Weak limit of the geometric sum of independent but not identically distributed random variables
AA Toda - arXiv preprint arXiv:1111.1786, 2011 - arxiv.org
arXiv preprint arXiv:1111.1786, 2011•arxiv.org
We show that when $\set {X_j} $ is a sequence of independent (but not necessarily
identically distributed) random variables which satisfies a condition similar to the Lindeberg
condition, the properly normalized geometric sum $\sum_ {j= 1}^{\nu_p} X_j $(where $\nu_p
$ is a geometric random variable with mean $1/p $) converges in distribution to a Laplace
distribution as $ p\to 0$. The same conclusion holds for the multivariate case. This theorem
provides a reason for the ubiquity of the double power law in economic and financial data.
identically distributed) random variables which satisfies a condition similar to the Lindeberg
condition, the properly normalized geometric sum $\sum_ {j= 1}^{\nu_p} X_j $(where $\nu_p
$ is a geometric random variable with mean $1/p $) converges in distribution to a Laplace
distribution as $ p\to 0$. The same conclusion holds for the multivariate case. This theorem
provides a reason for the ubiquity of the double power law in economic and financial data.
We show that when $\set{X_j}$ is a sequence of independent (but not necessarily identically distributed) random variables which satisfies a condition similar to the Lindeberg condition, the properly normalized geometric sum (where is a geometric random variable with mean ) converges in distribution to a Laplace distribution as . The same conclusion holds for the multivariate case. This theorem provides a reason for the ubiquity of the double power law in economic and financial data.
arxiv.org
以上显示的是最相近的搜索结果。 查看全部搜索结果