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[6] Weighing matrices appear in the engineering of spectrometers, image scanners, [6] and optical multiplexing systems. [5] The design of these instruments involve an optical mask and two detectors that measure the intensity of light. The mask can either transmit light to the first detector, absorb it, or reflect it toward the second detector.
A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set. The result of this application of a weight function is a weighted sum or weighted average .
In statistics, the Horvitz–Thompson estimator, named after Daniel G. Horvitz and Donovan J. Thompson, [1] is a method for estimating the total [2] and mean of a pseudo-population in a stratified sample by applying inverse probability weighting to account for the difference in the sampling distribution between the collected data and the target population.
One very early weighted estimator is the Horvitz–Thompson estimator of the mean. [3] When the sampling probability is known, from which the sampling population is drawn from the target population, then the inverse of this probability is used to weight the observations. This approach has been generalized to many aspects of statistics under ...
When treating the weights as constants, and having a sample of n observations from uncorrelated random variables, all with the same variance and expectation (as is the case for i.i.d random variables), then the variance of the weighted mean can be estimated as the multiplication of the unweighted variance by Kish's design effect (see proof):
The lower weighted median is 2 with partition sums of 0.49 and 0.5, and the upper weighted median is 3 with partition sums of 0.5 and 0.25. In the case of working with integers or non-interval measures , the lower weighted median would be accepted since it is the lower weight of the pair and therefore keeps the partitions most equal.
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