An Example of a Heavy Tailed Distribution
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| Natura: | Artículo científico |
| Lingua: | en |
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Escuela Regional de Matemáticas
2005
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| _version_ | 1876461133125124096 |
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| author | Norman Giraldo Gómez |
| author_facet | Norman Giraldo Gómez |
| contents | An Example of a Heavy Tailed Distribution Norman Giraldo Gómez Física, Astronomía y Matemáticas Regular variation probability of ruin heavy tailed distributions subexponential distributions decreasing hazard rate function We study some properties of the distribution function of a random variable of the form X=CD, where C and D are independent random variables. We assume that C is absolutely continuous and limited to afinite interval, such that its probability density function has definite limits at the endpoints of the interval and D is exponentially distributed. We show that the tail function ¯F(.):=1−F(·)is of regular variation and that the distribution function F is asymptotically equivalent to a log-gamma distribution. Then F can be considered as a heavy tailed distribution. It is also shown that it is contained is an special subclass of the subexponential distributions. 2005 artículo científico 0120-6788 https://www.redalyc.org/articulo.oa?id=46800105 en http://www.redalyc.org/revista.oa?id=468 Matemáticas: Enseñanza Universitaria application/pdf Escuela Regional de Matemáticas Matemáticas: Enseñanza Universitaria (Colombia) Num.1 Vol.XIII |
| format | Artículo científico |
| id | redalyc_46800105 |
| institution | Redalyc |
| language | en |
| publishDate | 2005 |
| publisher | Escuela Regional de Matemáticas |
| spellingShingle | An Example of a Heavy Tailed Distribution Norman Giraldo Gómez Física, Astronomía y Matemáticas Regular variation probability of ruin heavy tailed distributions subexponential distributions decreasing hazard rate function An Example of a Heavy Tailed Distribution Norman Giraldo Gómez Física, Astronomía y Matemáticas Regular variation probability of ruin heavy tailed distributions subexponential distributions decreasing hazard rate function We study some properties of the distribution function of a random variable of the form X=CD, where C and D are independent random variables. We assume that C is absolutely continuous and limited to afinite interval, such that its probability density function has definite limits at the endpoints of the interval and D is exponentially distributed. We show that the tail function ¯F(.):=1−F(·)is of regular variation and that the distribution function F is asymptotically equivalent to a log-gamma distribution. Then F can be considered as a heavy tailed distribution. It is also shown that it is contained is an special subclass of the subexponential distributions. 2005 artículo científico 0120-6788 https://www.redalyc.org/articulo.oa?id=46800105 en http://www.redalyc.org/revista.oa?id=468 Matemáticas: Enseñanza Universitaria application/pdf Escuela Regional de Matemáticas Matemáticas: Enseñanza Universitaria (Colombia) Num.1 Vol.XIII |
| title | An Example of a Heavy Tailed Distribution |
| topic | Física, Astronomía y Matemáticas Regular variation probability of ruin heavy tailed distributions subexponential distributions decreasing hazard rate function |
| url | https://www.redalyc.org/articulo.oa?id=46800105 |