This is my first post in CrossValidated and hope you can solve my problem. I've tried to calculate the bimodality coefficient (b) of two frequency distributions by using this formula:
where g is de skewness, K is the Kurtosis and n is the sample size. The b of a given emprirical distribution is then compared to a bencmark value of 0.555: higher numbers point toward bimodality whereas lower numbers point toward unimodality. I've been working with two frequency distributions in order to detect the degree of bimodality for each one. Here I show the two plots:
So, to have a quick look, it seems that the second distribution is more bimodal (two peaks) than the first one (hump-shaped). However, the bimodality coefficients do not say the same when I run in the R programme:
Kurtosis Skewness b 1 4.046225 1.927172 0.6602856 2 4.064557 1.843587 0.6145607
Apparently, both distributions are bimodal due to their b values are higher than 0.55. Seems logic for plot2 but plot1 has a clear unimodal distribution. Furthermore, I'm afraid that the values of Kurtosis and Skewness were incorrect. In theory, skewness values higher than 0 means that the distribution is right skewed but I could not see in the original plots. For Kurtosis >3 the distribution is leptokurkic which means to be sharper than a normal distribution.
Maybe I'm doing something wrong in the methodology to calculate Skewness and Kurtosis. I've used the e1071 package in R programme to calculate these variables by using the following script:
library("e1071") kurt<-kurtosis(frequency,type=2) skew<-skewness(frequency,type=2)
Formula type 2 for kurtosis: G_2 = ((n+1) g_2 + 6) * (n-1) / ((n-2)(n-3))
Formula type 2 for skewness: G_1 = g_1 * sqrt(n(n-1)) / (n-2)
It would be very useful to me if someone could explain me these results. Maybe I miss something in the methodology.
Thank you very much for your help!