Bound on mills ratio of Normal distribution Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Unknown result in probability theory relating CDF of any density to the CDF of normal distributionNormal distribution inequalityThe normal approximation of Poisson distributionAn interesting inequality about the cdf of the normal distributionChernoff-like bound for small intervals in tail distributionNormal approximation of tail probability in binomial distributionBivariate normal distribution $X$ and $Y$Inverse Mills ratio for non normal distributions.Normal distribution inequality related to the monotone likelihood ratio propertyTruncated normal random variable
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Bound on mills ratio of Normal distribution
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Unknown result in probability theory relating CDF of any density to the CDF of normal distributionNormal distribution inequalityThe normal approximation of Poisson distributionAn interesting inequality about the cdf of the normal distributionChernoff-like bound for small intervals in tail distributionNormal approximation of tail probability in binomial distributionBivariate normal distribution $X$ and $Y$Inverse Mills ratio for non normal distributions.Normal distribution inequality related to the monotone likelihood ratio propertyTruncated normal random variable
$begingroup$
How do I show the following bounds on the mills ratio :
$frac1x- frac1x^3 < frac1-Phi(x)phi(x) < frac1x- frac1x^3 +frac3x^5 $ for $ x>0$ where $Phi()$ is the CDF of the Normal distribution , and $phi()$ is the density function of the Normal distribution ?
Also , is there a similar bound when $x < 0$ ?
I am aware of the proof of the fact that the mills ratio is bounded below by $fracx1+x^2$ and above by $frac1x$ , but I am unable to prove this inequality .
probability-theory inequality
asked Mar 26 at 18:34
JohnJohn
363113
$endgroup$
add a comment |
$begingroup$
How do I show the following bounds on the mills ratio :
$frac1x- frac1x^3 < frac1-Phi(x)phi(x) < frac1x- frac1x^3 +frac3x^5 $ for $ x>0$ where $Phi()$ is the CDF of the Normal distribution , and $phi()$ is the density function of the Normal distribution ?
Also , is there a similar bound when $x < 0$ ?
I am aware of the proof of the fact that the mills ratio is bounded below by $fracx1+x^2$ and above by $frac1x$ , but I am unable to prove this inequality .
probability-theory inequality
asked Mar 26 at 18:34
JohnJohn
363113
$endgroup$
add a comment |
$begingroup$
How do I show the following bounds on the mills ratio :
$frac1x- frac1x^3 < frac1-Phi(x)phi(x) < frac1x- frac1x^3 +frac3x^5 $ for $ x>0$ where $Phi()$ is the CDF of the Normal distribution , and $phi()$ is the density function of the Normal distribution ?
Also , is there a similar bound when $x < 0$ ?
I am aware of the proof of the fact that the mills ratio is bounded below by $fracx1+x^2$ and above by $frac1x$ , but I am unable to prove this inequality .
probability-theory inequality
asked Mar 26 at 18:34
JohnJohn
363113
$endgroup$
How do I show the following bounds on the mills ratio :
$frac1x- frac1x^3 < frac1-Phi(x)phi(x) < frac1x- frac1x^3 +frac3x^5 $ for $ x>0$ where $Phi()$ is the CDF of the Normal distribution , and $phi()$ is the density function of the Normal distribution ?
Also , is there a similar bound when $x < 0$ ?
I am aware of the proof of the fact that the mills ratio is bounded below by $fracx1+x^2$ and above by $frac1x$ , but I am unable to prove this inequality .
probability-theory inequality
probability-theory inequality
asked Mar 26 at 18:34
JohnJohn
363113
asked Mar 26 at 18:34
JohnJohn
363113
asked Mar 26 at 18:34
JohnJohn
363113
asked Mar 26 at 18:34
JohnJohn
363113
asked Mar 26 at 18:34
JohnJohn
363113
363113
add a comment |
add a comment |
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