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I am fairly new to R and is exploring simulation to estimate the parameter n:

1) Z is a vector of n draws from N(0,1)

2) Probability of max(Z)>4 equals 0.25

What is the best way in R to estimate the parameter n to satisfy these two conditions? I got stuck trying to avoid looping or exhaustive search in the code. Thanks!

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migrated from quant.stackexchange.com Apr 3 '18 at 4:46

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  • $\begingroup$ - Is this homework? -What have you tried? -You did not try googling "distribution of the maximum of normal random variables" - This is unrelated to Quant Finance! Anyway have a look here: math.stackexchange.com/questions/89030/… $\endgroup$ – g g Apr 2 '18 at 20:21
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Guide:

You don't really need to carry out a simulation to find this quantity.

Find the CDF of $\max(Z)$

$$Pr(\max(Z)>4)=1-Pr(Z_1 \le 4, \ldots, Z_n \le 4)$$

then use the independence of $Z_i$ to get an expression in terms of CDF of $N(0,1)$.

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