“F-distribution”的概念、定义、翻译、参考文献-科学参考

F-distribution

Statistics

If Y₁ and Y₂ are independent random variables each having a chi-squared distribution with ν₁ and ν₂ degrees of freedom, respectively, then the ratio X, given by $F-distribution$ is said to have an F-distribution with ν₁ and ν₂ degrees of freedom. This may be written as the F_ν₁,ν₂-distribution. Evidently 1/X will have a F_ν₂,ν₁-distribution.
The form of the distribution was first given in 1922 by Sir Ronald Fisher, and it is sometimes still referred to as Fisher's F-distribution. In 1934 the distribution was tabulated (see Appendix VII) by Snedecor, who used the letter F in Fisher's honour. The distribution is therefore also referred to as the Snedecor F-distribution. The probability density function f of the F_ν₁,ν₂-distribution is given by $F-distribution$ where B is the beta function.
F-distribution. All F-distributions take values from 0 to ∞ and, for ν₁, ν₂>4, have mean and mode near 1.
The distribution has mean ν₂/(ν₂−2) provided that ν₂>2. The distribution has variance $F-distribution$ provided that ν₂>4. If ν₁≤2 there is a mode at 0, otherwise the mode is at $F-distribution$ If X has a t-distribution with ν degrees of freedom, then X² has an F_1,ν distribution.

Chemical Engineering

A statistical probability distribution used in the analysis of variance of two samples for statistical significance. It is calculated as the distribution of the ratio of two chi-square distributions and used, for the two samples, to compare and test the equality of the variances of the normally distributed variances.

Economics

A continuous distribution described by the probability density function

$f (x) = \frac{Γ (\frac{p + q}{2})}{Γ (\frac{p}{2}) Γ (\frac{q}{2})} {(\frac{p}{q})}^{p / 2} \frac{x^{\frac{p}{2} - 1}}{{(1 + \frac{p}{q} x)}^{(p + q) / 2}}, 0 < x < \infty$

where p and q are the degrees of freedom. Its moment-generating function does not exist. This distribution is used, for example, in finite sample inference in a linear regression model under the assumption that the underlying random error has normal distribution. For large q, (pF) has asymptotically chi-square distribution with p degrees of freedom.

单词	F-distribution
释义	F-distribution Statistics If Y₁ and Y₂ are independent random variables each having a chi-squared distribution with ν₁ and ν₂ degrees of freedom, respectively, then the ratio X, given by $F-distribution$ is said to have an F-distribution with ν₁ and ν₂ degrees of freedom. This may be written as the F_ν₁,ν₂-distribution. Evidently 1/X will have a F_ν₂,ν₁-distribution. The form of the distribution was first given in 1922 by Sir Ronald Fisher, and it is sometimes still referred to as Fisher's F-distribution. In 1934 the distribution was tabulated (see Appendix VII) by Snedecor, who used the letter F in Fisher's honour. The distribution is therefore also referred to as the Snedecor F-distribution. The probability density function f of the F_ν₁,ν₂-distribution is given by $F-distribution$ where B is the beta function. F-distribution. All F-distributions take values from 0 to ∞ and, for ν₁, ν₂>4, have mean and mode near 1. The distribution has mean ν₂/(ν₂−2) provided that ν₂>2. The distribution has variance $F-distribution$ provided that ν₂>4. If ν₁≤2 there is a mode at 0, otherwise the mode is at $F-distribution$ If X has a t-distribution with ν degrees of freedom, then X² has an F_1,ν distribution. Chemical Engineering A statistical probability distribution used in the analysis of variance of two samples for statistical significance. It is calculated as the distribution of the ratio of two chi-square distributions and used, for the two samples, to compare and test the equality of the variances of the normally distributed variances. Economics A continuous distribution described by the probability density function $f (x) = \frac{Γ (\frac{p + q}{2})}{Γ (\frac{p}{2}) Γ (\frac{q}{2})} {(\frac{p}{q})}^{p / 2} \frac{x^{\frac{p}{2} - 1}}{{(1 + \frac{p}{q} x)}^{(p + q) / 2}}, 0 < x < \infty$ where p and q are the degrees of freedom. Its moment-generating function does not exist. This distribution is used, for example, in finite sample inference in a linear regression model under the assumption that the underlying random error has normal distribution. For large q, (pF) has asymptotically chi-square distribution with p degrees of freedom.
随便看	completeness axiom of the real numbers completeness theorem complete orthonormal basis complete quadrangle complete set of residues complete solution complete term rewriting system complete tree completing the square completion complex Complex 14 Complex 39 complex algebra complex analysis complex analytic complexation complex conjugate complex exponential complex frequency complex function complex idea complex impedance complex instruction set computer complex ion