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The Fréchet distance between multivariate normal distributions

1982; Elsevier BV; Volume: 12; Issue: 3 Linguagem: Inglês

10.1016/0047-259x(82)90077-x

1095-7243

David Dowson, B. V. Landau,

Financial Risk and Volatility Modeling

The Fréchet distance between two multivariate normal distributions having means μX, μY and covariance matrices ΣX, ΣY is shown to be given by d2 = |μX − μY|2 + tr(ΣX + ΣY − 2(ΣXΣY)12). The quantity d0 given by d02 = tr(ΣX + ΣY − 2(ΣXΣY)12) is a natural metric on the space of real covariance matrices of given order.