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Fractal Analytics

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Aug
16
revised Is there a probability density function satisfying the following conditions?
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Aug
15
comment Is there a probability density function satisfying the following conditions?
@Fedja: No I still don't understand. Can you exemplify with one working example of a solution that works for all $y > 0$.
Aug
15
comment Is there a probability density function satisfying the following conditions?
@Nik, I had the same formulation that you have given and I can draw several distributions through $(0,1)$ and $(1,e^{-y})$. However satisfying condition 5 is the problem. For example $p(x,y) = e^{-yx^a}$ satisfies the first four conditions. Now if conditions 5 is also going to be true the we find that $y$ must be exactly equal to $\Gamma(1+1/a)^a$. But the minimum value of $\Gamma(1+1/a)^a$ is $e^{-\gamma}$. So this solutions is good for $y > e^{-\gamma}$ but it does not hold for $0 < y < e^{-\gamma}$. Likewise I have not been able to find a function $p(x,y)$ which satisfies 5 for all $y > 0$.
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Aug
14
comment Is there a probability density function satisfying the following conditions?
@NikWeaver: Yes that is correct
Aug
14
awarded  Custodian
Aug
14
revised Is there a probability density function satisfying the following conditions?
edited title
Aug
14
reviewed Reject Is there a probability density function satisfying the following conditions?
Aug
14
asked Is there a probability density function satisfying the following conditions?
Aug
2
revised Asymptotic bounds on $\pi^{-1}(x)$ (inverse prime counting function)
edited body
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8
awarded  Tumbleweed
Jun
28
revised Density of prime pairs whose gap is less than the average gap
edited body
Jun
28
accepted Density of prime pairs whose gap is less than the average gap
Jun
27
revised Density of prime pairs whose gap is less than the average gap
edited title
Jun
27
asked Density of prime pairs whose gap is less than the average gap