Graduate The name of this probability density function

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The probability density function f(y) = aeby - cy² is discussed, with participants questioning whether it represents a normal distribution. It is noted that completing the square in the exponent could suggest a normal distribution, but the function's support being y ∈ (0, ∞) indicates it may be a truncated normal distribution. The conversation highlights the importance of support in determining the classification of probability density functions. Overall, the function's characteristics lead to the conclusion that it is likely a truncated normal distribution.
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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.
 
I thought so too.
 

Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
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