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Total variation distance is half the absolute area between the two curves: Half the shaded area above. In probability theory, the total variation distance is a statistical distance between probability distributions, and is sometimes called the statistical distance, statistical difference or variational distance.
An important tool for calculating the Fréchet distance of two curves is the free-space diagram, which was introduced by Alt and Godau. [4] The free-space diagram between two curves for a given distance threshold ε is a two-dimensional region in the parameter space that consists of all point pairs on the two curves at distance at most ε:
A classification model (classifier or diagnosis [7]) is a mapping of instances between certain classes/groups.Because the classifier or diagnosis result can be an arbitrary real value (continuous output), the classifier boundary between classes must be determined by a threshold value (for instance, to determine whether a person has hypertension based on a blood pressure measure).
The chart's purpose was to provide a graphical representation of the function of C. F. Colebrook in collaboration with C. M. White, [6] which provided a practical form of transition curve to bridge the transition zone between smooth and rough pipes, the region of incomplete turbulence.
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.
In air at STP the mean free path of molecules is about 96 nm. Since electrons are much smaller, their average distance between colliding with molecules is about 5.6 times longer, or about 0.5 μm. This is a substantial fraction of the 7.5 μm spacing between the electrodes for minimal arc voltage.
Given any curve c : (a, b) → S, one may consider the composition X ∘ c : (a, b) → ℝ 3. As a map between Euclidean spaces, it can be differentiated at any input value to get an element (X ∘ c)′(t) of ℝ 3. The orthogonal projection of this vector onto T c(t) S defines the covariant derivative ∇ c ′(t) X.
In qualitative terms, a line integral in vector calculus can be thought of as a measure of the total effect of a given tensor field along a given curve. For example, the line integral over a scalar field (rank 0 tensor) can be interpreted as the area under the field carved out by a particular curve.