Mean and Standard Deviations of Log Normal Distributions

Ow, my head hurts...

I think I know what you mean, but if you are going to calculate the mean (average) Xbar .... then surely you don't need to convert to anyother disribution... or do you?

No, you're right, I don't need to take the log to just get the mean. I should have given a little bit more background.

I'm looking at data that has been entered into a database and the data seems to follow a lognormal distribution. I'm trying to catch errors in the database, so I'm taking the log of the data, that gives me a nice gaussian curve, then I'm taking three standard deviations from the mean of that gaussian which should only occur .4% of the time. In other words, if I'm finding data beyond 3 standard deviations, it's probably been entered incorrectly.

I just am not sure that my assumption that beyond the 3rd standard deviation only .4% of the data should exist is correct since I had to take the log of the data to get my nice distribution. Now if this was a normal distribution, like height, there would be no doubt, I'm just not sure about this data since I had to manipulate it to get it to be a gaussian distribution.

I really wish I could be more coherent in my explanation, the problem is I'm still learning this stuff and my vocabulary ain't so good in describing this subject.

It was very lucid to me...(but then I'm exceedingly smart... for a Cat) .

I'd just ammend your 'probably' to 'possibly' else you may end up with the sort of logic we have from our UK government which expects over half the school kids to be above average, and states that a school inspection result of 'satisfactory' isn't good enough

Del

Oh man do I agree. People just don't understand statistics and normally intelligent people make ridiculous statements all the time and just have no clue.

Do you have any statistics to prove that?

Just kidding!

It would be ironic if someone did a study of how many people do understand statistics beyond what is printed on the sports pages.

I wish I understood statistics better. I'm trying. As I said earlier in this post, the data was in a lognormal distribution, that's pretty certain because when I did a histogram of the log of the data it looked pretty gaussian. The thing is, if I'm being honest, I have no idea why that is. I have some vague reasons why it might form such a distribution, but to the precision that it does? I'd be lying if I said I understood why.

The thing about statistics, especially in a information society, is it is incredibly powerful when used correctly. My frustrations in the past have been getting people to use them correctly. I don't even try to fight it anymore when people present average of power law distributed data. I've just given up. Here's a link explaining why its bad:

Last paragraph on the page of this link

"68% of statistics are made up on the spot". Who said that?

Somebody using a bell curve

Todd Snider

hello

Statistics. Love it!!

You are wanting to "test" individual values against and expected outcome. It would seem suitable that IF the original distribution is non-gaussian and IF your "lognormal" transposition of that data makes it truly gaussian, THEN the rules for normal distributions are suitable to apply.

At worst, you've got a first cut method of filtering your original data.

It sounds like this would be better than applying central limit theorem to grouped samples in the original data. (Due to the effectively skewed values.)

You might want to consider a further refinement by considering your data as a "run chart" and looking at "X" and moving range.

I agree that at worst I'll have a rough estimate.

I'm afraid I'm not following you on the run chart idea. Basically an example data set that I'm looking at is continuous torque for motors. The values of continuous torque follow a lognormal distribution. I'm interested in the idea of applying a run chart to this data but I don't know how. Can you maybe give me a short example of how this may be done, or provide a link I could read.

Thanks,

Roger

I'll see what I can find to send to you showing the "formal" calculations.

The idea though is that there is more "information" if you consider the data value (as you intended) and also the difference of that value from the immediate preceding value.

What this "moving range" considers is how different is the value you are considering now compared to the previous value. There are also formula's for control limits for the moving range that provide similar "warnings" of out of control situations that may not be readily seen in the raw data alone.

Hello, me again.

For process control information, control charts, worked examples, different chart options and so on, try the following. It's required reference for automotive industry worldwide.

"Statistical Process Control" Copyrighted by DaimlerCrysler Corporation, Ford Motor Company and General Motors Corporation.

Copies can be obtained from AIAG at 248-358-3570 (I'm almost certain that's a US phone number) or http://www.aiag.org.

It's around 200 pages and can be used as a training resource. Has good "down to earth" definitions of the magic words used by statisticians and is focused on using the tool rather than deriving the maths.

I'll give this a look tomorrow when I have time, thanks.

I think I've a couple of copies spare Roger.

But I'm not sure its exactly what you're looking for, its primarily printed to show how to use SPC and the results of the SPC testing to predict what is happening to the process...

It doesn't, as far as I know, deal with the down to earth issues of statistical calculations.

It is about a decade since I last looked through it though, so I might be wrong.

John.

Too late to talk on it now, and may be the pink has rogered off

But my comments are (as an engineer with statistical back ground)

a) Pl check the validity of your assumption of lognormal distribution - data may look nicely normal on log but data itself could have been normal. There are graphical as well as statistical methods available for checking - eg mann whitney tests etc, easier is check on a normal curve. If you are still listening I can guide you

b) If it is lognormal - ensure it - afterwards anyway staistics do allow you to take the log and do your calculations (But X bar as told is on the data itself)

Hi, it probably is long past necessary, but maybe useful for somebody perusing google for a similar question. From what I understand, the relationship between the mean and variance (SD^2) of a lognormal distribution and it's associated normal distribution is the following:

Say that X is your lognormally distributed data and X' is your log-transformed data which is thus normally distributed (X' = log(X)). Then

Mean of X = exp[mu + (sigma^2)/2] and

Variance of X = (exp[sigma^2] - 1) * exp[2*mu + (sigma^2)]

where mu is the mean of X' (which is normally distributed), and sigma is the standard deviation of X'.

You can find this yourself easily on wikipedia actually: http://en.wikipedia.org/wiki/Log-normal_distribution

Cheers!

dan atkinson here wishing you a happy Hanukkah.