Simulating Univariate and Multivariate Tukey <svg     style="vertical-align:-4.698pt;width:12.875px;" id="M1" height="16.012501" version="1.1" viewBox="0 0 12.875 16.012501" width="12.875"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
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</svg> Distributions Based on the Method of Percentiles

The Cholesky decompositions for the MOP procedure <svg height="15.0875" id="M278" style="vertical-align:-2.3205pt" version="1.1" viewbox="0 0 64.324997 15.0875" width="64.324997" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>.

International Scholarly Research Notices

tab8

Table 8

Table 8: Simulating Univariate and Multivariate Tukey <svg     style="vertical-align:-4.698pt;width:12.875px;" id="M1" height="16.012501" version="1.1" viewBox="0 0 12.875 16.012501" width="12.875"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.022,-0,0,-.022,.062,10.1)"><path id="x1D454" d="M546 430q-14 -33 -37.5 -140t-38.5 -209q-29 -195 -156 -289q-29 -21 -70 -37t-78 -16q-62 0 -102.5 37t-40.5 69q0 27 26 48q19 15 25 -3q13 -43 46.5 -69t87.5 -26q55 0 83 21q29 22 50 65t43 140q14 64 29 163h-2q-55 -81 -149 -152q-59 -44 -102 -44q-23 0 -43.5 30
t-20.5 85q0 74 32.5 145.5t84.5 117.5q40 35 100 58.5t117 23.5q21 0 65 -8q30 -6 44 -6zM456 386q-40 16 -81 16q-29 0 -64 -13q-42 -17 -85 -97q-19 -36 -31.5 -86t-12.5 -86q0 -64 30 -64q20 0 52.5 21t60.5 52q74 81 95 123q26 62 36 134z" /></g>

		
	
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			<g transform="matrix(.022,-0,0,-.022,.062,16.025)"><path id="x210E" d="M499 88q-41 -46 -83.5 -73t-68.5 -27q-41 0 -19 98l52 225q10 43 8 59.5t-16 16.5q-37 0 -112 -65t-117 -135q-14 -42 -38 -179q-36 -7 -75 -20l-7 8l127 594q8 40 2.5 49t-35.5 9h-35l5 25q36 3 71.5 13t56.5 18t25 8q11 0 3 -38l-88 -417h2q77 102 195 167q44 24 79 24
q61 0 30 -130l-52 -220q-8 -33 4 -33q8 0 31 14.5t43 33.5z" /></g>

		
	
</svg> Distributions Based on the Method of Percentiles 

International Scholarly Research Notices

Simulating Univariate and Multivariate Tukey -and- Distributions Based on the Method of Percentiles

Table 8