Is there any difference in calculation of type 1 and 2 errors?

[Steve Jobs]

The question 60.2 is asking for type 1 error and 60.3 is asking for type 2 error but the formula(excel function) is the same. I'm confused, are they the same?

 

[David Harper CFA FRM]

I like that observation, it helps tease out the difference. Source question is here: https://forum.bionicturtle.com/threads/l2-t5-60-basel-ima-backtest.3610/

Please note the same function is used but:

• 60.2 which concerns the probability of a Type I error uses BINOMDIST = (X<=5, T=250 days, p=1%, CDF = true) = 95.9% and 1-95.9% = 4.1%; i.e., 1 - CDF
• 60.3 does not use (1 - CDF) but just the CDF: BINOMDIST(X<=3, T=250 days, p=3%, CDF = true) = 5.7%. That their values are nearby is a bit of an optical issue due the differences in the parameters.

The BINOMDIST function is indeed the same because, regardless, the VaR backtest essentially parses a binomial distribution into an one-tailed acceptance region (on the left) and a rejection region (on the right); i.e., when the exceptions (X) are high enough, at a certain point, the decision is to reject the null that the VaR model is accurate

• The Binomial CDF function--i.e., Excel's BINOMDIST(X<=x, T=250 days, p=%, CDF = true)--locates where accept/reject regions are based simply on the decision rule (60.2: reject at 6 or more which is "in the right tail", 60.3 accept at three or fewer which is "in the left region")
  
• In 60.2, Type II error is only possible when locating in the acceptance region: in one tailed test, that equal to the CDF
• In 60.3, Type I error is only possible when locating in the reject tail: in one tailed test, that is equal to (1- CDF)

 

[Steve Jobs]

At the beginning it was confusing but now I visualize it as a normal curve which has only positive values just like the school statistics questions on weight, length, number of bad quality products and so...but definitely need to practice more questions so not to be confused again.

 

[gitusrini]

Hi David, regarding Q 60.2 we would not be having access to Excel, how do I do this in the exam if theres a question like this? should I calculate probabilities for X=0, 1, 2, 3, 4, 5. I am sure I missing something here. Please help.

 

[David Harper CFA FRM]

Hi @gitusrini Yes, on the exam you would need to add them up. That's why my question is more a bit more tedious (sorry!) than you would actually encounter. See https://forum.bionicturtle.com/threads/l2-t5-60-basel-ima-backtest-jorion.3610/post-17011 ie..,

Ankur - my example is more tedious than you would see on the exam, apologies. At most, you'd accumulate ~ 2 or 3 PMFs to get the CDF (but, no, i don't think there is a shortcut), thanks

 

[gitusrini]

Hi @gitusrini Yes, on the exam you would need to add them up. That's why my question is more a bit more tedious (sorry!) than you would actually encounter. See https://forum.bionicturtle.com/threads/l2-t5-60-basel-ima-backtest-jorion.3610/post-17011 ie..,

Thank you so much David!