The name of this probability density function

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Ad VanderVen
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TL;DR
Looking for the name of some probability density function.
Does anyone knows the name of the probability density function

f(y) =aeby-cy2
 

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Isn't that just the normal distibution? Complete the square in the exponent.
 
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Could be, but this function has support $$y \in (0, \infty)$$.
 
I think that just makes it a truncated normal.
 

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