stas$cs’and’fattails’ -...
TRANSCRIPT
Sta$s$cs and Fat Tails
Mediocristan
Extremistan
-50
-40
-30
-20
-10
0
-50
-40
-30
-20
-10
0
Mediocristan/Extremistan
Law of Large Numbers
Problem central with Geosta's'cs • Synthesis of paper Taleb-‐Douady currently under (small) revision Physica A: Sta-s-cal Mechanics and Applica-ons
• This is another problem where sta$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.
Cen$le Contribu$on
• Share of the top q% with n observa$ons, where X is wealth (or something else), h is Cen$le:
Country A (Extreme Concentra$on)
0
200000
400000
600000
800000
1×106���� = �����
q= .01 in all exercise Both A and B countries have same n =103
Country B (Low Concentra$on)
0
5
10
15
20���� = �����
���� � � = �������The pool of A U B
����� + �����
�= ������The average of A and B
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.
����� � � ��
� �= ������
BIG DATA
