“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.
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