Generalized Cumulative Residual Entropy for Distributions with Unrestricted Supports

<table>Ten estimates of (a) <svg height="14.7125" id="M151" style="vertical-align:-3.22282pt" version="1.1" viewbox="0 0 36.525002 14.7125" width="36.525002" xmlns="http://www.w3.org/2000/svg">
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<tspan style="font-size: 12.50px; " x="0" y="0">𝑓</tspan>
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<text transform="matrix(1,0,0,-1,-65.01,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑆</tspan>
</text>
<text transform="matrix(1,0,0,-1,-58.21,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">𝛼</tspan>
<tspan style="font-size: 12.50px; " x="11.202688" y="0">)</tspan>
</text>
</g>
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</svg> and (b) <svg height="14.725" id="M152" style="vertical-align:-3.24037pt" version="1.1" viewbox="0 0 36.862499 14.725" width="36.862499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.725)">
<g transform="translate(72,-60.22)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑓</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.01,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝐶</tspan>
</text>
<text transform="matrix(1,0,0,-1,-57.94,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">𝛼</tspan>
<tspan style="font-size: 12.50px; " x="11.215191" y="0">)</tspan>
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</g>
</g>
</svg>.
Dotted line: mean estimate averaged from 200 realizations.</table>

Journal of Electrical and Computer Engineering

fig1

Figure 1

Figure 1: Generalized Cumulative Residual Entropy for Distributions with Unrestricted Supports 