Noncentral F-Distribution

Definition

Let $U\sim {\chi }^2(r_1,\lambda ),V\sim {\chi }^2(r_2)$ be independent random variables following Noncentral Chi-squared Distribution and Chi-squared Distribution, respectively, then $\frac{U/r_1}{V/r_2}\sim F(r_1,r_2,\lambda )$ where $r_1,r_2\in \mathbb{N}$ are degree of freedoms and $\lambda \in {\mathbb{R}}^{+}$ is non-centrality parameter.

Properties

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