Timeline for non-negative random variable
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 26, 2014 at 17:22 | comment | added | user16436 | I agree with you. That's the polynomial one should use. Thank you again, your suggestion is very helpful to me. | |
| Jul 25, 2014 at 7:24 | comment | added | Robert Israel | For the half-normal distribution, with the degree-4 polynomial $f(x) = 1 - (x - p_1)^2 (x - p_2)^2/(p1^2 p_2^2)$ with $p_1 = .773065746933609$, $p2 = 2.14702617243363$ I get $P(X>0) \ge 0.801242498847562$. So some improvement, but not huge. | |
| Jul 25, 2014 at 4:19 | vote | accept | user16436 | ||
| Jul 25, 2014 at 4:19 | comment | added | user16436 | Thank you very much. Using this method I was able to check that the Cauchy-Schwarz bound is the best you can get using degree two polynomials. I will try to see if it is possible to improve the $2/\pi$ bound for the half-normal distribution using polynomials of degree three or four. | |
| Jul 24, 2014 at 20:03 | history | answered | Robert Israel | CC BY-SA 3.0 |