Distinguishing between unimodal and bimodal normal data Normal distributions are always unimodal It looks like by "bimodal normal data" you mean a Gaussian Mixture Model (GMM) with 2 components (i e the PDF of the data is a convex combination of Gaussian PDF's) There are several techniques to estimate the number of components in a Gaussian Mixture Model -- Bayesian Information Criterion, Akiakie Information Criterion, Calinski-Harabasz, etc
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Is the sum of independent unimodal random variables still unimodal? I believe that if the independent random variables have identical unimodal distributions that are symmetrical about the mode, the sum will have unimodal distribution that is symmetric about the mode, but I don't have a proof worked out in detail The unimodality should follow from convolution and the Cauchy-Schwarz inequality
Efficient algorithm to find maximum of a unimodal sequence We want to find the maximum element $a_ {p}$ of a unimodal sequence reading as few elements is possible I want to make an algorithm that solves this problem and find its execution time