# How can I make a Kolmogorov-Smirnov test to check if my data distribution is exponential?

I made a histogram of my data, and the fitting line, but from some reason the fitting line doesn't fit to my graph. How can I make it fit to it?

How can I check if my data distribution is exponential?

I ran this code in R:

 x<-tazpits\$time_b_arraival_m
summary(x)
Min. 0.0000
1st Qu. 0.2200
Median  0.5550
Mean 0.9802
3rd Qu. 1.2400
Max. 6.2500

h<-hist(x,breaks=104,main="hisogram of time between arrival",
ylab = "frenqency of arriving", xlab = "time in min",
col = "yellow")
xfit<-seq(0,6.25,length=104)
yfit<-dexp(xfit,1/0.9802)
lines(xfit,yfit) ## 1 Answer

1. There are two problem with your histogram;

• the first is that your bins are far too narrow (you appear to have as many bins as observations, try having no more than 20 for that number of observations

• the second is that you're comparing counts with density. You need your histogram to be scaled to integrate to 1 as well (use freq=FALSE)

2. You should not use an ordinary Kolmogorov-Smirnov test while estimating parameters (as you did here). If you want the same form of test statistic, you could use a Lilliefors test for the exponential distribution -- though there are other alternatives.

• What do you mean with "You should not use an ordinary Kolmogorov-Smirnov test while estimating parameters"? What parameter is being estimated here? Thank you. – stats.and.r Apr 22 at 17:26
• The Kolmogorov-Smirnov is a test for a completely specified distribution, but when OP said it was exponential, they didn't specify which one. You see in the code where the OP computed the sample mean and then used it to draw an exponential density? That was estimating the mean of the exponential. If you use that value in a KS test, it makes the cdf of the resulting values closer to an exponential cdf than a random sample from an exponential would be (whose sample mean would differ from the specified mean) . This has a strong impact on the significance level ... ctd – Glen_b Apr 23 at 1:47
• ctd... specifically, you'll reject much less than you ask to when the null is true (and so reduce power when it's false). It's easy to see the effect on significance level by simulation from the null. We need a test that deals with these issues. There are many tests for general exponentiality; I merely mentioned the one that is based on a Kolmogorov-Smirnov (but it may not be the best possible choice) – Glen_b Apr 23 at 1:51