using normal distribution where mew is large and sigma is small

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hello, I have been trying to make use of normal distribution,where tha value for x lies in the range 0 to 1.The value of mew is quite large,like 0.3745*(10^5) and the values of sigma are very small,like 0.2634*(10^-5).In such situations when i apply the normpdf function,i get values as zero for all values of x.Is there any method possible so that i can get non-zero values.
  2 Comments
the cyclist
the cyclist on 23 Jul 2013
I don't fully understand your question.
What is "mew"? Is it the mean of your distribution?
If mew is the mean, and your sigma is so tiny, then only values very, very near mew are going to be big enough to calculate. If your values are too far away, then MATLAB will give zero.
Maybe you could post your code (if any) and describe in a bit more detail what you are trying to do.
dpb
dpb on 23 Jul 2013
Edited: dpb on 24 Jul 2013
If x--> 1 then
(x-mu)/sigma --> -0.4E5/0.3E-5 ~= 1E10
P(z=1E10) is infinitesimal
1-normcdf(5) ~ 2E-7 and you're going 10 orders of magnitude beyond that.
Or, another way to look at it, since P(z(+/-3)) is roughly the 0.001 percentiles, 99.9% of all values must be between those limits. With your values for mu/sigma, those values are
>> mu-3*sig
ans =
3.744999999209800e+04
>> mu+3*sig
ans =
3.745000000790200e+04
>> The difference is, of course, 6*sig or
>> 6*sig
ans =
1.580400000000000e-05
>>
Or yet another way to see the limits owing to computational difficulties in double precision floating point...
>> norminv(eps)
ans =
-8.1259
>>
The standardized z-value for the tail probability of the smallest difference between 1 and the next representable floating point value is only 8-something yet you are asking for z ~ 10E5 on an exponential function.
As the cyclist says, "What in the world are you thinking????" :J)

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