[Bug 1214482] Re: Not-grouping dependent packages in Phased Updates changes propability distribution for entire group of dependent packages.

[Marek Wrzosek]

The real probability distribution will be a sum of separate
distributions and will depend of fractions of user who installed i of n
packages. Below I pasted formula from LibO Math:

P(x)= sum from {i=1} to {n} a_i P_i(x) newline
0<= a_i <= 1 newline
a_i - "a fraction of users who installed" i "packages from a group of "n" dependent packages" newline
"to total amount of users who installed any number of packages from the same group" newline 
P_i(x) - "Probability distribution for" i "dependent packages"

The real probability distribution will be hard to predict, so leaving
this "as is" is against the KISS paradigm.

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https://bugs.launchpad.net/bugs/1214482

Title:
  Not-grouping dependent packages in Phased Updates changes propability
  distribution for entire group of dependent packages.

Status in “update-manager” package in Ubuntu:
  New

Bug description:
  I assume that you decided for uniform distribution in the random
  number generator. If group of dependent packages is installed only
  when all phased-update-percentage values (for each package) are
  smaller than the present percentage on server - it will change
  probability distribution for the whole group of packages.

  Just run this:

  figure(1)
  hist(rand(1,100000))
  for i = 2:10
  	figure(i)
  	hist(max(rand(i,100000)))
  endfor

  in octave and look at histograms for i>1 (i is the number of dependent
  packages).

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