I have a distribution which looks a bit binomial, though with a cutoff, i.e.:

$P(x) = 0$ if $x \le 0$, rises to a bell-shaped peak at around $x=0.2%$, appears to tail off exponentially until an abrubt cut such that $P(x)=0 $ if $x>1$.

I don't want to make any claim as to what kind of distribution this is, as the mechanism behind it is too complex to analyze. Are there some adjectives that formally describe its shape though? A word that means "a bit binomial-looking"?

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    $\begingroup$ the truncated binomial? $\endgroup$
    – user603
    Sep 27 '13 at 10:53
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    $\begingroup$ If $P(x) = 0$ for $x\le 0$ and $x>1$ then you only have support between 0 and 1? That doesn't look at all like a binomial? Binomial is a discrete distribution on positive integers so wouldn't "have a peak at 0.2". Perhaps a beta distribution would be a good match to what you are seeing? $\endgroup$
    – Corvus
    Sep 27 '13 at 11:26
  • $\begingroup$ @Sideshow Bob: Maybe something like a right truncated gamma distribution? $\endgroup$
    – Michael M
    Sep 27 '13 at 12:24
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    $\begingroup$ From this description--which is fine--there is no basis whatsoever to use terms like "binomial" or "beta" or "gamma" to describe the distribution. (The first two conflict with at least one element of the description, anyway.) Some general terms to research in this context include "truncated," "unimodal," and (positively) "skewed." $\endgroup$
    – whuber
    Sep 27 '13 at 13:24

You could use a graphical method, that is, you could compare it graphically to some given "null" distribution. The normal distribution is often used for this purpose, but you might choose others. For instance, for data measuring some (survival?) time, you could compare to some exponential distribution, say with the same mean. This could be done with a kind of QQ-plot, comparing sample quantiles to theoretical quantiles from the comparison distribution, or using the concept of relative distribution. Search this site.

For some examples of use of relative distributions see: What are good data visualization techniques to compare distributions?


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