Use log normal plot of cumulative weight vs size in phi units.

Unimodal give one straight line plot,

bimodal two different straight line plots

and the inflection point is the change of modal distributions.

Not uncommon for mixing of traction and saltation loads or traction and suspension loads mixing as velocity of transport decreases

Hi Praveen, they look unimodal to me but just looks can be deceptive. You can try the following: A mixture of two normal distributions has five parameters to estimate: the two means, the two variances and the mixing parameter. A mixture of two normal distributions with equal standard deviations is bimodal only if their means differ by at least twice the common standard deviation. To test this hypothesis, you will have to separate the two putative modes and look at the four statistical moments (mean, standard deviation, skewness, kurtosis) and their relationships. Do this for both cases (unimodal, and bimodal hypotheses). Identifying a mode for a continuous distribution requires smoothing or binning the data. The issue with binning is that the results often depend on where you place the bin cutpoints. It is not a simple problem and there are some websites that can give you ideas about how to do, going from do it yourself manually to algorithms if you are a bit of a programmer.

http://www.vassarstats.net/textbook/ch2pt1.html

http://www.itl.nist.gov/div898/handbook/eda/section3/histogr4.htm

If that does not work, you can go to this site and ask your question there too. It seems that whoever is responding is doing a lot of this stuff. I happened to be right in the middle of it too, and it is not simple. I don't have all the answers but I hope this still helps. Go to: http://stats.stackexchange.com/questions/45763/building-a-summary-for-values-drawn-from-a-bimodal-distribution

Also, I forgot (when you look at the statistical moments): A condition for a symmetrical distribution to be bimodal is that the kurtosis be less than three. I also found this:

Several tests of unimodality versus bimodality have been proposed:

Haldane suggested one based on second central differences (references below) Larkin later introduced a test based on the F test;

Benett created one based on the G test.

Tokeshi has proposed fourth test.

A test based on a likelihood ratio has been proposed by Holzmann and Vollmer.

Haldane JBS (1951) Simple tests for bimodality and bitangentiality. Ann Eugenics 16 (1) 359–364 DOI: 10.1111/j.1469-1809.1951.tb02488.x

Larkin RP (1979) An algorithm for assessing bimodality vs. unimodality in a univariate distribution. Behavior Research Methods 11 (4) 467-468 DOI: 10.3758/BF03205709

Bennett SC (1992) Sexual dimorphism of Pteranodon and other pterosaurs, with comments on cranial crests. J Vert Paleont 12 (4) 422-434

^ Tokeshi M (1992) Dynamics and distribution in animal communities; theory and analysis. Researches in Population Ecology 34:249–273

^ Barreto S, Borges PAV, Guo Q (2003) A typing error in Tokeshi’s test of bimodality. Global Ecology & Biogeography 12: 173–174

^ Holzmann H, Vollmer S (2008) A likelihood ratio test for bimodality in two-component mixtures – with application to regional income distribution in the EU. Advances in Statistical Analysis 92 (1) 57-69

Hi Praven, I don't mean to swamp your mailbox but since I am looking for that stuff for my own studies, I stumbled into this also. Could be useful:http://en.wikipedia.org/wiki/Mixture_density

And here is a good one: http://en.wikipedia.org/wiki/Bimodal_distribution

Dear Nathalie,

Thank you very much for such a nice and explanatory answer.

You are welcome, hope it helps. I am dealing with this right now and it is not always obvious...Good luck!

Use log normal plot of cumulative weight vs size in phi units.

Unimodal give one straight line plot,

bimodal two different straight line plots

and the inflection point is the change of modal distributions.

Not uncommon for mixing of traction and saltation loads or traction and suspension loads mixing as velocity of transport decreases

You can check paper by Smith et al (1997). In the paper,

http://onlinelibrary.wiley.com/doi/10.1029/97WR00365/abstract

Smith et al proposed a formula to calculate Bimodality parameter. This formula has been used by Almedeij (2010) and Bong et al (inpress) to determine the bimodality characteristics of urban drainage sediment.

Dear Peter and Charles,

Thanks for your suggestions. I'll try to plot log normal plot of cumulative weight vs size in phi units and also go through the paper.

The Author is VISHER ? ? Year sometime early 1970s

Fitting multiple Gaussian distributions to a distribution can be done using a method called Expectation Maximization. You can then use information theory to test if two distributions are a better fit than one distribution, though it helps if you have completely independent observations. The program CLUSTER works quite well. https://engineering.purdue.edu/~bouman/software/cluster/

You may want to look at some of the work by Kate Kranck and Tim Milligan. Kranck et al., 1996 a and b in Sedimentology. These are muddy sediments where flocculation is resposible for most of its transport and deposition. The papers give a good understanding of sorting of fine grained sediments.

Just try NOT to invent the wheel. Please.

You should at least read read:

Re-interpreting ‘segmented’ grain-size curves (pp. 47-51) Christiansen, C.; Blæsild, P.; Dalsgaard, K. Geological Magazine: Volume 121 (1984), Issue 1.

Christiansen, C. and Hartmann, D. (1991): The Hyperbolic Distribution. In Syvitski, J.P.M., (Ed.), Principle, Methods, and Applications of Particle Size Analysis. Cambridge University Press. pp. 237-248.

Hartman, D., (2007): From reality to model: Operationalism and the value chain of particle-size analysis of natural sediments. Sedimentary Geology, 202, 383–401.

A crutial technical question is related to how many fractions (dots on your curve) you have?

Hi, note that kurtosis and skewness parameter help discriminate bimodality. I use the aproach outlined in freeman and dale (2012; http://psych.nyu.edu/freemanlab/pubs/2012_BRM.pdf) to locate simple (monomodal) elongated shapes using edge map PDFs. 

Looking at your 4 examples, I would intuitively say that No. 1 is bimodal, No. 2 is trimodal, No. 3 is bimodal and No. 4 is bimodal.. With espect to skewness and kurtosis, these textural parameters are not reliable indicators of potentially mixed sediments because curve shapes change depending in which grain-size analysis method is used (cf. Flemming 2007: Sedimentary Geology 202-attached). The most reliable method is, in my opinion, the logarithmic settling velocity (psi) distribution.

Burg Flemming