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In statistics, the Bhattacharyya distance is a quantity which represents a notion of similarity between two probability distributions. [1] It is closely related to the Bhattacharyya coefficient , which is a measure of the amount of overlap between two statistical samples or populations.
Associated with the concept of a home range is the concept of a utilization distribution, which takes the form of a two dimensional probability density function that represents the probability of finding an animal in a defined area within its home range. [2] [3] The home range of an individual animal is typically constructed from a set of ...
This probability is given by the integral of this variable's PDF over that range—that is, it is given by the area under the density function but above the horizontal axis and between the lowest and greatest values of the range. The probability density function is nonnegative everywhere, and the area under the entire curve is equal to 1. The ...
A metric on a set X is a function (called the distance function or simply distance) d : X × X → R + (where R + is the set of non-negative real numbers). For all x, y, z in X, this function is required to satisfy the following conditions: d(x, y) ≥ 0 (non-negativity) d(x, y) = 0 if and only if x = y (identity of indiscernibles.
The probability density function (PDF) for the Wilson score interval, plus PDF s at interval bounds. Tail areas are equal. Since the interval is derived by solving from the normal approximation to the binomial, the Wilson score interval ( , + ) has the property of being guaranteed to obtain the same result as the equivalent z-test or chi-squared test.
In statistics, the Vuong closeness test is a likelihood-ratio-based test for model selection using the Kullback–Leibler information criterion. This statistic makes probabilistic statements about two models. They can be nested, strictly non-nested or partially non-nested (also called overlapping). The statistic tests the null hypothesis that ...
The first requirement ensures that the method of kernel density estimation results in a probability density function. The second requirement ensures that the average of the corresponding distribution is equal to that of the sample used. If K is a kernel, then so is the function K* defined by K*(u) = λK(λu), where λ > 0. This can be used to ...
y i is the number of times species i is represented in the total Y from another sample. D x and D y are the Simpson's index values for the x and y samples respectively. S is the number of unique species. C D = 0 if the two samples do not overlap in terms of species, and C D = 1 if the species occur in the same proportions in both samples ...