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The distribution of the sample correlation coefficient with one variable fixed

1968; The National Institute of Standards and Technology; Volume: 72B; Issue: 1 Linguagem: Inglês

10.6028/jres.072b.007

2376-5291

David Hogben,

Financial Risk and Volatility Modeling

For th e usual st raight•line model, in whi c h the ind ependen t variable ta kes on a fixed, kno wn se t of va lues, it is shown th at th e sample co rre latio n coeffi cie nt is di stributed as Q with (n-2) degrees of freedo m and noncentralit y O=({3 /CT) V~(Xi -X)2.The Q variate has bee n defin ed and studi ed e lse• wh ere by Hogben et al.It is noted th at the square of th e correlation coeffi cient is di stributed as a nonce ntral beta variab le.