Why there is more than one mode in a given distribution?



I am currently studying about the properties of a given distribution and while studying it I faced one distribution in which mode has more than one value which I am not able to understand .

In this plot there is two mode value one at 7 and other at 9.


There can be two clusters in the data, each mode pointing a cluster.

You may want to visualize the histograms by conditioning with the other variables in data set.


Hi @sid100158,

Let’s understand what mode is, mode is simply the highest occuring number in a numeric array.

Now see this array-

As you observe you will notice number 1 & 6 are occuring 3 times each. So this array had two modes 1 & 6.

Hope this helps.




you face a mixture of distributions here, you have two normal distributions, one with mu at 7 and the other at 9 (mean, mode). To come back to your point, you have two distributions and not one.
You have a pdf of form F(x) = Sum(wi * fi(x) ), i = 1 & 2 and w is the weight allocated to the single pdf. In your case w1 = w2 = 1 and fi(x) with normal distribution N( 7 or 9, 1.69) ( i have did not calculate the variance , just did approximation).

Hope this help.




to complement what I wrote yesterday, go through this document. It gives explanation and yes R code how to calculate the two distributions. Have fun .

Mixed distribution


In the foot size demonstration given above, the two modes probably represent the Gaussian peaks of overlapping male and female distribution. You can model the frequency of this distribution with a double Gaussian of the form f(x) = a*exp( -(x-x1)^2 / (sqrt(2)sigma1) ) + bexp( -(x-x2)^2 / (sqrt(2)*sigma2) ) and find the parameters using chi-squared minimisation.