Normal distribution: Difference between revisions

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 {{Quote|“We were seeing things that were 25-standard deviation moves, several days in a row.”
 :—David Viniar, Chief Financial Officer, [[Goldman]]}}
-''Twenty five'' standard deviations. That makes LTCM seem like a near certainty. The probability of a 25 standard deviation move<ref>Good [https://www.nottingham.ac.uk/business/who-we-are/centres-and-institutes/gcbfi/documents/cris-reports/cris-paper-2008-3.pdf paper on this from Nottingham University].</ref> is 1.309 x 10 ^ 130. You see this figure cited frequently, but to a lay person, it doesn't really make the same impact as writing it out, so let's to that.
+''Twenty five'' [[Standard deviation|standard deviations]]. That makes [[LTCM]]’s feeble ''ten'' sigma event seem a virutal certainty. We have it on good authority that the probability of a 25 standard deviation move is 1.309 x 10<sup>130</sup>. <ref>Good [https://www.nottingham.ac.uk/business/who-we-are/centres-and-institutes/gcbfi/documents/cris-reports/cris-paper-2008-3.pdf paper on this from Nottingham University].</ref> That looks a big number, but to a lay person, it doesn't really have the same impact as writing it out, so let's to that.
 {{Quote|1 day in 1.3 billion billion billion billion billion billion billion billion billion billion billion billion billion billion days.
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 ''or''
-day in 1300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 days.}}
+day in 1 300 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 days.}}
-By comparison, the earth is 1658 billion days old, and the universe itself ten times older than that. So we are talking about an event that you would only expect once in several billion billion billion billion billion lives of the universe, happening ''several days in a row''.
+By comparison, the earth is 1 658 000 000 000 days old, and the universe itself ten times older than that (16 580 000 000 000 000 days). So we are talking about an event that you would only expect once in several billion billion billion billion billion lives of the universe, happening ''several days in a row''.
-No, Mr Viniar: you weren’t seeing cosmologically-defying anomalies. ''Your models were wrong''. But enough already of the chutzpah.<ref>But, [[get your coat]], you know?</ref> The practical lesson is that, unless you are dealing with normally-distributed events, normal probabilities are a ''really'' bad proxy at the extremes. ''Ninety-nine per cent of the way there is nowhere. It isn’t good enough''.
+No, Mr Viniar: you weren’t seeing cosmos-defying anomalies. ''Your models were wrong''. But enough already of the chutzpah.<ref>But, [[get your coat]], you know?</ref> The practical lesson is that, unless you are dealing with normally-distributed events, normal probabilities are a ''really'' bad proxy at the extremes. ''Ninety-nine per cent of the way there is nowhere. It isn’t good enough''.
 ''All'' existential crises sit in the last 1 per cent — last 0.01 per cent, even — because the defining feature of an existential crisis is ''everyone panicking and selling at once''. These are, by definition, the events a normal distribution says will not happen, because events in a normal distribution are independent of each other.