[ home ] [ math / cs / ai / phy / as / chem / bio / geo ] [ civ / aero / mech / ee / hdl / os / dev / web / app / sys / net / sec ] [ med / fin / psy / soc / his / lit / lin / phi / arch ] [ off / vg / jp / 2hu / tc / ts / adv / hr / meta / tex ] [ chat ] [ wiki ]

/math/ - Mathematics

Name
Email
Subject
Comment
Verification
Instructions:
  • Press the Get Captcha button to get a new captcha
  • Find the correct answer and type the key in TYPE CAPTCHA HERE
  • Press the Publish button to make a post
  • Incorrect answer to the captcha will result in an immediate ban.
File
Password (For file deletion.)
25 Dec 2021Mathchan is launched into public
Return Catalog Bottom Refresh
0 / 1 / 0 / ?

File: dbqOJ.gif ( 239.17 KB , 1838x1304 , 1658138309873.gif )

Image
  No. 241
The picture below shows (in red) a sum of Gaussian kernels with different means, but all having variance 1, i.e.
f(x)=12π−−√∑i=1ne−12(x−μi)2 .
. The green curves show what I get if I select a point x0, and then "fit" a scaled Gaussian distribution g to f about x0, in the sense that I determine c and μ0 in the function
g(x):=c2π−−√e−12(x−μ0)2
so that g(x0)=f(x0) and g′(x0)=f′(x0). From numerical experimentation, it seems to always be the case that g(x)≤f(x) for all x. Does anyone know why this is so?

Return Catalog Top Refresh
0 / 1 / 0 / ?

[ home ] [ math / cs / ai / phy / as / chem / bio / geo ] [ civ / aero / mech / ee / hdl / os / dev / web / app / sys / net / sec ] [ med / fin / psy / soc / his / lit / lin / phi / arch ] [ off / vg / jp / 2hu / tc / ts / adv / hr / meta / tex ] [ chat ] [ wiki ]