Modesdistinct

Modesdistinct is a methodological concept used to identify and separate distinct modes in a distribution or density estimate. The term emphasizes distinguishing true structural peaks from minor fluctuations caused by sampling noise or smoothing artifacts.

In a statistical context, a mode is a local maximum of a probability density function. Modesdistinct introduces a criterion for deciding when two nearby local maxima should be treated as separate modes. Typically two peaks are considered distinct if the valley between them is sufficiently deep or if the separation between peaks exceeds a data-driven threshold. Thresholds can be absolute, percentile-based, or determined through resampling or cross-validation.

Procedure-wise, modesdistinct often follows a sequence: compute a smoothed density estimate (for example, via kernel density estimation with a chosen bandwidth), locate local maxima as candidate modes, and for each pair of adjacent maxima evaluate a separation measure based on peak heights, valley depth, and inter-peak distance. If the valley is too shallow or the peaks are not sufficiently separated, the two maxima may be merged into a single mode. Significance assessments, such as bootstrap or permutation tests, can be used to gauge whether observed separations are unlikely under the null of unimodality.

Applications of modesdistinct span pattern recognition, econometrics, genomics, and other fields where distinguishing subpopulations or regimes within a distribution is important. Limitations include sensitivity to smoothing parameters, sample size, and noise, which can induce spurious modes or obscure true structure.

See also: multimodality, kernel density estimation, peak detection, mean shift.