[R] Re: A somewhat off the line question to a log normal distribution

[Vito Ricci]

Dear Siegfried,

I believe your boss is wrong saying that:
>He also tried to explain me that the monthly means
>(based on the daily measurements) must follow a
>log-normal distribution too then over the course of a
year.

every statistician know that increasing the sample
size the sample distribution of the mean is proxy to a
gaussian distribution (Central Limit Theorem)
independently from the original distribution of data
(in your case log-normal).

See this:

The Central Limit Theorem is a statement about the
characteristics of the sampling distribution of means
of random samples from a given population. That is, it
describes the characteristics of the distribution of
values we would obtain if we were able to draw an
infinite number of random samples of a given size from
a given population and we calculated the mean of each
sample.

The Central Limit Theorem consists of three
statements:

[1] The mean of the sampling distribution of means is
equal to the mean of the population from which the
samples were drawn.

[2] The variance of the sampling distribution of means
is equal to the variance of the population from which
the samples were drawn divided by the size of the
samples.

--> [3] If the original population is distributed
normally (i.e. it is bell shaped), the sampling
distribution of means will also be normal. If the
original population is not normally distributed, the
sampling distribution of means will increasingly
approximate a normal distribution as sample size
increases. (i.e. when increasingly large samples are
drawn) <--

So results you got are just in this way!

I think your boss doesn't know well statistics!

Regards
Vito

You wrote:

Hello:

Oh yes I know it isn't so much related to R, but I
gather there are a 
lot of statisticians reading the mailing list.

My boss repeatedly tried to explain me the following.

==
Lets assume you have got daily measurements of a
variable in natural 
sciences. It turned out that the aformentioned daily
measurements follow 
a log-normal distribution when considered over the
course of a year. 
Okay. He also tried to explain me that the monthly
means (based on the 
daily measurements) must follow a log-normal
distribution too then over 
the course of a year.
==

I somehow get his explanation.

But I have measurements which are log-normal
distributed when evaluated 
on a daily basis over the course of a year  but they
are close to a 
Gaussian distribution when considered under the light
of monthly means 
over the course of a year.

Is such a latter case feasible. And if not why.

Regards,
Siegfried Gonzi


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