Question about PDF arithmetic
Page 1 of 1 • Share •
Question about PDF arithmetic
Suppose I have a measurement of the form µ±σ that represents a probability density function (PDF) with mean µ and confidence interval σ  basically how we're used to seeing measurements in papers. How does the arithmetic work for them? If I wanted to add or multiply two PDFs, what exactly would I do? This would be rather helpful for, for example, calculating the density of a transiting planet with reported mass and radius values.
I found a document that offered a way to multiply a univariate Guassian distribution here. I'm still toying with it. From what I've gathered so far from a programme I wrote to implement this, squaring a PDF should result in the confidence interval σ decreasing. For a sanity check, I went to a couple hot Jupiter discovery papers that report the impact parameter b as well as b^2. HATP55 b's paper seems to imply that squaring a PDF shrinks its confidence interval. but the paper for HATP56 b shows the confidence interval increasing when b is squared.
What is going on here? How does arithmetic work? Help
I found a document that offered a way to multiply a univariate Guassian distribution here. I'm still toying with it. From what I've gathered so far from a programme I wrote to implement this, squaring a PDF should result in the confidence interval σ decreasing. For a sanity check, I went to a couple hot Jupiter discovery papers that report the impact parameter b as well as b^2. HATP55 b's paper seems to imply that squaring a PDF shrinks its confidence interval. but the paper for HATP56 b shows the confidence interval increasing when b is squared.
What is going on here? How does arithmetic work? Help
_________________
Caps Lock: Cruise control for 'Cool'!
Sirius_Alpha Admin
 Number of posts : 3802
Location : Earth
Registration date : 20080406
Page 1 of 1
Permissions in this forum:
You cannot reply to topics in this forum

