Introduction to turbulence/Statistical analysis/Multivariate random variables

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 Revision as of 07:41, 1 June 2006 (view source)Michail (Talk | contribs)← Older edit Revision as of 18:21, 1 June 2006 (view source)Michail (Talk | contribs) (→Joint pdfs and joint moments)Newer edit → Line 2: Line 2: Often it is importamt to consider more than one random variable at a time. For example, in turbulence the three components of the velocity vector are interralated and must be considered together. In addition to the ''marginal'' (or single variable) statistical moments already considered, it is necessary to consider the '''joint''' statistical moments. Often it is importamt to consider more than one random variable at a time. For example, in turbulence the three components of the velocity vector are interralated and must be considered together. In addition to the ''marginal'' (or single variable) statistical moments already considered, it is necessary to consider the '''joint''' statistical moments. + + For example if $u$ and $v$ are two random variables, there are three second-order moments which can be defined $\left\langle u^{2} \right\rangle$ , $\left\langle v^{2} \right\rangle$ , and $\left\langle uv \right\rangle$. The product moment $\left\langle uv \right\rangle$ is called the ''cross-correlation'' or  ''cross-covariance''. The moments === The bi-variate normal (or Gaussian) distribution === === The bi-variate normal (or Gaussian) distribution === dssd dssd

Revision as of 18:21, 1 June 2006

Joint pdfs and joint moments

Often it is importamt to consider more than one random variable at a time. For example, in turbulence the three components of the velocity vector are interralated and must be considered together. In addition to the marginal (or single variable) statistical moments already considered, it is necessary to consider the joint statistical moments.

For example if $u$ and $v$ are two random variables, there are three second-order moments which can be defined $\left\langle u^{2} \right\rangle$ , $\left\langle v^{2} \right\rangle$ , and $\left\langle uv \right\rangle$. The product moment $\left\langle uv \right\rangle$ is called the cross-correlation or cross-covariance. The moments

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