0

I find the Gaussian distribution easy to comprehend with its two parameters: the mean $\mu$ centres it and the stdev $\sigma$ spreads it. However, what is its closest equivalent on a discrete finite (or semi-finite) domain? It is also important for me to maintain the "parameters" $\sigma$ and $\mu$ on this discretized (and potentially bounded) space since I want to control its centre and spread.

PS: Going through the list of discrete probability distributions, some do look like "discretized" Gaussians but their parameters aren't quite the centre and spread used in Gaussians. Examples of this are the Poisson or the Conway-Maxwell-Poisson distributions.

Tfovid
  • 163
  • In theory you want a quadratic log-pmf, but I don't think that gives closed forms for the mean or variance, or for the quadratic's coefficients in terms of them. – J.G. Dec 06 '20 at 10:48
  • 1
    You seem to want the mean and standard deviation to be exact. Do you have any other constraints, such as support on the non-negative integers? Otherwise choose a large $n$, let $Y \sim \text{Bin}(n,\frac12)$, and let $X=\mu + \frac{\sigma}{\sqrt{n}}(2Y-n)$ so $X$ has a discrete distribution on $n+1$ possible values with the desired mean and standard deviation and a close-to-normal distribution. – Henry Dec 06 '20 at 11:12
  • @Henry Regarding the support, I do indeed want to exclude non-negative integers (including zero). – Tfovid Dec 06 '20 at 11:21
  • @Tfovid "exclude"? – Henry Dec 06 '20 at 11:40
  • @Henry I meant the probability is zero for negative integers. – Tfovid Dec 06 '20 at 11:46

0 Answers0