Talk:Rosin–Rammler distribution

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This article now says:

The function is described by
R={e^{- \left( {\frac {D}{{\it Dm}}} \right) ^{n}}}.

In view of what it says later in the article, this would seem to be the cumulative distribution function, and I'm guessing it means as a function of the variable D, although it doesn't say so. I shouldn't have to guess, and I shouldn't have to read what it says later to understand this. This article also needs attention in a few other respects. Probably I'll be back later. Michael Hardy (talk) 22:26, 27 January 2008 (UTC)

This has improved. But I'm stuck on this point:

  • R is the retained weight fraction of particles with diameter > D

What does that mean? Does it mean that the total weight of all particles of diameter > D is that fraction of the total weight of all particles? It says "probability distribution". If the answer to the foregoing question is "yes" then that would mean probabilities are proportional to weights of Noodle snacks (talk) 12:20, 5 February 2008 (UTC)particles. Is that what is intended? Michael Hardy (talk) 21:20, 28 January 2008 (UTC)

I am not an expert on the distribution; however a mass fraction is essentially a concentration, a term which refers to the ratio of mass in a mixture. The reason that mass ratios are used would most likely be because the PSD is typically measured by a sieving technique. Typically a sample of a known weight of particles is passed through a set of sieves of known mesh sizes. The sieves are arranged in decreasing diameters. The weight of particles retained on each sieve after a period of vibration is measured and converted into a percentage of the total sample. Other measurement techniques such as laser granulometry would tend to give diameters in relation to percentage of particles, not percentage by mass. Making the assumption that the particles are of uniform density, then the percent by mass can me translated into percent by amount. However I think that which exactly the distribution represents will depend on the measurement technique. This will need further research before it is stated as fact. Noodle snacks (talk) 03:52, 29 January 2008 (UTC)

I believe that the article is now incorrect in specifically refering to mass fractions. This would only be the case when the function is fitted to data points taken with a measurement technique which gives mass fractions (ie by sieves analysis). When other measurement methods are used then it might not represent a mass fraction. Noodle snacks (talk) 03:27, 5 February 2008 (UTC) This article is now incorrect, have a closer read of what I said. It is only representitive of a mas

Can you be more specific? When you say "other measurement methods", do you mean things other than mass are measured? E.g. volume? Or number of particles? If so, would the distribution still be a Rosin-Rammler distribution? Michael Hardy (talk) 04:45, 5 February 2008 (UTC)
There are a huge variety of possible measurement techiques for measuring particle size distributions, see PSD measurement techniques for a bit of a list. Sieves analysis is one of the few methods that gives you results in terms of mass fraction, as opposed to percentage of particles. I have seen discussion related to fitting results obtained using other measurement techniques, in these cases the distribution wouldn't be fitted to a mass fraction. I think that it'd likely still be a Rosin-Rammler distribution (since making the assumption of uniform density makes a mass fraction analogous to a number of particles fraction). This needs to be researched before the article explicity states that the distribution is for use with mass fractions only. When I have more time I will try and find a reference that has an explicit statement either way. Noodle snacks (talk) 06:31, 5 February 2008 (UTC)

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The Rosin-Rammler distribution seems to be a mass or volume distribution, not a probability distribution. See http://www.erpt.org/014Q/nelsa-06.htm and also Google. Ferred (talk) 10:16, 5 February 2008 (UTC)

I can't view the page in its original form currently, it is down. Google has a cached version with no images unfortunately.

It is correct that mass, volume and number of particles are not equivilent, and that particle size distributions can be represented in terms of % mass, volume or particles. This doesn't mean that it isn't a probability distribution, just that the results are in terms of mass, volume or number particles. That article doesn't say that the distribution is not used for particles number fractions, but does confirm it can be used to give a volume fraction. My point is that which it represents depends upon the measurement technique used to get the data (which the distribution is then fitted to). That page will be a useful reference as far as the use to represent volume fractions goes.

That article does raise the point that for some particle distributions its useful to add together multiple functions with different parameters to get a better representation, however that is something that should most likely be mentioned on the PSDs page. Noodle snacks (talk) 12:20, 5 February 2008 (UTC)

As "pure" mathematicians understand the term, it would still technically be a probability distribution. Michael Hardy (talk) 21:40, 5 February 2008 (UTC)
Perhaps the sensible approach is to talk about the function in a purely mathematical sense, then discuss its uses etc?Noodle snacks (talk) 11:16, 7 February 2008 (UTC)

[edit] Merge Proposal

The two pages describe exactly the same function. The Weibull page is more mature mathematically and has been around longer, but there are a few useful notes on use with particle size distributions here that should be kept. —Preceding unsigned comment added by Noodle snacks (talk • contribs) 07:20, 8 February 2008 (UTC)

I agree, and nobody has disagreed, so I suggest you go ahead and perform a selective paste merger. --Qwfp (talk) 10:04, 12 February 2008 (UTC)