Degenerate-Generalized Likelihood Ratio Test for One-Sided Composite Hypotheses

<table>Comparison of ESS curves under the SPRT, the 2-SPRT, and the DGLRT for Case <a href="https://static.hindawi.com/articles/mpe/volume-2012/538342/figures/#casee2">2</a>: <svg height="14.9375" id="M183" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 52.712502 14.9375" width="52.712502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.9375)">
<g transform="translate(72,-60.05)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜃</tspan>
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<text transform="matrix(1,0,0,-1,-65.9,60.22)">
<tspan style="font-size: 8.75px; " x="0" y="0">0</tspan>
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<text transform="matrix(1,0,0,-1,-57.55,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="18.279387" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="21.405136" y="0">5</tspan>
</text>
</g>
</g>
</svg> and <svg height="14.6" id="M184" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 40.987499 14.6" width="40.987499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜃</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.9,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
<text transform="matrix(1,0,0,-1,-57.55,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">2</tspan>
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</g>
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</svg> for the exponential distribution with mean <svg height="10.9125" id="M185" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 20.475 10.9125" width="20.475" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="9.727334" y="0">𝜃</tspan>
</text>
</g>
</g>
</svg>.</table>

Mathematical Problems in Engineering

fig2

Figure 2

Figure 2: Degenerate-Generalized Likelihood Ratio Test for One-Sided Composite Hypotheses 