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# P.2 T5 Dowd study notes pg 10 confidence intervals

#### Stella G

##### New Member
Hello David,

Could you please let me know which are the relevant values you plug in the equation q+1.645*se(q) to obtain the 90% confidence intrerval [0.600, 2.690]?

Many thanks.

#### David Harper CFA FRM

##### David Harper CFA FRM (test)
Staff member
Hi @Stella.gkotsi Good question, because our current note really does not explain this adequately, sorry (cc: @Nicole Seaman including another edit for this note). So it is implementing Dowd's 3.27 .... .... he shows the calculation. Although mine is generated in its own excel (see sheet here https://www.dropbox.com/s/cpxnh4ituxnvpd9/0204-dowd-3-27.xlsx?dl=0), as below. For Bin Width = 0.10 (ie, first column):
• f(q) = "Probability within bin" = 1 - 94.463% - 4.505% = 1.032%
• Per formula 3.27, Lower CI = 1.645 - 1.645*sqrt[4.505%*(1-4.505%)/1000]/1.032% = 0.600, and
• Upper CI = 1.645 + 1.645*sqrt[4.505%*(1-4.505%)/1000]/1.032% = 2.690. I hope that's helpful! #### anniedu

##### New Member
Subscriber
Why divided by f(q) the probability within the bin?

#### David Harper CFA FRM

##### David Harper CFA FRM (test)
Staff member
Hi @anniedu Dowd shows the derivation (see below) of the standard error of the quantile estimator on page 70: 