A Method for Simulating Nonnormal Distributions with Specified <i>L</i>-Skew, <i>L</i>-Kurtosis, and <i>L</i>-Correlation

<table>Graph of the region for feasible combinations of (absolute value) <svg height="11.175" id="M273" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 9.8249998 11.175" width="9.8249998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>-skew <svg height="16.299999" id="M274" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 23.612499 16.299999" width="23.612499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> and <svg height="11.175" id="M275" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 9.8249998 11.175" width="9.8249998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>-kurtosis <svg height="12.0125" id="M276" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 14.675 12.0125" width="14.675" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> for global pdfs. An asymmetric <svg height="12" id="M277" style="vertical-align:-3.41937pt" version="1.1" viewbox="0 0 20.625 12" width="20.625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,0,0,-.012,8.675,11.763)"><path d="M608 643l-12 -19q-56 33 -145 33q-87 0 -154 -42q-68 -42 -68 -115q0 -74 66 -116q67 -42 176 -42q21 0 63 5l29 56q34 66 57 103q43 65 106 113q65 50 122 50q41 0 62 -22t21 -60q0 -67 -87 -144q-88 -76 -217 -110q-46 -101 -119 -186q-72 -83 -136 -108
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</svg>-<svg height="12" id="M278" style="vertical-align:-3.41937pt" version="1.1" viewbox="0 0 20.6 12" width="20.6" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,0,0,-.017,.062,7.675)"><path d="M484 406q0 -21 -22 -38q-10 -7 -18 -1q-15 11 -30 11q-30 0 -77.5 -37t-74.5 -67l79 -168q11 -23 19.5 -34.5t13 -14t10.5 -2.5q9 0 30 17.5t40 42.5l17 -23q-31 -45 -57.5 -69.5t-40.5 -29.5t-31 -5q-18 0 -32 13.5t-35 55.5q-34 71 -69 160q-36 -32 -59 -56
q-12 -27 -36 -158q-44 -7 -77 -15l-5 7l82 349q6 25 -2 25q-16 0 -72 -41l-14 22q44 41 89 69.5t66 28.5q19 0 19 -32q0 -16 -6 -43l-35 -160l146 143q94 92 136 92q20 0 33 -12t13 -30z" id="x1D705"></path></g>
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</svg> distributions will lie in the area above the curve graphed in the <svg height="16.299999" id="M279" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 23.612499 16.299999" width="23.612499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,0,0,-.017,.062,12.013)"><path d="M162 -163h-61v866h61v-866z" id="x7C"></path></g><g transform="matrix(.017,0,0,-.017,4.533,12.013)"><path d="M471 456q-22 -60 -37 -85q-20 -3 -84 -3q-9 0 -29 2t-29 2q-38 -145 -54 -234q-15 -80 14 -80q23 0 68 38l14 -25q-78 -83 -137 -83q-50 0 -50 64q0 25 7 57l67 266q-57 4 -98 -9t-80 -49l-20 21q14 18 27 31t36.5 30t56.5 26t73 9q26 0 82.5 -2t89.5 -2q21 0 32 5t24 24
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<g transform="matrix(.012,0,0,-.012,12.738,16.088)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
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<g transform="matrix(.017,0,0,-.017,19.075,12.013)"><path d="M162 -163h-61v866h61v-866z" id="x7C"></path></g>
</svg> and <svg height="12.0125" id="M280" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 14.675 12.0125" width="14.675" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,0,0,-.012,8.275,11.95)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g>
</svg> plane.</table>

International Scholarly Research Notices

fig3

Figure 3

Figure 3: A Method for Simulating Nonnormal Distributions with Specified <i>L</i>-Skew, <i>L</i>-Kurtosis, and <i>L</i>-Correlation 

International Scholarly Research Notices

A Method for Simulating Nonnormal Distributions with Specified L-Skew, L-Kurtosis, and L-Correlation

Figure 3