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In control theory, the RMSE is used as a quality measure to evaluate the performance of a state observer. [ 10 ] In fluid dynamics , normalized root mean square deviation (NRMSD), coefficient of variation (CV), and percent RMS are used to quantify the uniformity of flow behavior such as velocity profile, temperature distribution, or gas species ...
This is in contrast to RMSE which involves squaring the differences, so that a few large differences will increase the RMSE to a greater degree than the MAE. [ 4 ] Optimality property
This metric is well suited to intermittent-demand series (a data set containing a large amount of zeros) because it never gives infinite or undefined values [1] except in the irrelevant case where all historical data are equal.
The MSE either assesses the quality of a predictor (i.e., a function mapping arbitrary inputs to a sample of values of some random variable), or of an estimator (i.e., a mathematical function mapping a sample of data to an estimate of a parameter of the population from which the data is sampled).
For color images with three RGB values per pixel, the definition of PSNR is the same except that the MSE is the sum over all squared value differences (now for each color, i.e. three times as many differences as in a monochrome image) divided by image size and by three.
The earliest reference to a similar formula appears to be Armstrong (1985, p. 348), where it is called "adjusted MAPE" and is defined without the absolute values in the denominator. It was later discussed, modified, and re-proposed by Flores (1986).
Knowledge of g would be required in order to calculate the MSPE exactly; ... [1] Formulation. If the smoothing or fitting procedure has projection matrix (i.e., hat ...
In each, the centerline is at 0, the positive peak is at = and the negative peak is at = A rectangular pulse wave of duty cycle D, the ratio between the pulse duration and the period (T); illustrated here with a = 1. Graph of a sine wave's voltage vs. time (in degrees), showing RMS, peak (PK), and peak-to-peak (PP) voltages.