论文标题
在总和和至上之间的吸引力领域产生的密度：$α$ - sun运算符
On the Density arising from the Domain of Attraction between Sum and Supremum: the $α$-Sun operator
论文作者
论文摘要
我们探索密度函数$ h（x;γ，α）$，$ x \ in（0，\ infty）$，$γ> 0 $，$ 0 <α<1 $ $ x \ $ x \ $ x \ $ x <1 $ $ x \ $ x <1 $ $ x \ $ x \ $ x <1 $ $ x \ $ x <1 $ $ x \ $ x \ $ x \ $ x <1 $。参数$α$控制了这两种情况之间的插值，而$γ$参数是从中汲取基础随机变量的极值分布的类型。对于$α= 0 $，fréchet密度适用，而对于$α= 1 $，我们确定了特定的fox H功能，这是高几何函数的自然扩展到分数计算的领域。相比之下，中间$α$出现了一个全新的功能，这不是迄今为止所考虑的超几何函数的扩展之一。我们得出后一个函数的串联，积分和持续的分数表示。
We explore the analytic properties of the density function $ h(x;γ,α) $, $ x \in (0,\infty) $, $ γ> 0 $, $ 0 < α< 1 $ which arises from the domain of attraction problem for a statistic interpolating between the supremum and sum of random variables. The parameter $ α$ controls the interpolation between these two cases, while $ γ$ parametrises the type of extreme value distribution from which the underlying random variables are drawn from. For $ α= 0 $ the Fréchet density applies, whereas for $ α= 1 $ we identify a particular Fox H-function, which are a natural extension of hypergeometric functions into the realm of fractional calculus. In contrast for intermediate $ α$ an entirely new function appears, which is not one of the extensions to the hypergeometric function considered to date. We derive series, integral and continued fraction representations of this latter function.
