Talk:Log-normal distribution

message: I followed the link to the wikipedia page Multiplicative calculus and spent about an hour trying to determine whether it has any legitimacy.  I concluded that it does not.  In contrast log normal distributions are unarguably legitimate.  The multiplicative calculus link under 'See also' should be removed, for it is a waste of reader's time to refer them to some dubious article with no clear relevance to log normal distributions, save the shared multiplicative basis.
If you look at Talk:Multiplicative calculus you will find lengthy disputes about the legitimacy of the content with most contributors concluding that the article should be deleted.  Moreover, all the talk, save two entries, is a decade old. Cross-linking to distracting rubbish serves no one, even if the rubbish manages to cling to some tiny thread of legitimacy that prevents its deletion.  — Preceding unsigned comment added by 70.68.18.243 (talk) 19:03, 20 September 2019 (UTC)
thread_title: See also: multiplicative calculus ??

message: The pdf given in the box at rhs of page seems wrong and does not match the pdf given in the article.  In particular seems like first term of pdf should be 1/x sigma root (2pi).  I.e., factor of 1/x seems missing.  So term should be:  frac{1}{ x\sigma \sqrt{2 \pi}}  ? Hesitant to edit as this is my first foray into wikipedia talk and edits, plus its not obvious to me how to edit the box.
--QFC JRB (talk) 19:45, 2 May 2017 (UTC)
replies: text: I'm also noticing that while μ is listed as 0, the pdf appears centered about 1. Is this an error? Tommy2024 (talk) 22:17, 20 March 2024 (UTC)
thread_title: Error in lognormal pdf in box?

message: How do you derive the log-normal distribution from the normal distrubution?
By letting X ~ N(\mu, \sigma^2) and finding the distribution of Y = exp X.
D. Clason  — Preceding unsigned comment added by 128.123.198.136 (talk) 00:21, 11 November 2011 (UTC)
thread_title: Derivation of Log-normal Distribution

message: If Y=a^2; a is a log normal distribution ;
then What kind of distribution is Y?
:a is a lognormal distribution 
:so log(a) is a normal distribution
:log(a^2) = 2 log(a) is also a normal distribution
:a^2 is a lognormal distribution --Buglee 00:47, 9 May 2006 (UTC)
replies: text: I've just attended to this. Michael Hardy 00:52, 14 February 2007 (UTC)
thread_title:  Could I ask a question? 

message: There are formulas that use Erf and formulas that use the cdf of the normal distribution, IMHO this is confusing, because those functions are related but not identical. Albmont 15:02, 23 August 2006 (UTC)
thread_title:  Erf and normal cdf 

message: Please remember that Wikipedia articles need to be accessible to people like high school studends, or younger, or without any background in math. I consider myself rather knowledgable in math (had it at college level, and still do) but (taking into account English is not my native language) I found the lead to this article pretty difficult. Please make it more accessible.-- Piotr Konieczny aka Prokonsul Piotrus | talk  22:48, 31 August 2006 (UTC)
replies: text: To expect all Wikipedia math articles to be accessible to high-school students is unreasonable.  Some can be accessible only to mathematicians; perhaps more can be accessible to a broad audience of professionals who use mathematics; others to anyone who's had a couple of years of calculus and no more; others to a broader audience still.  Anyone who knows what the normal distribution is, what a random variable is, and what logarithms are, will readily understand the first sentence in this article.  Can you be specific about what it is you found difficult about it? Michael Hardy 23:28, 31 August 2006 (UTC)
thread_title:  Technical 

message: I think the definition of X as normal and Y as lognormal in the beginning of the page should be changed. The rest of the page treats X as the log normal variable. —The preceding unsigned comment was added by 213.115.25.62 (talk) 17:40, 2 February 2007 (UTC)
thread_title:  X log normal, not normal. 

message: log normal, sometimes, it is a little bit confusing for me, so a little bit note here:
For variable Y, if X=log(Y) is normal, then Y is log normal, which says after being taken log, it becomes normal. Similarly, there might be exponential normal: for variable Z, exp(Z) is normal.  However, exp(Z) can never be normal, so the name log normal. Furthermore, if X is normal, then log(X) is undefined. 
In other cases, variable X is in whatever distribution (XXX), we need a name for the distribution of Y=log(X) (in the case it is defined). X=exp(Y), Such a name should exponential XXX. For instance, X is in IG, then Y=log(X) is in exponential IG. Jackzhp 15:37, 13 July 2007 (UTC)
thread_title: the name: log vs exponential

message: Wikipedia policy (see WP:CITE#HOW) suggests citation of specific pages in specific books or peer-reviewed articles to support claims made in Wikipedia. Surely this applies to mathematics articles just as much as it does to articles about history, TV shows, or anything else?
I say this because I was looking for a formula for the partial expectation of a lognormal variable, and I was delighted to discover that this excellent, comprehensive article offers one. But how am I supposed to know if the formula is correct? I trust the competence of the people who wrote this article, but how can I know whether or not some mischievous high schooler reversed a sign somewhere? I tried verifying the expectation formula by calculating the integral myself, but I got lost quickly (sorry! some users of these articles are less technically adept than the authors!) I will soon go to the library to look for the formula (the unconditional expectation appears in some books I own, but not the partial expectation) but that defeats the purpose of turning to Wikipedia in the first place.
Of course, I am thankful that Wikipedia cites one book specifically on the lognormal distribution (Aitchison and Brown 1957). That reference may help me when I get to the library. But I'm not sure if that was the source of the formula in question. My point is more general, of course. Since Wikipedia is inevitably subject to errors and vandalism, math formulas can never be trusted, unless they follow in a highly transparent way from prior mathematical statements in the same article. Pages like this one would be vastly more useful if specific mathematical statements were backed by page-specific citations of (one or preferably more) books or articles where they could be verified. --Rinconsoleao 15:11, 28 September 2007 (UTC)
replies: text: Normally I do not do this because I think it is rude, but I really should say  because you are headed to the library and will be able to add good cites. Even if we had a good source for it, the formula could still be incorrect due to vandalism or transcription errors. Such is the reality of Wikipedia.  Can you write a program to test it, perhaps? Acct4 15:23, 28 September 2007 (UTC)

text: I believe Aitchinson and Brown does have that formula in it, but since I haven't looked at that book in many years I wouldn't swear by it.  I will have to check.  I derived the formula myself before adding it to Wikipedia, unfortunately there was a slip up in my post which was caught by an anonymous user and corrected.  FWIW, at this point I have a near 100% confidence in its correctness.  And I am watching this page for vandalism or other problems.  In general your point is a good one. Encyclops 22:34, 28 September 2007 (UTC)
thread_title:  This page lacks adequate citations!! 

message: As requested by Rinconsoleao and others, here is a derivation of the partial expectation formula. It is tedious, so I do not include it in the article itself.
We want to find 
:g(k)=\int_k^{\infty} x f(x) dx
where f(x) is the lognormal distribution 
:f(x)=\frac{1}{x \sigma \sqrt{2 \pi}}\exp\left(-\frac{(\ln x -\mu)^2}{2 \sigma^2}\right)
so we have
:g(k)=\int_k^{\infty} \frac{1}{\sigma \sqrt{2 \pi}} \exp\left(-\frac{(\ln x -\mu)^2}{2 \sigma^2}\right)dx
Make a change of variables
y = \frac{\ln x - \mu}{\sigma} and  dx=\sigma \exp(\sigma y + \mu) dy  giving
:\int_{y=(\ln k-\mu)/\sigma}^{\infty} \frac{1}{\sigma \sqrt{2 \pi}}\exp(-\frac{1}{2}y^2)\sigma\exp(\sigma y +\mu)dy
combine the exponentials together
:\int \frac{1}{\sqrt{2 \pi}} \exp(-\frac{1}{2}y^2+\sigma y+\mu) dy
fix the quadratic by 'completing the square'
:\int \frac{1}{\sqrt{2 \pi}} \exp[-\frac{1}{2}(y-\sigma)^2+(\mu+\frac{1}{2}\sigma^2)] dy
at this point we can pull out some stuff from the integral
:g(k) = \exp(\mu+\frac{\sigma^2}{2}) \frac{1}{\sqrt{2 \pi}} \int_{y=(\ln K-\mu)/\sigma}^{\infty} \exp(-\frac{1}{2}(y-\sigma)^2) dy
one more change of variable
:v=y-\sigma and dy=dv
gives
:g(k)=\exp(\mu+\frac{\sigma^2}{2}) \frac{1}{\sqrt{2 \pi}} \int_{v=(\ln k-\mu)/\sigma-\sigma}^{\infty} \exp(-\frac{1}{2} v^2)dv
We recognize the integral and the fraction in front of it as the complement of the cdf of the std normal rv
:g(k)=\exp\left(\mu+\frac{\sigma^2}{2}\right)\left[1-\Phi(\frac{\ln k -\mu-\sigma^2}{\sigma})\right]
using 1-\Phi(x)=\Phi(-x) we finally have
:g(k)=\exp\left(\mu+\frac{\sigma^2}{2}\right) \Phi\left(\frac{-\ln k +\mu+\sigma^2}{\sigma}\right)
Regards, Encyclops (talk) 21:49, 29 August 2009 (UTC)
thread_title:  Derivation of Partial Expectation 

message: Some examples would be nice!  —Preceding unsigned comment added by 146.113.42.220 (talk) 16:41, 8 February 2008 (UTC)
replies: text: One example is neurological reaction time. This distribution has been seen in studies on automobile braking and other responses to stimuli. See also mental chronometry.--IanOsgood (talk) 02:32, 26 February 2008 (UTC)

text: This is also useful in telecom. in order to compute slow fading effects on a transmitted signal. -- 82.123.94.169 (talk) 14:42, 28 February 2008 (UTC)

text: I recall reading on wiki that high IQs are log-normally distributed. Also, incomes (in a given country) are approximately as well. Elithrion (talk) 21:26, 2 November 2009 (UTC)
thread_title:  examples for log normal distributions in nature/economy? 

message: If the relationship between the log-normal distribution and the normal distribution is right, then I don't understand why \mu needs to be greater than 0 (since \mu is expected to be a real with no boundary in the normal distribution). At least, it can be null since it's the case with the graphs shown for the pdf and cdf (I've edited the article in consequence). Also, that's not \sigma that needs to be greater than 0, but \sigma^2 (which simply means that \sigma can't be null since it's a real number). -- 82.123.94.169 (talk) 15:04, 28 February 2008 (UTC)
replies: text: Yes, you're right: \sigma can't be negative or null (it's also obvious reading the PDF formula). I was confused by the Normal Distribution article where only \sigma^2 is expected to be positive (which is also not sufficient there). Thanks for your answer, and sorry for that. I guess \mu can't be negative as well because that would be meaningless if it was (even if it would be mathematically correct). -- 82.123.102.83 (talk) 19:33, 13 March 2008 (UTC)
thread_title:  Parameters boundaries ? 

message: Although yes, any base is OK, the derivations and moments, etc. are all done assuming a natural logarithm. Although the distribution would still be lognormal in another base b, the details would all change by a factor of ln(b). A note should probably be added in this section, that we are using by convention the natural logarithm here. (And possibly re-mention it in the PDF.) --128.59.111.72 (talk) 22:59, 10 March 2008 (UTC)
thread_title:  Logarithm Base 

message: I think it should be highlighted in the article that the Log-normal distribution is the analogue of the normal distribution in this way: if we take n independent distributions and add them we "get" the normal distribution (NB: here I am lazy on purpose, the precise idea is the Central Limit Theorem). If we take n positive independent distributions and multiply them, we "get" the log-normal (also lazy). Albmont (talk) 11:58, 5 June 2008 (UTC)
replies: text: This is to some extent expressed (or at least suggested) where the article says "A variable might be modeled as log-normal if it can be thought of as the multiplicative product of many small independent factors". Perhaps it could be said better, but the idea is there. Encyclops (talk) 14:58, 5 June 2008 (UTC)
replies: text:  So we're talking about the difference between "expressed (or at least suggested)" on the one hand, and on the other hand "highlighted". Michael Hardy (talk) 17:39, 5 June 2008 (UTC)
replies: text:  Yes, the ubiquity of the log-normal in Finance comes from this property, so I think this property is important enough to deserve being stated in the initial paragraphs. Just MHO, of course. Albmont (talk) 20:39, 5 June 2008 (UTC)

text: The factors need to have small departure from 1 ... I have corrected this, but can someone think of a rephrasing for the bit about "the product of the daily return rates"? Is a "return rate" defined so as to be close to 1 (no profit =1) or close to zero (no profit=0)? Melcombe (talk) 13:49, 11 September 2008 (UTC)
replies: text: The "return rate" should be the one "close to 1 (no profit == 1)."  The author must be talking about discount factors rather than rates of return.  Rates of return correspond to specific time periods and are therefore neither additive nor multiplicative.  Returns are often thought of as normally distributed in finance, so the discount factor would be lognormally distributed.  I'll fix this.  Alue (talk) 05:14, 19 February 2009 (UTC)

text: Moreover, it would be nice to have a reference for this section. 188.97.0.158 (talk) 14:21, 4 September 2012 (UTC)
thread_title:  Product of "any" distributions 

message: Why the pdf value would be greater than 1 in the pdf picture?
Am I missing something here? I am really puzzled.  —Preceding unsigned comment added by 208.13.41.5 (talk) 01:55, 11 September 2008 (UTC)
replies: text: Why are you puzzled?  When probability is concentrated near a point, the value of the pdf is large.  That's what happens here?  Could it be that you're mistaking this situation with that of probability mass functions?  Those cannot exceed 1, since their values are probabilities.  The values of a pdf, however, are not generally probabilities. Michael Hardy (talk) 02:20, 11 September 2008 (UTC)

text: Just to put it another way, the area under a pdf is equal to one, not the curve itself. Encyclops (talk) 03:01, 11 September 2008 (UTC)
thread_title:  Why the pdf value would be greater than 1 in the pdf picture? 

message: Here's the whole summary to my last edit:
: 
: Two problems: X is more conventional here, and the new edit fails to distinguish between capital for the random variable and lower case for the argument to the density function.
: 
Michael Hardy (talk) 20:15, 18 February 2009 (UTC)
thread_title:  My edit summary got truncated 

message: Something seems a bit odd with the plots. In particular the CDF plot appears to demonstrate that all the curves have a mean at about 1, but if the underlying parameter µ is held fixed, we should see P = 0.5 at around x=3 for sigma = 3/2; and at around 1.35 for sigma=1, and all the way at e^50 for sigma=10. The curves appear to have been plotted with the mean of the lognormal distribution fixed at (µ+o^2/2)=1? ~confused~
: Don't confuse the expected value with the point at which the probability is one-half. The latter is well-defined for the Cauchy distribution, while the former is not; thus although x=1 is the point at which all these distributions have P[x < 1] = 1/2; it's not the expected value. Hurr hurr, let no overtired idiots make this mistake again. (signed, Original Poster)  —Preceding unsigned comment added by 140.247.249.76 (talk) 09:26, 29 April 2009 (UTC)
replies: text:  We had this discussion on this page in considerable detail before, a couple of years ago.  Yes, they're accurates; they're also somewhat counterintuitive. Michael Hardy (talk) 16:40, 17 June 2009 (UTC)
thread_title:  Are the plots accurate? 

message: I commented out this table:
Confidence interval bounds	log space        	geometric
3σ lower bound            	\mu - 3\sigma\,\!	\mu_\mathrm{geo} / \sigma_\mathrm{geo}^3\,\!
2σ lower bound            	\mu - 2\sigma\,\!	\mu_\mathrm{geo} / \sigma_\mathrm{geo}^2\,\!
1σ lower bound            	\mu - \sigma\,\! 	\mu_\mathrm{geo} / \sigma_\mathrm{geo}\,\!
1σ upper bound            	\mu + \sigma\,\! 	\mu_\mathrm{geo} \sigma_\mathrm{geo}\,\!
2σ upper bound            	\mu + 2\sigma\,\!	\mu_\mathrm{geo} \sigma_\mathrm{geo}^2\,\!
3σ upper bound            	\mu + 3\sigma\,\!	\mu_\mathrm{geo} \sigma_\mathrm{geo}^3\,\!
The table has nothing to do with confidence intervals as those are normally understood.  I'm not sure there's much point in doing confidence intervals for the parameters here as a separate topic from confidence intervals for the normal distribution.
: 
Obviously, you cannot use μ and σ to form confidence intervals.  They're the things you'd want confidence intervals for!  You can't observe them.  If you could observe them, what would be the point of confidence intervals? Michael Hardy (talk) 16:43, 17 June 2009 (UTC)
replies: text: , I think I agree with you. I think the confidence intervals on parameters are sometimes called "credibility intervals". They are obtained through a Bayesian analysis, using a prior, and where the posterior distribution on the parameters gives the credibility interval. Correct me if I'm wrong. Attic Salt (talk) 00:50, 6 June 2020 (UTC)
thread_title:  Nonsense about confidence intervals 

message: In the relation section, we should mention the scaling & inverse of a log normal variable:
* If X \sim \operatorname {Log-N} (\mu, \sigma^2)  then X + c is called shifted log-normal. E(X+c)=E(X)+c, var(X+c)=var(X)
* If X \sim \operatorname {Log-N} (\mu, \sigma^2) , then Y=aX is also log normal, F_Y(y)=F_X(\frac{y}{a}) and f_Y(y)=\frac{1}{a}f_X(\frac{y}{a}), E(Y)=aE(X), E(Y^2)=a^2E(X^2)
* If X \sim \operatorname {Log-N} (\mu, \sigma^2) , the Y=\frac{1}{X} is called inverse log normal,
F_Y(y)=1-F_X(\frac{1}{y}) and f_Y(y)=\frac{1}{y^2}f_X(\frac{1}{y}) EY=?, var(Y)=?
Jackzhp (talk) 12:53, 28 July 2009 (UTC)
replies: text: If Y=aX then Y\sim\operatorname{logN}(\mu+\ln a,\sigma^2), formulas for ƒ and F are immediate application of the formulas from the beginning of the article. If Y=1/X then Y\sim\operatorname{logN}(-\mu,\sigma^2), and again formulas immediately follow. It's actually much easier to work with this representation because one may want to calculate not only mean+variance, but other quantities as well. ... stpasha » talk » 18:32, 28 July 2009 (UTC)
thread_title: Scaling & inverse

message: As User:Encyclops proves above, the formula in the "partial expectation" section is the quantity \int_k^{\infty} x f(x) dx. 
However, a recent edit defined the term "partial expectation" as a synonym for the "conditional expectation" E(x|x>k).
That doesn't seem correct; it seems unlikely that the uncommon term "partial expectation" would be a synonym for the more standard term "conditional expectation". Instead, it makes sense that "partial expectation" would mean part of the expectation, as this definition states.
Anyway, regardless of semantics, \int_k^{\infty} x f(x) dx is not E(x|x>k). Instead, \int_k^{\infty} x f(x) dx is E(x|x>k)prob(x>k).
Therefore, the current "partial expectation" section is incorrect. It is self-consistent if we instead define "partial expectation" as E(x|x>k)prob(x>k). So I will make that change. (unsigned edit by 213.170.45.3 )
::Well that is one definition of "partial expectation" that you have found, and I can't find another. If you make the change to be a formal definition of the term then include the citation, otherwise you might change the text to avoid it being a "definition" at all. 08:54, 24 September 2009 (UTC)
thread_title: Partial expectation again

message: I would like to start a new section on properties, where one of the properties is, that data that arise from the the log-normal distribution has a symmetric Lorenz curve (see also Lorenz asymmetry coefficient), any objections?
Christian Damgaard  —Preceding unsigned comment added by Christian Damgaard (talk • contribs) 10:36, 13 October 2010 (UTC)
replies: text: The present section "Characterization" might reasonably be split-up, some of it going into a new section headed "Properties". But "Characterization" doesn't mean here what it usually means so the rest could be renamed. Adding the info you suggest seems OK. Melcombe (talk) 12:24, 13 October 2010 (UTC)
thread_title: Properties?

message: Is the median of the distribution of the random variable, after converting it to its logarithm, the same as the corresponding median after logarithmizing the whole distribution? Theoretically, it should, because the ranks of the values from smallest to largest should remain the same. If so, it should be mentioned in the article. Mikael Häggström (talk) 05:58, 1 March 2011 (UTC)
thread_title:  Is the median the same? 

message: The approximate mean and variance for the sum Y=\textstyle\sum_{j=1}^n X_j, for i.i.d. log-normal 
X_j \sim \operatorname{Log-\mathcal{N}}(\mu_j, \sigma^2), are given incorrectly, I think.  The expressions below for \sigma_Z  and \mu_Z are meant to be for an approximately normally distributed Z\approx log(Y). So that
\begin{align}
  & \operatorname{E}[Y] \approx e^{\mu_Z + \tfrac{1}{2}\sigma^2_Z}, \\
  & \operatorname{Var}[Y] \approx e^{2\mu_Z + \sigma^2_Z} (e^{\sigma^2_Z} - 1)  \\
\end{align}
and thus direct substitution (for constant \sigma) gives
 
\operatorname{Var}[Y] \approx \operatorname{Var}[e^Z] = e^{\sigma^2} (e^{\sigma^2} - 1)  \textstyle\sum_{j=1}^n e^{2\mu_j}
as expected, since the variance of the sum of i.i.d. variables equals to the sum of variances for each variable. 
I therefore suggest changing approximated by another log-normal distribution Z 
to 
approximated by a normal distribution Z \approx log(Y). 
 
Please let me know if I am wrong. The references to Gao and to Fenton & Wilkinson should also be cited correctly.  — Preceding unsigned comment added by Raiontov (talk • contribs) 05:43, 15 November 2011 (UTC)
thread_title:  Related distributions 

message: The pdf and cdf graphs of the normal distribution are very beautiful. If the log-normal ones were changed in the same way (thicker lines, grid, ...) I think the article would be more legible. Jbbinder (talk) 12:16, 18 June 2012 (UTC)
thread_title:  Improvement of pictures 

message: In the table on the right it reads
Parameters	σ2 > 0 — log-scale, μ ∈ R — shape (real)
Surely, the use of "shape" must be a mistake. The shape of the distribution is determined by σ2 while the location is determined by μ. This fact can easily be verified by plotting \frac{1}{x\sqrt{2\pi}\sigma}\ e^{-\frac{\left(\ln x-\mu\right)^2}{2\sigma^2}} normalized by its maximum value as a function of \frac{x}{\mu}. Curves with varying μ will coincide. Changing σ2 on the other hand will change the shape of the pdf.
In my opinion it would be better if the table entry read
Parameters	σ2 > 0 — log-scale (shape), μ ∈ R — location (real)
Comments?  — Preceding unsigned comment added by 193.11.28.112 (talk) 13:33, 24 October 2013 (UTC)
thread_title:  Confusion about location and shape in the Probability distribution table, row on parameters 

message: The formula is clearly wrong (although it was correctly coppied from the reference given).
The formula given is:
\mu=\ln\left(\frac{m^2}{\sqrt{v+m^2}}\right)
But the fraction inside the logarythim is clearly not "dimensionless" and it should be.
I have done the calculation on my own and I arrived at a similar (and dimension consisntent) result:
\mu=\ln\left(\frac{m}{\sqrt{v+m^2}}\right) = \frac{1}{2}\ln\left(\frac{m^2}{v+m^2}\right)
G Furtado (talk) 00:34, 1 December 2013 (UTC)
thread_title:  Wrong formula for parameter μ as a function of the mean and variance 

message: Power law distributions are very similar to but not the same as log-normal distributions.  This is mentioned in the power-law article. It should also be brought up here.  — Preceding unsigned comment added by 211.225.33.104 (talk) 05:08, 11 July 2014 (UTC)
thread_title:  Power laws 

message: Hello fellow Wikipedians,
I have just added archive links to  on Log-normal distribution. Please take a moment to review my edit. If necessary, add  after the link to keep me from modifying it. Alternatively, you can add  to keep me off the page altogether. I made the following changes:
*Added archive https://web.archive.org/20150509101241/http://wireless.per.nl/reference/chaptr03/shadow/shadow.htm to http://wireless.per.nl/reference/chaptr03/shadow/shadow.htm
When you have finished reviewing my changes, please set the checked parameter below to true to let others know.
Cheers. —cyberbot IITalk to my owner:Online 10:23, 29 August 2015 (UTC)
thread_title:  External links modified 

message: An error appears to have been made in converting the entropy to use a base-unspecific log.
\mu + \frac{1}{2} \ln(2\pi e \sigma^2)
gives
\log(\sigma e^{\mu+\tfrac12} \sqrt{2\pi} )
rather than
\log(2\pi\sigma^2 e^{\mu+\tfrac12})
I've made the same change in the page itself.  — Preceding unsigned comment added by 208.78.228.100 (talk) 00:22, 23 February 2016 (UTC)
thread_title:  Base-unspecific entropy incorrect 

message: Would it be clearer to group the argument to the ``ln`` (natural log) function together like this? In scipy.stats and many textbooks there is a ``loc`` (location) parameter that is equivalent to the mean for symmetric distributions, but not the assymetric log-normal distribution. The ``loc`` parameter must be included within the natural log operation but the mean should not (for the log normal distribution only) like (ln(x - loc) - mu)^2. So being explicit about the grouping may help comprehension and comparison to the notation in other texts and code.
Hobsonlane (talk) 17:23, 18 April 2016 (UTC)
thread_title:  Notation/Grouping Clarification in Formula 

message: Proposal to use the following graph on the page about the Lognormal distribution:
  — Preceding unsigned comment added by StijnDeVuyst (talk • contribs) 14:15, 2 December 2016 (UTC)
replies: text: I think this plot has a typo on the log normal distribution, shouldn't `X ~ lnN(mu, s^2)`  say `lnX ~ N(mu, s^2)` ? Kornel.j.k (talk) 08:27, 8 April 2024 (UTC)
thread_title:  Graph explaining relation between normal and lognormal distribution 

message: The sigma=1,mu=0 curve in the PDF plot is misleading, since it looks like the PDF is linear in a neighborhood of x=0. I think this is because it was plotted using too few sample points. The fact that the PDF is so small near zero is important in applications, so the graph should not hide it.  — Preceding unsigned comment added by 77.88.71.157 (talk) 10:13, 9 February 2017 (UTC)
thread_title:  Plots misleading due to coarse sampling 

message: It strikes me as odd to call μ and σ respectively location and scale parameter. They function as such in the underlying normal distribution, but not in the derived log-normal distribution. Madyno (talk) 20:37, 9 May 2017 (UTC)
replies: text: I have expunged all of the statements to the effect that those are location and scale parameters for this family of distributions. That is far worse than "odd". Michael Hardy (talk) 20:49, 10 May 2017 (UTC)
thread_title:  Location and scale 

message: Within this article I found the notation
:  \ln \mathcal N \, 
apparently being used to refer to the lognormal density function, and earlier I found (and got rid of) the use of \mathcal N for the normal density. If \mathcal N is a normal density, then \log \mathcal N should denote the logarithm of the normal density, not the density of the lognormal. Michael Hardy (talk) 21:01, 10 May 2017 (UTC)
thread_title:  "\ln\mathcal N" ? 

message: The claim that μ and σ are location and scale parameters for the family of lognormal distributions is beyond horrible. Michael Hardy (talk) 21:06, 10 May 2017 (UTC)
replies: text: I have added to the article the statement that eμ is a scale parameter for the lognormal family of distributions. Michael Hardy (talk) 21:36, 10 May 2017 (UTC)
thread_title:  "location and scale" 

message: If X is a dimensional random variable (i.e. it has physical units, like a lot of the examples) then what are the units of quantities like \log X and its mean \mu?
We can take the log of 1.85 but how do we take the log of 1.85 metres?Fathead99 (talk) 14:48, 24 July 2017 (UTC)
replies: text: We don't take the log of such a quantity. Normally the log is taken from the dimensionless ratio of the quantity itself and some reference value. Madyno (talk) 20:40, 26 July 2017 (UTC)
thread_title: Dimensions 

message: Colors and standard deviations do not match between the plots, which could be confusing to a casual reader  — Preceding unsigned comment added by Mwharton3 (talk • contribs) 21:21, 22 August 2018 (UTC)
thread_title:  PDF and CDF plots confusing 

message: Could someone explain what the geometric mean of a random variable is? Madyno (talk) 22:26, 25 January 2019 (UTC)
replies: text: https://en.wikipedia.org/wiki/Geometric_mean It is the antilogarithm of the mean logarithm of the values of a random variate.207.47.175.199 (talk) 17:41, 2 June 2022 (UTC)
thread_title:  Geometric mean 

message: The section "Occurrence and applications" contains a misleading link. Specifically, "log-Lévy distributions" links to https://en.wikipedia.org/wiki/L%C3%A9vy_skew_alpha-stable_distribution, a URL that redirects to https://en.wikipedia.org/wiki/Stable_distribution, a page that does not have the annotation "Redirected from log-Lévy distributions" at its top. Now, consistent with the redirected URL, the Stable distribution page does contain the annotation "(Redirected from Lévy skew alpha-stable distribution)". But the Stable distribution page never actually says anything at all about "Lévy skew" anything, and for that matter, never anything at all about "log-Lévy" anything. There's just a complete, total disconnect. Page Notes (talk) 16:13, 12 March 2019 (UTC)
thread_title:  log-Lévy distribution bug report 

message: At the end of the intro, the article currently says "The log-normal distribution is the maximum entropy probability distribution for a random variate X—for which the mean and variance of ln(X) are specified."
Are we sure this is correct? I tried looking at the source, and it barely seems to mention the log-normal distribution at all, let alone argue that the log-normal distribution is the maximum entropy probability distribution for any random variable for which the mean and variance of the ln of the variable is defined.
I haven't spent lots of time looking into this, so sorry if I'm missing something. SanjayRedScarf (talk) 23:00, 18 February 2023 (UTC)
thread_title:  Is it really the max entropy distribution? 

message: Someone is changing the location parameter  \mu  which is such as  \mu \in (-\infty,\ +\infty)  to be just \mu > 0  which is mistaken. Please someone review and block the user IP. 45.181.122.234 (talk) 02:50, 27 November 2023 (UTC)
thread_title:  Location parameter modifications 

message: The pdf plot in the top right states each distribution has mean = 0. Visually, it appears each distribution has mean = 1. Drewscottt (talk) 01:46, 20 March 2024 (UTC)
thread_title:  PDF plot mean value