A first‐order autoregressive model for the joint distribution of a time dependent random variable and its derivative
作者： Nils Mole , Lawrence Chan
DOI: 10.1002/ENV.1103
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摘要: A first-order autoregressive (AR(1)) model is analysed to investigate the relationship between a time dependent random variable Γt and its derivative . This motivated by problem of turbulent dispersion gas cloud or plume in atmosphere, where square derivative, , also interest. It shown that general Dt are correlated, with their correlation proportional skewness Γt. The probability distributions innovations Yt Dt, joint Yt, derived for number assumed latter include normal, exponential, gamma (of integer order), uniform, sum uniform distributions. lack reversibility AR(1) apparent asymmetric when has exponential distribution. Comparisons made some experimental observations. Copyright © 2011 John Wiley & Sons, Ltd.
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