Gary D. Tasker
1983
<p><span>The probability density function for the sample serial correlation coefficient </span><i>r</i><span><span> </span>can be approximated by</span><i>f</i><span>(</span><i>r</i><span>) = (β(½, ½(</span><i>T</i><span><span> </span>+ 1)))</span><sup>−1</sup><span>(1 −<span> </span></span><i>r</i><sup>2</sup><span>)</span><sup>½(<i>T</i>− 1</sup><span>)(1+<span> </span></span><i>c</i><sup>2</sup><span><span> </span>− 2</span><i>cr</i><span>)</span><sup>−½(<i>T</i></sup><span>), whereβ is the Beta function,<span> </span></span><i>T</i><span>=<span> </span></span><i>n</i><span>− 2,<span> </span></span><i>c</i><span><span> </span>= ρ − [(1 + ρ)/(</span><i>n</i><span><span> </span>− 3)],<span> </span></span><i>n</i><span><span> </span>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<span> </span></span><i>n</i><span><span> </span>=10, 20, and 30.</span></p>
application/pdf
10.1029/WR019i002p00579
en
American Geophysical Union
Approximate sampling distribution of the serial correlation coefficient for small samples
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