parametric
(adjective)
of, relating to, or defined using parameters
Examples of parametric in the following topics:
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Parametric Surfaces and Surface Integrals
- A parametric surface is a surface in the Euclidean space $R^3$ which is defined by a parametric equation.
- A parametric surface is a surface in the Euclidean space $R^3$ which is defined by a parametric equation with two parameters: $\vec r: \Bbb{R}^2 \rightarrow \Bbb{R}^3$.
- Parametric representation is the most general way to specify a surface.
- The curvature and arc length of curves on the surface can both be computed from a given parametrization.
- The same surface admits many different parametrizations.
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Parametric Equations
- is a parametric equation for the unit circle, where $t$ is the parameter.
- Thus, one can describe the velocity of a particle following such a parametrized path as follows:
- One example of a sketch defined by parametric equations.
- Note that it is graphed on parametric axes.
- Express two variables in terms of a third variable using parametric equations
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The Role of the Model
- Fully-parametric.
- Non-parametric.
- Semi-parametric.
- One component is treated parametrically and the other non-parametrically.
- More complex semi- and fully parametric assumptions are also cause for concern.
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Calculus with Parametric Curves
- Parametric equations are equations which depend on a single parameter.
- Thus, one can describe the velocity of a particle following such a parametrized path as:
- Writing these equations in parametric form gives a common parameter for both equations to depend on.
- Writing in parametric form makes this easier to do.
- A trajectory is a useful place to use parametric equations because it relates the horizontal and vertical distance to the time.
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Distribution-Free Tests
- It includes non-parametric descriptive statistics, statistical models, inference, and statistical tests).
- These play a central role in many non-parametric approaches.
- In these techniques, individual variables are typically assumed to belong to parametric distributions.
- In terms of levels of measurement, non-parametric methods result in "ordinal" data.
- Non-parametric statistics is widely used for studying populations that take on a ranked order.
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Surfaces in Space
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Kruskal-Wallis H-Test
- The Kruskal–Wallis one-way analysis of variance by ranks is a non-parametric method for testing whether samples originate from the same distribution.
- Allen Wallis) is a non-parametric method for testing whether samples originate from the same distribution.
- The parametric equivalent of the Kruskal-Wallis test is the one-way analysis of variance (ANOVA).
- Since it is a non-parametric method, the Kruskal–Wallis test does not assume a normal distribution, unlike the analogous one-way analysis of variance.
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Arc Length and Speed
- Arc length and speed in parametric equations can be calculated using integration and the Pythagorean theorem.
- Since there are two functions for position, and they both depend on a single parameter—time—we call these equations parametric equations.
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Linear Equations
- The parametric form of a linear equation involves two simultaneous equations in terms of a variable parameter $t$, with the following values:
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Line Integrals
- where $r: [a, b] \to C$ is an arbitrary bijective parametrization of the curve $C$ such that $r(a)$ and $r(b)$ give the endpoints of $C$ and $a$.
- where $\cdot$ is the dot product and $r: [a, b] \to C$ is a bijective parametrization of the curve $C$ such that $r(a)$ and $r(b)$ give the endpoints of $C$.