parametric

(adjective)

of, relating to, or defined using parameters

Related Terms

Examples of parametric in the following topics:

  • 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.

  • 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

  • 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.

  • 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.

  • 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.

  • Surfaces in Space

  • 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.

  • 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.

  • Linear Equations

    • The parametric form of a linear equation involves two simultaneous equations in terms of a variable parameter $t$, with the following values:

  • 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 $C$.