Laurent Simula
New member
- Joined
- Oct 21, 2019
- Messages
- 1
Hi,
I am stuck with the following problem. Let p be between 0 and 1, distributed according to a truncated lognormal distribution, with cdf H(p) and pdf h(p). I would like to find conditions for [MATH]\frac{1-H(p)}{p h(p)}[/MATH] be decreasing on an interval starting from 0.
I have been taking the derivative of this expression and found that it is decreasing provided [MATH]-p h^2(p) - h(p) + (h(p))^2 - p h'(p) + p h(p) h'(p) <0[/MATH]. However, this is not a very easily interpretable condition.
Any hints would be helpful. Thanks a lot.
Laurent
I am stuck with the following problem. Let p be between 0 and 1, distributed according to a truncated lognormal distribution, with cdf H(p) and pdf h(p). I would like to find conditions for [MATH]\frac{1-H(p)}{p h(p)}[/MATH] be decreasing on an interval starting from 0.
I have been taking the derivative of this expression and found that it is decreasing provided [MATH]-p h^2(p) - h(p) + (h(p))^2 - p h'(p) + p h(p) h'(p) <0[/MATH]. However, this is not a very easily interpretable condition.
Any hints would be helpful. Thanks a lot.
Laurent