Equivalent of a flipped lognormal distribution What distribution could represent a "flipped" (skewed left) lognormal distribution?
For ex: what name would you do to the distribution in the figure below?

I fitted the histogram with a Beta distribution since the values of regularity are between 0 and 1. Is that correct? Is there a better/more flexible approach? I use Matlab..
 A: A reversed Lognormal ...  
I will use the notation here that is common in defining the Johnson family, since the latter commonly provides a 3 or 4 parameter version of the Lognormal that captures that which you seek.
If $Z \sim N(0,1)$, and $Y=\exp\big({\frac{Z-\gamma}{\delta }}\big)$, then $Y$ has a Lognormal distribution with pdf say $f(y)$:
$$f(y) = \frac{\delta}{y \sqrt{2 \pi }} {\exp\big[{-\frac{1}{2} \big(\gamma +\delta  \log (y)\big)^2}\big]}  \quad \quad \text{ for } y > 0$$
Applying a second transform $X=\xi -Y$ yields the reversed Lognormal that you seek, with pdf say $g(x)$:
$$g(x) = \frac{\delta}{(\xi -x) \sqrt{2 \pi }} {\exp\big[{-\frac{1}{2} \big(\gamma +\delta  \log (\xi -x)\big)^2}\big]} \quad \quad \text{ for } x< \xi$$
Example 
The following diagram represents grouped data from Table 1 in Pretorius (1930, p.148). Here, $X$ denotes barometric height (grouped data), while the vertical axis denotes observed frequency. 


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*The blue square curve represents the grouped data

*The red curve is a fitted reverse Lognormal using the automated JohnsonSL function from the mathStatica package for Mathematica.



References


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*Pretorius, S. J. (1930), Skew bivariate frequency surfaces, examined in the light of numerical illustrations, Biometrika, 22, 109-223.

A: Independent of scale (min,max of x-values), a beta distribution can have a left tail, and so can a power function distribution.  However, if your data did result in a left tail on a histogram, you could probably fit it very well using the stable distribution, which has four parameters.  The stable is used in QF (quantitative finance) to fit log-returns of asset prices, and can take on mixtures of distributions like Cauchy, Laplace, non-central Student's t, beta, logistic, normal, etc.  Don't look for it in software packages, since it's not that popular of a distribution in statistics.  
