The Asymptotic Distribution of Maxima of Independent and Identically Distributed Sums of Correlated or Non-Identical Gamma Random Variables and its Applications
In this paper, we show that the asymptotic probability density function (pdf) of the maxima of n independent and identically distributed (i.i.d.) sums of independent non-identically (i.n.i.d.) distributed gamma random variables (RVs) is a Gumbel pdf using Extreme Value Theory (EVT). We will also sho...
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| Veröffentlicht in: | IEEE transactions on communications 2012-09, Vol.60 (9), p.2747-2758 |
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| container_title | IEEE transactions on communications |
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| creator | Kalyani, S. Karthik, R. M. |
| description | In this paper, we show that the asymptotic probability density function (pdf) of the maxima of n independent and identically distributed (i.i.d.) sums of independent non-identically (i.n.i.d.) distributed gamma random variables (RVs) is a Gumbel pdf using Extreme Value Theory (EVT). We will also show that the asymptotic pdf of the maxima of n i.i.d. sums of correlated gamma RVs is a Gumbel pdf. Some applications in wireless communication are discussed where the maxima of n i.i.d. sums of correlated gamma RVs and maxima of n i.i.d. sums of i.n.i.d. gamma RVs arise. We discuss the utility of our results in the context of these applications. |
| doi_str_mv | 10.1109/TCOMM.2012.071912.110311 |
| format | Article |
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We discuss the utility of our results in the context of these applications.</description><subject>Applied sciences</subject><subject>Confluent Lauricella functions</subject><subject>Exact sciences and technology</subject><subject>extreme value theory</subject><subject>Gumbel distribution</subject><subject>Multipath channels</subject><subject>OFDM</subject><subject>proportional fair scheduler</subject><subject>Rayleigh channels</subject><subject>Shape</subject><subject>Signal to noise ratio</subject><subject>Systems, networks and services of telecommunications</subject><subject>Telecommunications</subject><subject>Telecommunications and information theory</subject><subject>Teletraffic</subject><subject>Wireless communication</subject><issn>0090-6778</issn><issn>1558-0857</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpFkE1OwzAQhS0EEqVwAjbesEwZx24cL6sApVJLJShsI9txhFH-ZKcSvQ1HxWlQWdgzGr_35PkQwgRmhIC432XbzWYWA4lnwIkIJYwpIWdoQubzNIJ0zs_RBEBAlHCeXqIr778AgAGlE_Sz-zR44Q9117e91fjB-t5Zte9t2-C2xBv5bWs5dKumMJ0JV9Nj2RR4NXRWy6o6_LtMgd_2tR_0WeucqeQwah1-aZvo5MBLWYfQ1xDT1vhDOitVZfwx1vYeL7quCrrhD_4aXZSy8ubmr07R-9PjLnuO1tvlKlusI01B9JEiBaGcJAU3ihuhaZkoZbiIGaRAWaEo1VKXIFgKSpJU8NIwXUqiFYsLRugUpWOudq33zpR558Lm7pATyAfS-ZF0PpDOR9L5SDpY70ZrJ33YrnSy0daf_HESUItwpuh21FljzOk5iRlnNKW_UJGLbw</recordid><startdate>20120901</startdate><enddate>20120901</enddate><creator>Kalyani, S.</creator><creator>Karthik, R. 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M.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>IEEE transactions on communications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Kalyani, S.</au><au>Karthik, R. M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Asymptotic Distribution of Maxima of Independent and Identically Distributed Sums of Correlated or Non-Identical Gamma Random Variables and its Applications</atitle><jtitle>IEEE transactions on communications</jtitle><stitle>TCOMM</stitle><date>2012-09-01</date><risdate>2012</risdate><volume>60</volume><issue>9</issue><spage>2747</spage><epage>2758</epage><pages>2747-2758</pages><issn>0090-6778</issn><eissn>1558-0857</eissn><coden>IECMBT</coden><abstract>In this paper, we show that the asymptotic probability density function (pdf) of the maxima of n independent and identically distributed (i.i.d.) sums of independent non-identically (i.n.i.d.) distributed gamma random variables (RVs) is a Gumbel pdf using Extreme Value Theory (EVT). We will also show that the asymptotic pdf of the maxima of n i.i.d. sums of correlated gamma RVs is a Gumbel pdf. Some applications in wireless communication are discussed where the maxima of n i.i.d. sums of correlated gamma RVs and maxima of n i.i.d. sums of i.n.i.d. gamma RVs arise. We discuss the utility of our results in the context of these applications.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TCOMM.2012.071912.110311</doi><tpages>12</tpages></addata></record> |
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| language | eng |
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| source | IEEE Electronic Library (IEL) |
| subjects | Applied sciences Confluent Lauricella functions Exact sciences and technology extreme value theory Gumbel distribution Multipath channels OFDM proportional fair scheduler Rayleigh channels Shape Signal to noise ratio Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Teletraffic Wireless communication |
| title | The Asymptotic Distribution of Maxima of Independent and Identically Distributed Sums of Correlated or Non-Identical Gamma Random Variables and its Applications |
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