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

chi-squared distribution

Mathematics

A type of non-negative continuous probability distribution, normally written as the χ‎²-distribution, with one parameter ν‎ called the degrees of freedom. The distribution (see appendix 15) is skewed to the right and has the property that the sum of independent random variables each having a χ‎²-distribution also has a χ‎²-distribution. It is used in the chi-squared test for measuring goodness of fit, in tests on variance and in testing for independence in contingency tables. It has mean ν‎ and variance 2ν‎.

Statistics

If Z₁, Z₂,…, Z_ν are ν independent standard normal variables (see normal distribution), and if Y is defined by $chi-squared distribution$ then Y has a chi-squared distribution with ν degrees of freedom (written as $chi-squared distribution$ ). The probability density function f is given by $chi-squared distribution$ where Γ is the gamma function. The form of the distribution was first given by Abbe in 1863 and was independently derived by Helmert in 1875 and Karl Pearson in 1900. It was Pearson who gave the distribution its current name.
The chi-squared distribution has mean ν and variance 2ν. For ν≤2 the mode is at 0; otherwise it is at (ν−2). A chi-squared distribution is a special case of a gamma distribution. The case ν=2 corresponds to the exponential distribution. Percentage points for chi-squared distributions are given in Appendix VIII.
Chi-squared distribution. All chi-squared distributions have ranges from 0 to ∞. Their shape is determined by the value of ν. If ν>2 then the distribution has a mode at (ν−2); otherwise the mode is at 0.

Computer

An important probability distribution with many uses in statistical analysis. Denoted by the Greek symbol Χ‎², it is the distribution of the sum of squares of f independent random variables, each being drawn from the normal distribution with zero mean and unit variance. The integer f is the number of degrees of freedom. Critical values of the probability distribution are widely available in tables, but exact calculations involve the incomplete gamma function. The most common applications are
1. (a) testing for interactions between different classifications of data using contingency tables;
2. (b) testing goodness-of-fit;
3. (c) forming confidence intervals for estimates of variance.

单词	chi-squared distribution
释义	chi-squared distribution Mathematics A type of non-negative continuous probability distribution, normally written as the χ‎²-distribution, with one parameter ν‎ called the degrees of freedom. The distribution (see appendix 15) is skewed to the right and has the property that the sum of independent random variables each having a χ‎²-distribution also has a χ‎²-distribution. It is used in the chi-squared test for measuring goodness of fit, in tests on variance and in testing for independence in contingency tables. It has mean ν‎ and variance 2ν‎. Statistics If Z₁, Z₂,…, Z_ν are ν independent standard normal variables (see normal distribution), and if Y is defined by $chi-squared distribution$ then Y has a chi-squared distribution with ν degrees of freedom (written as $chi-squared distribution$ ). The probability density function f is given by $chi-squared distribution$ where Γ is the gamma function. The form of the distribution was first given by Abbe in 1863 and was independently derived by Helmert in 1875 and Karl Pearson in 1900. It was Pearson who gave the distribution its current name. The chi-squared distribution has mean ν and variance 2ν. For ν≤2 the mode is at 0; otherwise it is at (ν−2). A chi-squared distribution is a special case of a gamma distribution. The case ν=2 corresponds to the exponential distribution. Percentage points for chi-squared distributions are given in Appendix VIII. Chi-squared distribution. All chi-squared distributions have ranges from 0 to ∞. Their shape is determined by the value of ν. If ν>2 then the distribution has a mode at (ν−2); otherwise the mode is at 0. Computer An important probability distribution with many uses in statistical analysis. Denoted by the Greek symbol Χ‎², it is the distribution of the sum of squares of f independent random variables, each being drawn from the normal distribution with zero mean and unit variance. The integer f is the number of degrees of freedom. Critical values of the probability distribution are widely available in tables, but exact calculations involve the incomplete gamma function. The most common applications are (a) testing for interactions between different classifications of data using contingency tables; (b) testing goodness-of-fit; (c) forming confidence intervals for estimates of variance.
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