Cubic mean

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The cubic mean (written as ) is a specific instance of the generalized mean with .

Contents

Definition

For real numbers the cubic mean is defined as:

   [1] [2] [3]

For example, the cubic mean of two numbers is:

.

Applications

It is used for predicting the life expectancy of machine parts. [3] [4] [5] [6]

Related Research Articles

In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals. Originally, they arose in connection with the problem of finding the arc length of an ellipse and were first studied by Giulio Fagnano and Leonhard Euler. Modern mathematics defines an "elliptic integral" as any function f which can be expressed in the form

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Square root Number whose square is a given number

In mathematics, a square root of a number x is a number y such that y2 = x; in other words, a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is x. For example, 4 and −4 are square roots of 16, because 42 = (−4)2 = 16. Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by where the symbol is called the radical sign or radix. For example, the principal square root of 9 is 3, which is denoted by because 32 = 3 ⋅ 3 = 9 and 3 is nonnegative. The term (or number) whose square root is being considered is known as the radicand. The radicand is the number or expression underneath the radical sign, in this case 9.

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Students <i>t</i>-distribution Probability distribution

In probability and statistics, Student's t-distribution is any member of a family of continuous probability distributions that arise when estimating the mean of a normally-distributed population in situations where the sample size is small and the population's standard deviation is unknown. It was developed by English statistician William Sealy Gosset under the pseudonym "Student".

Cubic equation Polynomial equation of degree 3

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Pearson correlation coefficient Measure of linear correlation

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Rayleigh distribution Probability distribution

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In continuum mechanics, the Froude number is a dimensionless number defined as the ratio of the flow inertia to the external field. Named after William Froude (;), the Froude number is based on the speed–length ratio which he defined as:

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von Mises distribution Probability distribution on the circle

In probability theory and directional statistics, the von Mises distribution is a continuous probability distribution on the circle. It is a close approximation to the wrapped normal distribution, which is the circular analogue of the normal distribution. A freely diffusing angle on a circle is a wrapped normally distributed random variable with an unwrapped variance that grows linearly in time. On the other hand, the von Mises distribution is the stationary distribution of a drift and diffusion process on the circle in a harmonic potential, i.e. with a preferred orientation. The von Mises distribution is the maximum entropy distribution for circular data when the real and imaginary parts of the first circular moment are specified. The von Mises distribution is a special case of the von Mises–Fisher distribution on the N-dimensional sphere.

In crystallography, atomic packing factor (APF), packing efficiency, or packing fraction is the fraction of volume in a crystal structure that is occupied by constituent particles. It is a dimensionless quantity and always less than unity. In atomic systems, by convention, the APF is determined by assuming that atoms are rigid spheres. The radius of the spheres is taken to be the maximum value such that the atoms do not overlap. For one-component crystals, the packing fraction is represented mathematically by

In mathematics, a lemniscatic elliptic function is an elliptic function related to the arc length of a lemniscate of Bernoulli studied by Giulio Carlo de' Toschi di Fagnano in 1718. It has a square period lattice and is closely related to the Weierstrass elliptic function when the Weierstrass invariants satisfy g2 = 1 and g3 = 0.

The root-mean-square deviation (RMSD) or root-mean-square error (RMSE) is a frequently used measure of the differences between values predicted by a model or an estimator and the values observed. The RMSD represents the square root of the second sample moment of the differences between predicted values and observed values or the quadratic mean of these differences. These deviations are called residuals when the calculations are performed over the data sample that was used for estimation and are called errors when computed out-of-sample. The RMSD serves to aggregate the magnitudes of the errors in predictions for various data points into a single measure of predictive power. RMSD is a measure of accuracy, to compare forecasting errors of different models for a particular dataset and not between datasets, as it is scale-dependent.

Poisson distribution Discrete probability distribution

In probability theory and statistics, the Poisson distribution, named after French mathematician Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.

References

  1. "calculation formulas" (PDF).
  2. Svarovski, Ladislav (31 October 2000). Solid-Liquid Separation. ISBN   9780080541440 . Retrieved 2015-01-20.
  3. 1 2 "Equivalent Load". Creative Motion Control. Archived from the original on 2015-01-20. Retrieved 2015-01-19.
  4. "ISO 4301-1-1986 Cranes and lifting appliances; Classification; Part 1 : General". www.iso.org. 1986. also available from "freestd.us" . Retrieved 2015-01-20.
  5. Babu & Sridhar (2010). Design of Machine Elements. ISBN   9780070672840 . Retrieved 2015-01-20.
  6. Harris, Tedric A.; Kotzalas, Michael N. (9 October 2006). Essential Concepts of Bearing Technology, Fifth Edition. ISBN   9781420006599 . Retrieved 2015-01-20.