1
$\begingroup$

In order to test my program I need to calculate 95% confidence intervals (preferably even CDF) for a distribution of a renewal process with hypoexponentially distributed holding times: $X = X_{\lambda_1} + X_{\lambda_2}$, where $X_{\lambda_i}$ is an exponential distribution with ratio $\lambda_i$.

If the holding times were distributed exponentially I would use available implementation of Poisson distribution. However, with hypoexponential holding times I have no idea:

  • whether there is a particular name for such distribution,
  • how can I calculate such CDF (excluding Monte Carlo simulations).

I would appreciate any help.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
0
$\begingroup$

I have found that for sufficiently long times the renewal process may be approximated by a normal distribution $N({t \over \mu}, {\sigma \sqrt{t} \over \mu^{3 \over 2}} )$, where $\mu$ and $\sigma^2$ are (respectively) the expected value and variation of $X$ (which can be calculated as given in https://en.wikipedia.org/wiki/Hypoexponential_distribution).

Source: Henry C. Tuckwell 1988 Introduction to theoretical neurobiology v. 2 p. 197

Improve this answer
$\endgroup$

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.