Peakness

Peakness refers to a concept in signal processing and data analysis that describes the degree to which a signal or distribution is concentrated around a central point or a few points. It quantifies how "sharp" or "pointed" a peak is compared to a flatter or more spread-out distribution. A high peakness value indicates that the data is highly concentrated around its mean or mode, suggesting a strong central tendency. Conversely, a low peakness value signifies that the data is more dispersed, with less emphasis on a single central point.

Different statistical measures can be used to quantify peakness, with kurtosis being a common example. Kurtosis measures the "tailedness" and "peakedness" of a probability distribution relative to a normal distribution. A distribution with high kurtosis (leptokurtic) has heavier tails and a sharper peak than a normal distribution, while a distribution with low kurtosis (platykurtic) has lighter tails and a flatter peak. Understanding peakness is important in various fields, including finance, where it can indicate the likelihood of extreme events, and in image processing, where it helps in identifying salient features.