2011年9月8日 星期四

20110908雜選 [馬鈴薯分佈 + 帕金森定律 + best self-promoter一名]

80/20定律其實就是Pareto Dist. (數學可證!如下推導)

f(x) follow Pareto dist, with \alpha = 2 and x_m = 1 (w.l.o.g)
then \mu = \int_1^{\inf} x \times f(x) dx is regarded as the total wealth of a society.

then \int_1^{median} x \times f(x) dx = \mu \times \[ 1 - \sqrt{0.5} \]
which can be interpreted as " \sqrt{0.5}, or 70.7% of total wealth is held in the richer 50% of the society"

and we again calculate  \int_1^{Q_3} x \times f(x) dx = \mu \times \[ 1 - \sqrt{0.25} \], which turns to
" 50% of total wealth is held in the richer 25% of the society"

the relationship characterize the 80/20 rule (when it applies to a series of richer and richer subpopulations)
and we can then calculate that \alpha = log(0.2)/log(0.8) = 7.212567 to have the 80/20 rule.

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Parkinson's Law
  "Work expands so as to fill the time available for its completion."
Parkinson's Law of Triviality
  A committee spent 2.5 min on a $10M atomic reactor agenda,
while discussed 45 min with possible $300 something saved on a bicycle shed agenda.
" that the time spent on any item of the agenda will be in inverse proportion to the sum involved"

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Found it when I searched for "Total Immersion" (TI) swimming techniques and doubted
on what sport(s) this guy won national titles


When I searched his book "The 4-hour workweek", 80/20 rule and Parkinson's Law were mentioned.
DEAL Definition, Elimination, Automation, and Liberation, I found only the second one has some gold,
the first one is non-informative, while the others sounds like Pyramid scheme (or mouse society) kind of spam to me.

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