meanAt

MeanAt is a name used in programming and statistics to describe a function that computes a mean value relative to a specified reference point, location, or subset of data. It is not a universally standardized mathematical operator, but a convention chosen by libraries or codebases to indicate a localized mean calculation. MeanAt functions are often used to implement smoothing, neighborhood statistics, or local summaries where the mean is taken over a subset rather than the entire dataset.

Common forms and parameters include:

- A time- or index-based mean around a position i with a fixed window size w. In this form, the mean is computed over data points from max(1, i-w) to min(n, i+w).

- A spatial or distance-based mean around a reference location, using a radius r or a kernel function to weight observations by distance. In this form, closer data points contribute more to the mean according to the chosen weighting scheme.

Optional parameters may include handling for missing values (for example, excluding NaNs) and choices about boundary behavior when the neighborhood extends beyond the data’s edges.

Implementation notes:

- Edge behavior is important; windows near the start or end of the data are typically truncated.

- Missing data can be omitted or imputed prior to calculation.

- The computational cost is proportional to the size of the neighborhood for each evaluation, making meanAt potentially more expensive than a global mean when used repeatedly.

Applications include time series smoothing, spatial data analysis, and image processing where local averages serve as simple denoising or feature-estimation tools. See also moving average, kernel mean, local smoothing.