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Approximate sampling distribution of the serial correlation coefficient for small samples
Author(s) -
Tasker Gary D.
Publication year - 1983
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr019i002p00579
Subject(s) - mathematics , statistics , monte carlo method , correlation coefficient , autocorrelation , correlation , distribution (mathematics) , combinatorics , physics , mathematical analysis , geometry
The probability density function for the sample serial correlation coefficient r can be approximated by f ( r ) = (β(½, ½( T + 1))) −1 (1 − r 2 ) ½( T − 1 )(1+ c 2 − 2 cr ) −½( T ), whereβ is the Beta function, T = n − 2, c = ρ − [(1 + ρ)/( n − 3)], n is the number of observations, and ρ is the population lag one serial correlation. This distribution is derived from a large Monte Carlo study at points between ρ= −0.9 and ρ = 0.9 and for n =10, 20, and 30.