“beta distribution”的概念、定义、翻译、参考文献-科学参考

beta distribution

Mathematics

If X is a random variable with probability density function given by $f (x, α, β) = \frac{1}{B (α, β)} x^{α - 1} {(1 - x)}^{β - 1} 0 \leq x \leq 1$ where B(α‎, β‎) is a beta function and λ‎, ν‎, x all > 0, then we say that X has a beta distribution with parameters α‎, β‎. The beta distribution has mean $\frac{α}{α + β}$ and variance $\frac{α β}{{(α + β)}^{2} (α + β + 1)} .$

Statistics

A distribution often used as a prior distribution for a proportion. The probability density function, for a random variable X having a beta distribution is $beta distribution$ where α and β are positive parameters, and B is the beta function. The name appears in a 1911 publication by Gini. The distribution has mean $beta distribution$ and variance $beta distribution$ If both α>1 and β>1, the distribution has mode at $beta distribution$ If both α<1 and β<1 then the distribution is U-shaped, whereas, if just one of α and β is<1, then the distribution is J-shaped.
If Y₁, Y₂,…, Y_k are independent random variables, with Y_j having a chi-squared distribution with ν_j degrees of freedom, then the ratio $beta distribution$ has a beta distribution with and .
Beta distribution. The distribution has a variety of shapes, which depend on the values of α and β.

单词	beta distribution
释义	beta distribution Mathematics If X is a random variable with probability density function given by $f (x, α, β) = \frac{1}{B (α, β)} x^{α - 1} {(1 - x)}^{β - 1} 0 \leq x \leq 1$ where B(α‎, β‎) is a beta function and λ‎, ν‎, x all > 0, then we say that X has a beta distribution with parameters α‎, β‎. The beta distribution has mean $\frac{α}{α + β}$ and variance $\frac{α β}{{(α + β)}^{2} (α + β + 1)} .$ Statistics A distribution often used as a prior distribution for a proportion. The probability density function, for a random variable X having a beta distribution is $beta distribution$ where α and β are positive parameters, and B is the beta function. The name appears in a 1911 publication by Gini. The distribution has mean $beta distribution$ and variance $beta distribution$ If both α>1 and β>1, the distribution has mode at $beta distribution$ If both α<1 and β<1 then the distribution is U-shaped, whereas, if just one of α and β is<1, then the distribution is J-shaped. If Y₁, Y₂,…, Y_k are independent random variables, with Y_j having a chi-squared distribution with ν_j degrees of freedom, then the ratio $beta distribution$ has a beta distribution with and . Beta distribution. The distribution has a variety of shapes, which depend on the values of α and β.
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