User talk:Dr. J. Rodal

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Hello, Dr. J. Rodal, and welcome to Wikipedia! Thank you for your contributions, especially what you did for Beta distribution. I hope you like the place and decide to stay. Here are some pages that you might find helpful:

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Welcome to Wikipedia :)

Hello dear Dr. J. Rodal,

I just noticed your huge contribution to the article on the Beta distribution - thank you so much!

With regards, Tal Galili (talk) 20:30, 5 August 2012 (UTC)

Nice work on the beta distribution. Thank you. DrMicro (talk) 12:12, 11 August 2012 (UTC)

Thank you for the comment. WP is a remarkable project but a little more civility and positive fb would go a long way.

		The Original Barnstar
		For your outstanding work on the beta distribution DrMicro (talk) 08:47, 14 August 2012 (UTC)

Length of Beta distribution article

Thank you for asking for my opinion. I had anticipated this problem arising as I watch your (excellent) work on this topic. There is both a practical reason as well as a more opinionated one for this comment. As you will be aware WP is hosted on an MySQL server. It has a HUGE workload WP being one of the most popular sites on the Web. Each page call up puts pressure on the servers. Long pages place more of a load than do shorter ones. The sys admins who baby sit the servers would prefer we would not try to hammer them too badly as they do cost money to replace.

It has been suggested that pages probably should not exceed 100k in length before being subdivided. This as far as I can determine is a figure picked out of the air. There are more than a few pages that exceed this limit by some margin. This probably isn't a huge issue when the page is rarely referenced but for a popular page its length may be a problem. I have had to split a few pages I created when they began to grow a bit on the long side.

There are also more opinionated reasons for this suggestion. Readability tests show that articles that are too long - in print - are harder for an average reader than a series of shorter ones. Web readability is generally lower than paper based (about 70% if I recall the figure correctly). WP tries to aim for a general reader as well as the more expert. And even experts do get a tad tired reading very long pages.

In short there are probably fairly good reasons for this suggestion. The difficulty we all face with a long page we have largley created is where to split the pages up. This isn't always an easy call. The suggested limit of 100k is a tab arbitrary but probably not ridiculous. I do think that the work you have done here is well beyond the call of duty and I and I'm sure other really do appreciate it. However it might be a reasonable thing to split the page up into a number of smaller pages at sensible break points. DrMicro (talk) 15:03, 10 October 2012 (UTC)

You are very welcome. It more than a little unfortunate that the majority of editors here - at least in my experience - tend not to explain the reasons for such comments. I suspect it is because they themselves re not aware of the reasons for the suggested guidelines. More than a few treat the Manual of Style guidance like holy writ and show no appreciation of the material itself. I mention this as if you continue return to WP it is virtually certain you will (sadly) bump into a few of them. The mathematics pages are in general edited by a relatively polite group - probably because we are probably the biggest consumers of each others work.

If there is ever anything else I can be of assistance with please don't hesitate to ask. DrMicro (talk) 15:39, 10 October 2012 (UTC)

A thought. In splitting a page while it may be necessary to move much of a section onto a new page it is often helpful to leave an 'abstract' of the new page on the original. While there may well be better examples of this practice elsewhere on WP one page that illustrates this is the page Hepatitis C virus. This page has sections on the epidemiology and evolution with links to additional material on other pages.DrMicro (talk) 15:39, 10 October 2012 (UTC)

Talkback

Hello, Dr. J. Rodal. You have new messages at Jason Quinn's talk page.
Message added 16:58, 10 October 2012 (UTC). You can remove this notice at any time by removing the {{Talkback}} or {{Tb}} template.

Jason Quinn (talk) 16:58, 10 October 2012 (UTC)

Robustness of Mean and Median sample estimators for Bimodal distributions

I may perhaps have missed this factoid in the beta distribution article but in case it isnt present it may be worth including somewhere in it.

• Bimodal distributions (including the beta distribution) have the peculiar property that the mean is a more robust sample estimator than the median. Reference: Mosteller F, Tukey JW (1977) Data analysis and regression: a second course in statistics. Reading, Mass, Addison-Wesley Pub Co

My apologies for forgetting to sign the last note. I'm glad you think that factoid may be worthy of inclusion. I will try and find the page in the book.

Re length of article. I think your suggestion of separating off the 2 and 4 parameter cases is a good idea. I suspect it is easier to concentrate on the peculiarities if of each in a separate article.DrMicro (talk) 12:23, 11 October 2012 (UTC)

Regarding your question on length of article modifications: All of WP is permantantly a work in progress :) What I would suggest is a 'cut and paste' method. Cut the sections you feel would be best in a new article and create a new page for this section. This does generate some overlap with the original page but each article should stand or fall on its own merits.

Your point about the median and the mean makes a LOT of sense. Thank you for that insight. DrMicro (talk) 13:07, 11 October 2012 (UTC)

A thought. I presume by your question that you were concerned about the incompleteness of a cut and paste approach to article creation. Dont be. This isnt a paper that has to be complete before submission. WP has many many articles in various stages of composition - far too many IMHO that should be worked on rather than having new ones created. That having been said it is a poorly understood fact that most editors while happy to work on a page that has been created do not want to create new pages. The best approach here is to chose a section that would make a fairly complete article by itself, cut it out of the page, paste it into a new page. The new page will need a bit of work - often copying the lede part of the original and modifying as necessary is the best approach. Also on the original page a small 'abstract' section is often very useful with a link to the new article.DrMicro (talk) 15:11, 11 October 2012 (UTC)

As ever glad to be of help :) DrMicro (talk) 15:21, 11 October 2012 (UTC)

Thank you. Well done finding this page :) This is a subtle point. Normally the median is considered more robust than the mean and may be recommended for this reason. Clearly this is not the case if the distribution has a beta distribution. I suspect this point may apply to any bimodal distribution.DrMicro (talk) 18:26, 11 October 2012 (UTC)

My bad. You have already covered this point.DrMicro (talk) 18:27, 11 October 2012 (UTC)

Again thank you. This is what WP is supposed at least in part to be about: collaberation to improve the material here. Another point I did come across that might be of interest: the kurtosis of a distribution is a measure of the probability mass around the two points: the mean +/- the standard deviation. Given the flexbility of the beta distribution this may be worth exploring further.DrMicro (talk) 18:54, 11 October 2012 (UTC)

Another random thought :) I have been trying to track down useable material on bimodal distributions in general. One piece that I did come across is are the formulas for the first four moments of the sum of two arbitrary distributions. I am not aware of any work on the sum of two (or more) beta distributions but I suspect there is some out there. Regardless I suspect the moments of the sum of two beta distributions would be of interest to somebody and they may be worth including. Any thoughts?DrMicro (talk) 19:00, 11 October 2012 (UTC)

I concur with you over the material on kurtosis. There is one difficulty there: it is a much read article. It may attract a few opinionated and frequently poorly informed editors who might well be rude. Be warned. Re moments of a sum: the formulae are all on the bimodal distribution page with the required reference. Its 'only' a matter of copy and paste. The question is: is it worth adding in and if so where to put it? These questions I suspect you are better placed to answer than most :) DrMicro (talk) 19:24, 11 October 2012 (UTC)

A paper that might interest you but one I have not been able to access is - Baker GA (1930) Transformations of bimodal distributions. Ann Math Stat 1 (4) 334-344. From what I understand Baker proposed a transformation from a bimodal to a unimodal distribution. DrMicro (talk) 19:29, 11 October 2012 (UTC)

A little digging has shown that there are a number of papers that use mixtures of beta distributions. For that reason it may be worth adding in a section on the moments. DrMicro (talk) 21:55, 11 October 2012 (UTC)

Your work on Beta distribution

I wanted to voice my appreciation for your work recently on the Beta distribution article, which I have referred to time and time again. The last thing I'd want is for you to be dissuaded to edit by bureaucratic processes, so I furthermore wanted to assure you my article length concerns are purely feedback from an interested reader, rather than borne from a busybody desire to clear Special:LongPages ;). I hope the 2/4 parameter splitting goes some way to alleviating article length problems, on top of introducing greater clarity. --Iae (talk) 11:56, 12 October 2012 (UTC)

Re sums of beta distributions

This topic I think would merit a new but linked page. I have been doing a little digging. Mixtures of beta distributions - and indeed other distributions - beta + some other distribution - are topics of some importance. The earlier work on mixtures seems to have concentrated on mixtures of normal distributions but I presume that - at least in part - because of the increasing power of computers other distributions are also being considered. There is also the related problem: if I have a data set how do I fit a beta (or other) distribution to the data and test its fit. This is admittedly more a problem for statistics than probability. Both topics could I think live happily on the same page. DrMicro (talk) 10:04, 13 October 2012 (UTC)

Might be of interest

You may have seen this paper before. If you havent I think you might find it of interest

http://www.economics.soton.ac.uk/staff/aldrich/aldrich%20bootstrapping.pdf

DrMicro (talk) 13:46, 23 November 2012 (UTC)

Dear Dr Rodal

I am delighted that you found that article to be of interest. I also found it to be worth a read. I dont know if you explored the links on the PDF but if you did not I suspect you might find them also of interest.

http://www.economics.soton.ac.uk/staff/aldrich/Figures.htm

http://www.economics.soton.ac.uk/staff/aldrich/Mathematical%20Words.htm

DrMicro (talk) 08:12, 24 November 2012 (UTC)

Beta distribution and PERT estimates

Dear Dr. Rodal,

your work on the beta distribution is fantastic and I'd first of all like to express my gratitude for your contributions to Wikipedia. Concerning the beta distribution I am especially interested in the application in the field of project estimation. The article states that for values alpha = 3 - sqrt(2) and beta = 3 + sqrt(2) the PERT estimate has been shown "to exhibit average errors of 40% in the mean an 549% in the variance". As reference it uses the DRMI Newsletter linked in the footnote. However, in that newsletter it is said that "In particular, the PERT formulas are exact ... when alpha = 3 - sqrt(2) and beta = 3 + sqrt(2)" (page 6 bottom right). Maybe I've overlooked something but aren't these contradictory statements? I would appreciate if you could give me a hint as to where my understanding is false. Otherwise we should maybe clarify this point in the article itself.

Kind regards from Bavaria, Germany

Carl — Preceding unsigned comment added by 62.245.205.130 (talk) 05:24, 15 April 2014 (UTC)

Dear Carl, thank you for your kind words and special thanks for catching the above mentioned error. I have corrected the article accordingly.Dr. J. Rodal (talk) 12:24, 15 April 2014 (UTC)

Thank you very much for that clarification! Kind regards, Carl --62.245.205.130 (talk) 13:02, 17 April 2014 (UTC)

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