Constructing Matrix Exponential Distributions by Moments and Behavior around Zero

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr class="thead"><td align="left"> </td><td align="center">1st</td><td align="center">2nd</td><td align="center">3rd</td><td align="center">4th</td><td align="center">5th </td></tr><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr><td align="left">Lognormal</td><td align="center">1.13315</td><td align="center">1.64872</td><td align="center">3.08022</td><td align="center">7.38906</td><td align="center">22.7599</td></tr><tr><td align="left">Order-3 ME</td><td align="center">1.13315</td><td align="center">1.64872</td><td align="center">3.08022</td><td align="center">7.58974</td><td align="center">24.5879</td></tr><tr class="table-tr"><td colspan="6"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Moments of the lognormal distribution and moments of the second matching ME distribution. 

Mathematical Problems in Engineering

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Table 1

Table 1: Constructing Matrix Exponential Distributions by Moments and Behavior around Zero 