Hello,(adsbygoogle = window.adsbygoogle || []).push({});

Suppose we have the following set of independent and identically distributed exponential random variables: [tex]\gamma_1,\,\gamma_2,\ldots ,\,\gamma_N[/tex]. If we arrange them in ascending order we get the following order statistics: [tex]\gamma^{(1)}\leq\gamma^{(2)}\leq\cdots\leq\gamma^{(N)}[/tex].

I need to find the moment generating function (MGF) of the highest order statistics, i.e.: [tex]\mathcal{M}_{\gamma^{(N)}}(s)=E_{\gamma^{(N)}}[\text{e}^{s\,\gamma}][/tex] in terms of the MGFs of the exponential RVs. Is there any way to connect these MGFs?

Thanks in advance

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# The MGF of Order Statistics

Loading...

Similar Threads - Order Statistics | Date |
---|---|

A What is first and Second order Dependence? | Dec 3, 2016 |

CDF and PDF of order statistics | May 28, 2012 |

Extreme value theory and limiting distributions for i.i.d. order statistics | Jan 10, 2012 |

Poisson counting process & order statistics | Oct 13, 2009 |

Order Statistics PDF | Oct 3, 2009 |

**Physics Forums - The Fusion of Science and Community**