# Is a range of values from an exponential distribution still exponentially distributed?

I have to generate numbers of two different exponential distribution ($$e_1, e_2$$) with parameters respectively $$\lambda_1$$ and $$\lambda_2 = k \lambda_1$$, with $$0. But I also want to discard all the values from $$e_1$$ larger than $$B$$ and also discard all the values from $$e_2$$ smaller than $$B$$.

My question is: are these two sets of numbers still exponentially distributed? And in case, do they have the same $$\lambda_1$$ and $$\lambda_2 = k \lambda_1$$ parameters?

• Which two sets? The original ones are exponentially distributed by construction, whereas after censoring them at $B,$ neither can possibly be exponentially distributed because all exponential variables are supported on $[0,\infty).$
– whuber
Nov 30, 2019 at 14:13

No, they’re not exponentially distributed any more. Plot their histograms to convince yourself. There are special cases though. If $$B<0$$, $$e_2$$ will still be exponential because you drop no samples.