Talk:Bimodal distribution

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I added nl:Bimodale distributie for the Dutch version to the article, but it doesn't show up? That's strange...

It's there. It worked. Nederlands is listed in the sidebar. Deco 19:49, 20 June 2006 (UTC)

What happens when we have two local maxima, but these maxima are different? For example, the experiment "roll a d6, if d6 = 1, then sample from a N(100,1), else sample from a N(0,1)". I would call this bimodal, even though the peak near x = 100 is 1/5 higher than the peak near x = 0. Albmont 10:09, 2 January 2007 (UTC)

Yes, I think it is misleading that Figure 1 shows the two peaks as being equal. I made it clear in the text at least that we are only talking about local maxima. I also linked to mode (statistics) and edited that page to note that local as well as global maxima of a pdf are commonly referred to as modes. Eclecticos 03:15, 21 January 2007 (UTC)

The article says (more or less) that X = αY + (1 − α)Z is usually a bimodal distribution. This is not precise: the correct way is that the variable whose density is fX = αfY + (1 − α)fZ is usually bimodal. Albmont 14:28, 1 February 2007 (UTC)

Also does a bimodal distribution have to be continuous, it can also be discrete, right?

[edit] Sex and height probably not a good example

The article currently states: "A good example [of a bimodal distribution] is the height of a person. The heights of males form a roughly normal distribution, as do those of females. Each of these distributions is unimodal. However, if we plot a single histogram of the entire population, we see two peaks—one for males and one for females." I suspect the statement about there existing two peaks in the overall histogram is empirically false in this case of the heights of women and men. The effect size article demonstrates the use of Cohen's d and Hedges's ĝ by stating the effect size of the sex difference in height as calculated from data from a UK sample, giving values of d=1.72 and ĝ=1.76. However, if you plot the sum of two normal distributions with equal variances and means separated by 1.76 standard deviations (try it), there is in fact only one local maximum; you don't really see bimodality in the overall population distribution unless the means of the sexes are separated by two or more standard deviations. I suggest that a better example be chosen to illustrate this article, unless the data in the effect size article is wrong (in which case that article should be edited), or I am somehow mistaken. Z. M. Davis 17 December 2007 (UTC)

I agree. Note that the sum of two shifted Gaussian distributions with the same standard deviation will be unimodal unless the means differ by more than the standard deviation since mean +/-σ are the inflection points of the Gaussian distribution. —Ben FrantzDale (talk) 15:37, 30 January 2008 (UTC)

[edit] Measure?

Is there a quantitative measure of bimodalness or multimodalness? Kurtosis would tell us something, I suppose... —Ben FrantzDale (talk) 15:37, 30 January 2008 (UTC)