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CT Zhu
CT Zhu
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We know that $X\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$ and $Y\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$ then $X+Y\sim {\mathrm {Logistic}}(2\alpha ,\beta )$.

I am wondering, what will be $X+Y+Z$ like, if $Z\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$ also. And more generally what will be $\sum X_{i}$ be if $X_{i}\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$.

A practical example would be a device whose lifespan follows $X\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$. But the device can be repaired, instantaneously once failed, for $i$ times.

We know that $X\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$ and $Y\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$ then $X+Y\sim {\mathrm {Logistic}}(2\alpha ,\beta )$.

I am wondering, what will be $X+Y+Z$ like, if $Z\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$ also. And more generally what will be $\sum X_{i}$ be if $X_{i}\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$.

A practical example would be a device whose lifespan follows $X\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$. But the device can be repaired, instantaneously once failed, for $i$ times.

We know that $X\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$ and $Y\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$ then $X+Y\sim {\mathrm {Logistic}}(2\alpha ,\beta )$.

I am wondering, what will be $X+Y+Z$ like, if $Z\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$ also. And more generally what will $\sum X_{i}$ be if $X_{i}\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$.

A practical example would be a device whose lifespan follows $X\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$. But the device can be repaired, instantaneously once failed, for $i$ times.

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CT Zhu
CT Zhu
  • 328
  • 2
  • 9

Repairable system and the sum of GEV random variables

We know that $X\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$ and $Y\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$ then $X+Y\sim {\mathrm {Logistic}}(2\alpha ,\beta )$.

I am wondering, what will be $X+Y+Z$ like, if $Z\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$ also. And more generally what will be $\sum X_{i}$ be if $X_{i}\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$.

A practical example would be a device whose lifespan follows $X\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$. But the device can be repaired, instantaneously once failed, for $i$ times.