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[null,{"$f":"MID(CELL(\"filename\",C1),SEARCH(\"[\",CELL(\"filename\",C1))+1,SEARCH(\".\",CELL(\"filename\",C1))-SEARCH(\"[\",CELL(\"filename\",C1))-1)","v":"HPtn Risk - Validating tests"}]
[null,{"$f":" \" \" &RIGHT(CELL(\"filename\", C4), LEN(CELL(\"filename\", C4)) - SEARCH(\"]\", CELL(\"filename\", C4)))","v":" Backtesting - binomial"}]
[null,null,"Prof. Hugues Pirotte"]
[null,null,"version 2011"]
[]
[null,1,"Explanation"]
[null,null,"If all observations are independent, and if I ask you what's the total probability"]
[null,null,"of having a particular \"set\" of results in a sample of 3 obs where only 1 is an exception, like…. "]
[null,null,"obs1","obs2","obs3"]
[null,null,"above","below","below"]
[null,null,0.05,0.95,0.95,{"$f":"C14*D14*E14","v":4.5124999999999998E-2}]
[null,null,0.95,0.05,0.95,{"$f":"C15*D15*E15","v":4.5124999999999998E-2}]
[null,null,0.95,0.95,0.05,{"$f":"C16*D16*E16","v":4.5124999999999998E-2}]
[null,null,null,null,null,{"$f":"SUM(F14:F16)","v":0.135375}]
[]
[null,2,"With a binomial distribution directly…"]
[null,null,3,"n"]
[null,null,1,"#of exceptions"]
[null,null,0.05,"proba(exception)"]
[null,null,{"$f":"BINOMDIST(C21,C20,C22,FALSE)","v":0.13537500000000002},"total proba to have only 1 exception in a sample of 3"]
[null,null,{"$f":"BINOMDIST(C21,C20,C22,TRUE)","v":0.99275000000000002},"total proba to have up to 1 exception in a sample of 3"]
[null,null,{"$f":"1-C24","v":7.2499999999999787E-3},{"$f":"\"You have only \"&ROUND(C25*100,2)&\"% of chances to have more than 1 exception\"","v":"You have only 0.72% of chances to have more than 1 exception"}]
[]
[null,3,"Our test…"]
[null,null,null,null,null,null,null,"% of chances to have"]
[null,null,"n","k","n-k","p","1-p","more than k exceptions"]
[null,null,100,8,{"$f":"C30-D30","v":92},0.05,{"$f":"1-F30","v":0.95},{"$f":"1-BINOMDIST(D30,C30,F30,TRUE)","v":6.3089590627448788E-2}]