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A formula which was derived earlier by Scott. [2] Swapping the order of the integration and expectation is justified by Fubini's Theorem . The Freedman–Diaconis rule is derived by assuming that f {\displaystyle f} is a Normal distribution , making it an example of a normal reference rule .
Spawning triggers allow many fish to synchronize their breeding, making it more probable that individual fish will find a mate. In most cases, if these triggers were not present, male and female fish would not meet at the right stage and the number of offspring would be reduced.
In robotics, Vector Field Histogram (VFH) is a real time motion planning algorithm proposed by Johann Borenstein and Yoram Koren in 1991. [1] The VFH utilizes a statistical representation of the robot's environment through the so-called histogram grid, and therefore places great emphasis on dealing with uncertainty from sensor and modeling errors.
In addition, the choice of appropriate statistical graphics can provide a convincing means of communicating the underlying message that is present in the data to others. [1] Graphical statistical methods have four objectives: [2] The exploration of the content of a data set; The use to find structure in data; Checking assumptions in statistical ...
A v-optimal histogram is based on the concept of minimizing a quantity which is called the weighted variance in this context. [1] This is defined as = =, where the histogram consists of J bins or buckets, n j is the number of items contained in the jth bin and where V j is the variance between the values associated with the items in the jth bin.
Histogram equalization will work the best when applied to images with much higher color depth than palette size, like continuous data or 16-bit gray-scale images. There are two ways to think about and implement histogram equalization, either as image change or as palette change.
Sturges's rule [1] is a method to choose the number of bins for a histogram.Given observations, Sturges's rule suggests using ^ = + bins in the histogram. This rule is widely employed in data analysis software including Python [2] and R, where it is the default bin selection method.
The goal of density estimation is to take a finite sample of data and to make inferences about the underlying probability density function everywhere, including where no data are observed. In kernel density estimation, the contribution of each data point is smoothed out from a single point into a region of space surrounding it.