I have plotted this curve using the default kernel density estimate function in R
I am looking for some standard distribution which could be close to this. Is there any standard bimodal distribution ?
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While I am not aware of anything that can be called ''standard'' bimodal distribution, in this particular case, mixture normal distribution seems to be appropriate at first glance. The pdf of such distribution is essentially the linear combination of two (or more) - not necessarily equal means or equal variances - normal distribution's pdf. (Thus the mixing weight is also a further parameter.)
R package mixtools provides tools for estimating such distributions.