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Conditionally on $\\pi=p$, its lifetime $\\Xi$ satisfies $$\n  \\mathbb P(\\Xi\\ge k\\mid \\pi=p)=p^{k^\\gamma},\n  \\, k\\in\\mathbb{N}_0, $$ where $\\gamma>0$. The distribution of $\\pi$ is assumed to have right-edge density $$\n  f_\\pi(u)\\sim (1-u)^{\\beta-1}\n  L\\left(\\frac1{1-u}\\right),\n  \\, u\\uparrow1, $$ where $\\beta>0$ and $L:(0,\\infty)\\to(0,\\infty)$ is a slowly varying function at infinity. 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Each particle has an independent survival parameter $\\pi\\in(0,1)$. Conditionally on $\\pi=p$, its lifetime $\\Xi$ satisfies $$\n  \\mathbb P(\\Xi\\ge k\\mid \\pi=p)=p^{k^\\gamma},\n  \\, k\\in\\mathbb{N}_0, $$ where $\\gamma>0$. The distribution of $\\pi$ is assumed to have right-edge density $$\n  f_\\pi(u)\\sim (1-u)^{\\beta-1}\n  L\\left(\\frac1{1-u}\\right),\n  \\, u\\uparrow1, $$ where $\\beta>0$ and $L:(0,\\infty)\\to(0,\\infty)$ is a slowly varying function at infinity. 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