2
$\begingroup$

I'm modelling data from a behavioural task. Participants do a few hundred trials. On each trial, they see a sequence of letters at a point on the screen and one of these letters appears surrounded by a white circle. Their task is to report the letter within the circle. Any response they make can be mapped onto a point in time on the trial relative to the white circle because there are no repeats in the sequences that they see. A response of the letter in the circle would have a value of 0; one letter before would have a score of -1; the letter after would have a score of 1 and so on. We've been modelling the distribution of these temporal errors with a mixture of a uniform distribution and some other, non-uniform distribution. Up until now the non-uniform distribution has been Gaussian, but certain theoretical considerations have led us to consider that we need a positively skewed component with a domain that is bounded at zero instead of the Gaussian. I considered using the lognormal distribution, but this is a bad choice because it is undefined at zero.

What positively skewed distributions can model values of zero and greater?

I'm using Matlab. Something that has a PDF written in that language would be great (I'm a scientist, not a statistician).

$\endgroup$
  • 1
    $\begingroup$ Truncating nearly any distribution below at $0$ is going to increase its skewness. That gives you a huge array of possible solutions (and every solution can be expressed in such a form). To keep this thread from being overly (and uselessly) broad, could you please be more specific about what you're modeling and what you're trying to accomplish? $\endgroup$ – whuber Jul 31 '18 at 11:41
  • $\begingroup$ Thanks @whuber. I've edited the post with more detail $\endgroup$ – ivan.k Aug 1 '18 at 1:14
1
$\begingroup$

You could take any distribution defined on $(0,\infty)$ and simply shift it to the left by a small $\epsilon$. Then you would get negative values in $(-\epsilon,0)$, which I guess is not what you are looking for.

Alternatively, your skewed component might derive from a two-stage data generating process that might either generate a zero or a nonzero value. If this sounds like something that might be present in your application, you might want to look into , i.e., s between a point mass at zero and a second distribution, which in turn could be supported on $(0,\infty)$ or $[0,\infty)$.

Zero inflated models are more common with , but there are applications for zero-inflated gamma distributions. And the gamma distribution has the advantage of being positively skewed. The skewness of a mixture is not overly hard to calculate.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.