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A weighting curve is a graph of a set of factors, that are used to 'weight' measured values of a variable according to their importance in relation to some outcome. An important example is frequency weighting in sound level measurement where a specific set of weighting curves known as A-, B-, C-, and D-weighting as defined in IEC 61672 [1] are used.
A commonly used weighting is the A-weighting curve, which results in units of dBA sound pressure level. Because the frequency response of human hearing varies with loudness, the A-weighting curve is correct only at a level of 40- phon and other curves known as B- , C- and D-weighting are also used, the latter being particularly intended for the ...
A graph of the A-, B-, C- and D-weightings across the frequency range 10 Hz – 20 kHz Video illustrating A-weighting by analyzing a sine sweep (contains audio). A-weighting is a form of frequency weighting and the most commonly used of a family of curves defined in the International standard IEC 61672:2003 and various national standards relating to the measurement of sound pressure level. [1]
Radiation weighting factors that go from physical energy to biological effect must not be confused with tissue weighting factors. The tissue weighting factors are used to convert an equivalent dose to a given tissue in the body, to an effective dose, a number that provides an estimation of total danger to the whole organism, as a result of the ...
The result of this application of a weight function is a weighted sum or weighted average. Weight functions occur frequently in statistics and analysis, and are closely related to the concept of a measure. Weight functions can be employed in both discrete and continuous settings.
where is the smoothing factor, and . In other words, the smoothed statistic is a simple weighted average of the current observation and the previous smoothed statistic . Simple exponential smoothing is easily applied, and it produces a smoothed statistic as soon as two observations are available.
For normally distributed random variables inverse-variance weighted averages can also be derived as the maximum likelihood estimate for the true value. Furthermore, from a Bayesian perspective the posterior distribution for the true value given normally distributed observations and a flat prior is a normal distribution with the inverse-variance weighted average as a mean and variance ().
Dosimetry attempts to factor in this effect with radiation weighting factors. Linear energy transfer is closely related to stopping power, since both equal the retarding force. The unrestricted linear energy transfer is identical to linear electronic stopping power, as discussed below.