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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 $0<k<1$. 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?

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  • $\begingroup$ 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 $[0,\infty).$ $\endgroup$
    – whuber
    Nov 30, 2019 at 14:13

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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.

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  • $\begingroup$ I expected that. Thanks $\endgroup$
    – linofex
    Nov 30, 2019 at 13:02

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