murphy djmuser at gmail.com
Wed Apr 27 04:53:07 CEST 2011

```Hi:

Try this (and note the use of vectorization rather than a loop):

rate <- 3
dta <- -log(1 - runif(1000))/rate
hist(dta, nclass = 30, probability = TRUE)
x <- c(0.001, seq(0, 3, by = 0.01))
lines(x, dexp(x, rate = 3))

This is the difference in timings between the vectorized and iterative
methods of generating the samples:

> system.time(replicate(1000, -log(1 - runif(1000))/rate))
user  system elapsed
0.10    0.00    0.09
> system.time(replicate(1000, { dt <- numeric(1000)
+ i <- 1
+ for(i in 1:1000){
+         r <- runif(1)
+         dt[i] <- log(1-r)/(-rate)
+         i <- i+1
+  } }))
user  system elapsed
9.35    0.00    9.40

Vectorization is usually your friend in R, and it pays to use it when
available. All of the d*, p*, q* and r* functions, where * denotes the
suffix for a distribution, are vectorized, as are most of the
functions in base R. A happy by-product is that it also makes for more

HTH,
Dennis

On Tue, Apr 26, 2011 at 3:19 PM, Juanjuan Chai <chaij at umail.iu.edu> wrote:
> Hi all,
>
> I tried to plot the density curve using the data from simulation. I am sure
> that the data should be exponentially distributed, but the plot of density
> curve always starts from (0,0) which is not the case for exponential
> distribution. Is there any way around this, to keep the curve dropping at 0?
>
> Thanks.
>
> The following are the codes I tested:
>
> data <- vector()
> rate <- 3
> i <- 1
> for(i in 1:1000){
>        r <- runif(1)
>        data[i] <- log(1-r)/(-rate)
>        i <- i+1
> }
> plot(density(data))
>
> -JJ
>
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