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Parametric equation The first two types are known as analytic, or non-parametric, representations of curves; when compared to parametric representations for use in CAD applications, non-parametric representations have shortcomings. In particular, the non-parametric representation depends on the choice of the coordinate system and does not lend itself well to geometric transformations, such as rotations, translations, and scaling; non-parametric representations therefore make it more difficult to generate points on a curve. These problems can be addressed by rewriting the non-parametric equations in parametric form.
Sign test A template for the sign test using Excel is available at
Integration using parametric derivatives In mathematics, integration by parametric derivatives is a method of integrating certain functions.
Parametric model Parametric models are contrasted with the semi-parametric, semi-nonparametric, and non-parametric models, all of which consist of an infinite set of "parameters" for description. The distinction between these four classes is as follows:
Exact test Parametric tests, such as those described in exact statistics, are exact tests when the parametric assumptions are fully met, but in practice the use of the term "exact" (significance) "test" is reserved for those tests that do not rest on parametric assumptions – non-parametric tests. However, in practice most implementations of non-parametric test software use asymptotical algorithms for obtaining the significance value, which makes the implementation of the test non-exact.
Parametric model Some statisticians believe that the concepts "parametric", "non-parametric", and "semi-parametric" are ambiguous. It can also be noted that the set of all probability measures has cardinality of continuum, and therefore it is possible to parametrize any model at all by a single number in (0,1) interval. This difficulty can be avoided by considering only "smooth" parametric models.
Parametric statistics Since a parametric model relies on a fixed parameter set, it assumes more about a given population than non-parametric methods do. When the assumptions are correct, parametric methods will produce more accurate and precise estimates than non-parametric methods, i.e. have more statistical power. As more is assumed when the assumptions are not correct they have a greater chance of failing, and for this reason are not a robust statistical method. On the other hand, parametric formulae are often simpler to write down and faster to compute. For this reason their simplicity can make up for their lack of robustness, especially if care is taken to examine diagnostic statistics.
Parallel parametric test The parallel parametric test is an emerging strategy for wafer-level parametric testing that involves concurrent execution of multiple tests on multiple scribe line test structures. If offers the potential for increasing test throughput with existing test hardware, in response to market pressure on fabs to minimize test times. The figure illustrates the differences in the amount of time required to complete tests sequentially as compared to the same tests in parallel.
Parametric statistics Parametric functions were mentioned by R. Fisher in his work "Statistical Methods" for "Research Workers" in 1925 which created the foundation for modern statistics.
Parametric model In statistics, a parametric model or parametric family or finite-dimensional model is a family of distributions that can be described using a finite number of parameters. These parameters are usually collected together to form a single "k"-dimensional "parameter vector" "θ" = ("θ", "θ", …, "θ").
Parametric oscillator If the parameters vary at roughly "twice" the natural frequency of the oscillator (defined below), the oscillator phase-locks to the parametric variation and absorbs energy at a rate proportional to the energy it already has. Without a compensating energy-loss mechanism provided by formula_2, the oscillation amplitude grows exponentially. (This phenomenon is called parametric excitation, parametric resonance or parametric pumping.) However, if the initial amplitude is zero, it will remain so; this distinguishes it from the non-parametric resonance of driven simple harmonic oscillators, in which the amplitude grows linearly in time regardless of the initial state.
Parametric statistics Parametric statistics is a branch of statistics which assumes that sample data comes from a population that follows a probability distribution based on a fixed set of parameters. Most well-known elementary statistical methods are parametric. Conversely a non-parametric model differs precisely in that the parameter set (or feature set in machine learning) is not fixed and can increase, or even decrease if new relevant information is collected.
Parametric process (optics) Alternatively, non-parametric processes often involve loss (or gain) and give rise to:
Location test The following tables provide guidance to the selection of the proper parametric or non-parametric statistical tests for a given data set.
Nonparametric statistics The wider applicability and increased robustness of non-parametric tests comes at a cost: in cases where a parametric test would be appropriate, non-parametric tests have less power. In other words, a larger sample size can be required to draw conclusions with the same degree of confidence.
Optical parametric amplifier Optical parametric generation (OPG) (also called "optical parametric fluorescence", or "spontaneous parametric down conversion") often precedes optical parametric amplification.
DAP (software) Dap is a command line driven program. Using its internal commands, one can perform tests on means and percentiles, correlation, ANOVA, categorical analysis, linear and logistic regression analysis and non parametric statistics.
Parametric surface The local shape of a parametric surface can be analyzed by considering the Taylor expansion of the function that parametrizes it. The arc length of a curve on the surface and the surface area can be found using integration.
Parametric polymorphism In programming languages and type theory, parametric polymorphism is a way to make a language more expressive, while still maintaining full static type-safety. Using parametric polymorphism, a function or a data type can be written generically so that it can handle values "identically" without depending on their type. Such functions and data types are called generic functions and generic datatypes respectively and form the basis of generic programming.
Parametric equation The parametric equations for the hypotrochoids are: