the score and Wald tests has been proposed. This method can distinguish between unimodal and bimodal distributions when the underlying distributions are known. Antimode tests Statistical tests for the antimode are known. Otsu's method Otsu's method is commonly employed in computer graphics to determine the optimal separation between two distributions. General tests To test if a distribution is other than unimodal, several additional tests have been devised: the bandwidth test, the dip test, the excess mass test, the MAP test, the mode existence test, the runt test, the span test, and the saddle test. An implementation of the dip test is available for the R programming language. The p-values for the dip statistic values range between 0 and 1. P-values less than 0.05 indicate significant multimodality and p-values greater than 0.05 but less than 0.10 suggest multimodality with marginal significance. Silverman's test Silverman introduced a bootstrap method for the number of modes. The test uses a fixed bandwidth which reduces the power of the test and its interpretability. Under smoothed densities may have an excessive number of modes whose count during bootstrapping is unstable. Bajgier-Aggarwal test Bajgier and Aggarwal have proposed a test based on the kurtosis of the distribution. Special cases Additional tests are available for a number of special cases: Mixture of two normal distributions A study of a mixture density of two normal distributions data found that separation into the two normal distributions was difficult unless the means were separated by 4–6 standard deviations. In astronomy the Kernel Mean Matching algorithm is used to decide if a data set belongs to a single normal distribution or to a mixture of two normal distributions. Beta-normal distribution This distribution is bimodal for certain values of is parameters. A test for these values has been described. Parameter estimation and fitting curves Assuming that the distribution is known to be bimodal or has been shown to be bimodal by one or more of the tests above, it is frequently desirable to fit a curve to the data. This may be difficult. Bayesian methods may be useful in difficult cases. Software Two normal distributions A package for R is available for testing for bimodality. This package assumes that the data are distributed as a sum of two normal distributions. If this assumption is not correct the results may not be reliable. It also includes functions for fitting a sum of two normal