Statistical Inferences and Applications of the Half Exponential Power Distribution

<table class="table-group" id="tab6"><tr><td><table class="table"><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr class="thead"><td align="left">Model </td><td align="center"><span style="width: 9.7250004px;"><svg height="12.1875" id="M150" style="vertical-align:-1.32405pt" version="1.1" viewbox="0 0 9.7250004 12.1875" width="9.7250004" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.875,11.388)"><path d="M470 557l-12 -25q-103 25 -223 64q-128 -41 -223 -64l-12 25q172 77 224 109h22q57 -35 224 -109z" id="xF5C01"></path></g><g transform="matrix(.017,-0,0,-.017,.063,11.925)"><path d="M548 455q-32 -77 -74 -77q-37 0 -103 10l-3 -2q36 -30 48.5 -62t12.5 -80q0 -103 -75 -179.5t-175 -76.5q-70 0 -113 45t-43 128q0 115 83.5 200.5t209.5 85.5q31 0 77.5 -4t67.5 -4q36 0 62 30zM350 274q0 54 -17 86q-19 35 -57 35q-50 0 -90 -37.5t-59 -91.5t-19 -109
q0 -61 24.5 -96.5t65.5 -35.5q51 0 87.5 46.5t50.5 100.5t14 102z" id="x1D70E"></path></g>
</svg></span></td><td align="center"><span style="width: 10.2px;"><svg height="17.1875" id="M151" style="vertical-align:-3.50804pt" version="1.1" viewbox="0 0 10.2 17.1875" width="10.2" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,2.863,11.388)"><path d="M470 557l-12 -25q-103 25 -223 64q-128 -41 -223 -64l-12 25q172 77 224 109h22q57 -35 224 -109z" id="xF5C01"></path></g><g transform="matrix(.017,-0,0,-.017,.063,12.763)"><path d="M570 304q0 -108 -87 -199q-40 -42 -94.5 -74t-105.5 -43q-41 0 -65 11l-29 -141q-9 -45 -1.5 -58t45.5 -16l26 -2l-5 -29l-241 -10l4 26q51 10 67.5 24t26.5 60l113 520q-54 -20 -89 -41l-7 26q38 28 105 53l11 49q20 25 77 58l8 -7l-17 -77q39 14 102 14q82 0 119 -36
t37 -108zM482 289q0 114 -113 114q-26 0 -66 -7l-70 -327q12 -14 32 -25t39 -11q59 0 118.5 81.5t59.5 174.5z" id="x1D45D"></path></g>
</svg></span></td><td align="center">Log lik. </td><td align="center">AIC </td><td align="center">BIC </td></tr><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr><td align="left">HN </td><td align="center">1.5135 (0.1064) </td><td align="center">— </td><td align="center">−115.1666</td><td align="center">232.3332</td><td align="center">234.9483</td></tr><tr><td align="left">HEP </td><td align="center">0.9689 (0.1298) </td><td align="center">0.8815 (0.1677) </td><td align="center">−103.2537 </td><td align="center">210.5074 </td><td align="center">215.7376 </td></tr><tr class="table-tr"><td colspan="6"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Maximum likelihood parameter estimates (with (SD)) of the HN and HEP models for the life of fatigue fracture data.

Journal of Quality and Reliability Engineering

tab6

Table 6

Table 6: Statistical Inferences and Applications of the Half Exponential Power Distribution 