Presently I am handling a highly positively skewed geochemical dataset. After several attempts, I have prepared a 3 parameter lognormal distribution (using natural log and additive constant c). The descriptive statistic parameters obtained are log-transformed mean (α) and standard deviation (β). The subsequent back-transformed mean and standard deviation (BTmean and BTsd) are based on the formula
BTmean = e ^ (α + (β^2/2)) - c
BTsd = Sqrt [(BTmean)^2) (e ^(β^2)-1)] - c
However, someone suggests to use Lagrange Multiplier. I am not sure about the
1) Equation using the Lagrange Multiplier
2) How to derive the value of Lagrange multiplier in my case.
Kindly advise.
Regards
Wow you have a real problem here. Let's do the Lagrange multiplier see any common advanced calculus book. Back transform of the lognormal function see the first attachment. The second attachment is my fav advanced calculus book download from the z-library. Good luck David Booth
I don't suppose the z-library pays for permission/royalties?
Ajoy Kumar Padhi, I wonder why you need to transform and then backtransform? Is that what you are saying? Are you doing this for heteroscedasticity in regression? If so, don't transform at all. Use a regression weight in weighted least squares regression.
....................
This could help:
For estimated residuals in regressions of form
y = y* + (e_0)(z^~gamma),
for finite populations, where gamma, the coefficient of heteroscedasticity is approximate because e is not epsilon, and using y* for predicted-y, here is a simple approach:
https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity, as determined by Ken Brewer,
and
https://www.researchgate.net/publication/333642828_Estimating_the_Coefficient_of_Heteroscedasticity
with
https://www.researchgate.net/publication/333659087_Tool_for_estimating_coefficient_of_heteroscedasticityxlsx
.....
https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression, and the various updates and references there.
@james as a matter of fact they do. There have been lawsuits going both ways by publishers. When the library looses they apologize and pay. Facts are just about as important here as in science.please do your research then draw your conclusions you remember like science. If you want to comeplain about something try plagiarism here on.RG.. I'VE had multiple papers and my name plagiarized right here on RG and they refuse to do anything about it. Look at the lab I allegedly belong to and they refuse to even let me out of it let alone withdraw those papers.
If you wish to follow up.on.this go right ahead.
David Booth
David - Didn't mean to offend. - So they have been sued, huh? Just asking. I think that many people don't realize that just because something is available, doesn't necessarily make it legal.
Thanks - Jim
Ajoy Kumar Padhi -
To get this back on track, I was asking you why you would transform and then backtransform, if that is what you are doing. As I said, this is at least sometimes done to handle heteroscedasticity in regression, but if so, I suggest weighted least squares (WLS) regression instead, with no transformation. Your software may let you enter a regression weight expression, see the references I gave you, and the software will then incorporate this into your parameters, and it will impact predictions and especially variances.
But if you are doing something else, other than handling heteroscedasticity in regression, please state what you are doing if you are allowed.
Thanks - Jim
David will likely think this is complete rubbish, but here is what one librarian had to say about Z-Library.
So there are outright “We pirate stuff’ sites like Mobilism and ZLibrary. These are places that are basically set up to pirate things and have no veneer of legality to them.
Source: https://www.librarian.net/stax/5103/ask-a-librarian-what-is-the-deal-with-free-ebook-sites/
Bruce I am sure that any good librarian could serve as a copyright attorney.which I had to get to free up one of my papers that was plagiarised from RG. Thanks for your interest in this matter. My suggestion is that you look at plagiarised material from RG I have plenty of information that I could send you. Better watch your stuff or you may find yourself or your stuff plagiarised from RG.May the Force be with you. David Booth
James to get back on track once again you will find that back transformation is sometimes recommended in statistics I draw attention to the attached Google search properly attributed as you will notice . Best wishes David Booth
The formulae given look wrong. The easiest way to get correct formulae is to think of the transformation in two stages (add a constant then take the logarithm) and to get formulae for moments by doing the back transformation in corresponding two stages.
Good reasons for doing back transformations is to get estimates of the percentage points on the original scale ... done by back-transforming the percentage points from the transformed scale. This is better than trying to use the back-transformed mean and standard deviation.
Lagrange multipliers to not relate to this question, which is mainly about random variables whose parameters are known. Lagrange multipliers may be useful when it comes to fitting a distribution and testing particular values of the parameters. You should find a good book to provide you details of what this involves. For practical purposes you might think it best to just think of a suitable round value for c, rather than estimating/testing the value.
- Badges
- Science topic
- Similar topics
- Geoscience
- Cartography
- Mapping