[fluka-discuss]: What is the relation between sample size and particle

From: Jyoti <jyoti.grg_at_britatom.gov.in>
Date: Thu, 19 Dec 2019 12:37:05 +0100

Dear Ricardo

Thanks for your reply.
Sorry, in previous mail, some equations are not visible properly. Kindly
consider this mail.


I have gone through the pdf and some of my doubts are not cleared.



1. In FLUKA, suppose, no of histories (N) = 1E+5. The spawn value = 10
and no of cycles 5.

So, when spawn 1, cycle 1, these 1E+5 no of histories will not be s=
imulated together. Rather, it will be divided into X no of batches with N/X=
 histories. For each batch, we will get a mean value of our estimator. So, =
for X no of batches, we will get X no of means which if we plot, we will ge=
t a sampling distribution of sample (or batch) means. Is my concept correct=


If it is correct, then we can call this X as sample size. Now, since, in FL=
UKA input, we are giving only total no history, not the batch size, what do=
es FLUKA decide as batch size? Is there any predefined parameter assigned f=
or batch size? For central limit theorem to be valid, the sample size shoul=
d be greater than 30 so that whatever be the population distribution, the s=
ampling distribution of sample means will always be a normal distribution.=


2. For each sampling distribution of sample (or batch) means, the central l
imit theorem is valid. Also, each distribution has their own mean ( )(mean
of sampling distribution of sample means) and standard deviation ( ) (SD of
 sampling distribution of sample means).

Each SD satisfy the relation where x = a random variable of our estimator
, X = no of batches (or sample size), =CF=83 =3D SD of population distrib
ution. Now for spawn 1, generally we give 5 cycles. So we will get 5 an
d 5 . Then what is the method to get the final SD of our estimator?

For spawns > 1, many such and will be generated. How can we merge those res=
ults to get a single value of and for our estimator





Thanks and Regards
Jyoti



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