(Ted Harding) wrote:
Not quite sure of your point here, Thomas. I certainly wasn't writing on the basis that the boss had claimed that they were either independent or identically disitributed, and the paragraph you quote was in reposnse to:
"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."
which I interpreted as arguing that "if daily data log-normal, then monthly means must consequently be log-normal", i.e. that the mean of log-normals is log-normal; and I was simply pointing out that this is a false implication (which would be the case even if the data are neither independent nor identically distributed, except in the extreme case where they are all copies of the one log-normal variable).
Granted I later used i.i.d log-normals as examples; but then pointed out that the mean of log-normals could remain sufficiently skew that a log-normal could still be a useful distribution to adopt.
Hello:
Let me cut short it. The variables in questions are "aerosol optical depth measurements" (go to the NASA 'AERONET' site if you want to learn more about it). It is likely that not everybody knows what it is meant by it; but one can think on "temperature measurements" for a good proxy, though not directly related to my variables.
My data base was not based on a single observing station; I have used 50 stations for my evaluation. The stations were located in Europe. Although, the data base was rather scattered because some stations didn't observe every day and every month, even.
But thanks again for the useful tips (especially the link to the CLT). It is rather this: my paper had been rejected. But we know: we will struggle as long as the paper will eventually get accepted ( I have a colleague and friend with a good name at NASA who daily motivates me not to give up).
There were other reasons too but one complaint from a reviewer actually was that there exists a paper that "aerosol optical depths" are rather skewed to the left.
My argument actually was that my averaging removed quite a lot of outliers. Okay, honestly speaking: at that time I didn't know about the CLT.
I recalculated the matter, based on a log normal distribution, and it turned out that after transforming the variables to a log-normal distribution the median and mean become similar and comparable to my "heavy averaged former means". Surely, there is one difference to my former averaging: the 3. quantile and the maximum value is larger due to the log-normal distribution.
Regards, Siegfried Gonzi
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