Evaluating the tail of a distribution

Question

I have data which is exponentially distributed, but my $x$-values are cut off at 500, so there is no tail, and I want to visualise how that tail would look like. How can I do this?

Answer 1

The question asks for how to visualise the tail of the distribution, which entails estimating its parameters. Since this is exponential, there is one parameter, the rate $\lambda$, which may be estimated from $n$ samples $a_i$ as the inverse of their mean: $$\hat\lambda=\frac n{\sum_ia_i}$$ The plot beyond the cutoff may now be easily drawn by the pdf's formula $\lambda e^{-\lambda x}$.