TY - GEN
T1 - The mean of Marshall–Olkin-dependent exponential random variables
AU - Fernández, Lexuri
AU - Mai, Jan Frederik
AU - Scherer, Matthias
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2015.
PY - 2015
Y1 - 2015
N2 - The probability distribution of (Formula Presented.), where the vector (Formula Presented.) is distributed according to the Marshall–Olkin law, is investigated. Closed-form solutions are derived in the general bivariate case and for d ∈ {2, 3, 4} in the exchangeable subfamily. Our computations can, in principle, be extended to higher dimensions, which, however, becomes cumbersome due to the large number of involved parameters. For the Marshall–Olkin distributions with conditionally independent and identically distributed components, however, the limiting distribution of Sd/d is identified as d tends to infinity. This resultmight serve as a convenient approximation in high-dimensional situations. Possible fields of application for the presented results are reliability theory, insurance, and credit-risk modeling.
AB - The probability distribution of (Formula Presented.), where the vector (Formula Presented.) is distributed according to the Marshall–Olkin law, is investigated. Closed-form solutions are derived in the general bivariate case and for d ∈ {2, 3, 4} in the exchangeable subfamily. Our computations can, in principle, be extended to higher dimensions, which, however, becomes cumbersome due to the large number of involved parameters. For the Marshall–Olkin distributions with conditionally independent and identically distributed components, however, the limiting distribution of Sd/d is identified as d tends to infinity. This resultmight serve as a convenient approximation in high-dimensional situations. Possible fields of application for the presented results are reliability theory, insurance, and credit-risk modeling.
UR - http://www.scopus.com/inward/record.url?scp=84947590901&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-19039-6_3
DO - 10.1007/978-3-319-19039-6_3
M3 - Conference contribution
AN - SCOPUS:84947590901
SN - 9783319190389
T3 - Springer Proceedings in Mathematics and Statistics
SP - 33
EP - 50
BT - Marshall–Olkin Distributions - Advances in Theory and Applications
A2 - Durante, Fabrizio
A2 - Cherubini, Umberto
A2 - Mulinacci, Sabrina
PB - Springer New York LLC
T2 - International conference on Marshall-Olkin Distributions - Advances in Theory and Applications, 2013
Y2 - 2 October 2013 through 3 October 2013
ER -