Plot normal distribution that range from -1 to 1

Hi all, My question should be simple: I would plot a standard distribution with mu = 0 sigma = 1 that ranges between -1 and +1

Thanks

[dpb]

Well, maybe not... :)

What to do with the tails? Just truncate or do you think you want the range of the distribution itself to also be bounded?

[gianluca mattei]

the tails should not be truncated but within the range

Answer 1

[dpb]

Well, per the comment, you can't have both...try

x=linspace(-1,1);
plot(x,normpdf(x,0,1/3.5))

You can adjust the divisor for how narrow to make the actual SD to fit what you think the visual representation should be, but the standard z will have to cover the range to produce the tails in a normal. "That's just the way it is"

[gianluca mattei]

this works!

But I miss something, how do you chose the standard dev?

[dpb]

Purely arbitrary to get as much of the tail as you think you needs must have in the range specified [-1 1] here.

The precise way would be to pick a given tail percentage exceedance and then back out the Z for that and then compute SD from z=(x-u)/s. For u=0 that simply reduces to x/s which is the above.

>> 1-normcdf(0,3.5)
ans =
  0.9998
>>

so the above includes ~99.96% (two-sided) of the distribution in range. Of course, it's still an unbounded distribution and there's nothing to say that some rare event won't generate a value in one of those tail areas.