Abstract
In this paper, we show that the conjecture, made by Samanthi et al. (2016), on the ordering of Gini indexes of multivariate normal risks with respect to the strength of dependence, is not true. By using the positive semi-definite ordering of covariance matrices, we can obtain the usual stochastic order of the Gini indexes for multivariate normal risks. This can be generalized to multivariate elliptical risks. We also investigate the monotonicity of the Gini indexes in the usual stochastic order when the covariance (dispersion, resp.) matrices of multivariate normal (elliptical, resp) risks increase componentwise. In addition, we derive a large deviation result for the Gini indexes of multivariate normal risks.
| Original language | English |
|---|---|
| Pages (from-to) | 151-158 |
| Number of pages | 8 |
| Journal | Insurance: Mathematics and Economics |
| Volume | 88 |
| DOIs | |
| Publication status | Published - 2019 Sept |
Bibliographical note
Funding Information:We are grateful to the reviewer for valuable comments and suggestions, which greatly improved this paper. B. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) ( NRF-2017R1A2B4012676 ). J. Kim’s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2017R1D1A1B03029542 ).
Publisher Copyright:
© 2019 Elsevier B.V.
Keywords
- Elliptical distribution
- Gini index
- Large deviation
- Positive semi-definite
- Usual stochastic order
ASJC Scopus subject areas
- Statistics and Probability
- Economics and Econometrics
- Statistics, Probability and Uncertainty