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OtherANALYSIS AND COMMENTARY

Heavy-Tailed Distribution of Seclusion and Restraint Episodes in a State Psychiatric Hospital

Paul D. Whitehead and Fredrik Liljeros
Journal of the American Academy of Psychiatry and the Law Online February 2011, 39 (1) 93-99;
Paul D. Whitehead
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Fredrik Liljeros
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    Figure 1.

    The number of patients with k total seclusions is a rapidly decaying curve, wherein multiple small events coexist with a few relatively large events: 207 patients required 1 SRE, while one patient required 310 SREs (34 times the mean). In contrast to a normal, or bell-shaped, distribution, there was no peak at an average or typical value, and the distribution was highly right-skewed, denoting the existence of hubs.

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    Figure 2.

    A double-logarithmic cumulative plot, p(k) ≥ k of the data (circles). The accompanying line shows the best-fit power-law function in the form p(k) = Ck−a for the distribution between a minimum of one to a maximum of 310 SREs.

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    Figure 3.

    Illustration of how the estimated power-law function slope exponent a changes up to a maximum of 100 SREs when fitting the slope via a maximum-likelihood procedure, with bootstrapping for 95 percent confidence intervals. As it deviates from a straight line, a power-law type of heavy distribution is ruled out; a stretched-exponential function may better account for the data.

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Journal of the American Academy of Psychiatry and the Law Online: 39 (1)
Journal of the American Academy of Psychiatry and the Law Online
Vol. 39, Issue 1
February 2011
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Heavy-Tailed Distribution of Seclusion and Restraint Episodes in a State Psychiatric Hospital
Paul D. Whitehead, Fredrik Liljeros
Journal of the American Academy of Psychiatry and the Law Online Feb 2011, 39 (1) 93-99;

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Heavy-Tailed Distribution of Seclusion and Restraint Episodes in a State Psychiatric Hospital
Paul D. Whitehead, Fredrik Liljeros
Journal of the American Academy of Psychiatry and the Law Online Feb 2011, 39 (1) 93-99;
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