Reputation
1,388
Next privilege 2,000 Rep.
Edit questions and answers
Badges
14 31
Newest
 Yearling
Impact
~63k people reached

  • 0 posts edited
  • 0 helpful flags
  • 410 votes cast
2d
awarded  Yearling
Feb
25
awarded  Popular Question
Jan
30
awarded  Nice Question
Jan
7
awarded  Nice Answer
Nov
29
awarded  Popular Question
Oct
22
awarded  Nice Answer
May
15
revised Why could Mertens not prove the prime number theorem?
[Edit removed during grace period]
May
2
awarded  Yearling
Mar
31
awarded  Notable Question
Mar
6
awarded  Popular Question
Sep
25
awarded  Favorite Question
Jul
2
awarded  Curious
May
12
awarded  Notable Question
May
2
awarded  Yearling
Aug
16
revised Is there a probability density function satisfying the following conditions?
edited tags
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 $y > 0$.
Aug
15
awarded  Necromancer
Aug
15
awarded  Nice Question
Aug
14
comment Is there a probability density function satisfying the following conditions?
@NikWeaver: Yes that is correct