Stas$cs’and’FatTails’ -...
Transcript of Stas$cs’and’FatTails’ -...
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Sta$s$cs and Fat Tails
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Mediocristan
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Extremistan
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Mediocristan/Extremistan
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Law of Large Numbers
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Problem central with Geosta's'cs • Synthesis of paper Taleb-‐Douady currently under (small) revision Physica A: Sta-s-cal Mechanics and Applica-ons
• This is another problem where sta$s$cal methods fail with fat tails.
• Ignoring fat tails self-‐contradictory when people alarmed at (wealth or other) “concentra$on” since
concentra$on ófaJailedness • Cen$le measures super-‐addi've. • Both PikeJy and his detractors (Financial Times) made the same mistake.
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Cen$le Contribu$on
• Share of the top q% with n observa$ons, where X is wealth (or something else), h is Cen$le:
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Country A (Extreme Concentra$on)
0
200000
400000
600000
800000
1×106���� = �����
q= .01 in all exercise Both A and B countries have same n =103
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Country B (Low Concentra$on)
0
5
10
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20���� = �����
���� � � = �������The pool of A U B
����� + �����
�= ������The average of A and B
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Adjus$ng by the Mean Income
����� + �����
�= ������
����� � � �� � = ������
Case 1: Making A and B have exactly same average, but keeping their previous concentra$on. Case 2: Making A and B have varia$ons in average makes concentra$on.
����� � � ��
� �= ������
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BIG DATA
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