scholarly journals Asymptotic results for linear combinations of spacings generated by i.i.d. exponential random variables

Metrika ◽  
2022 ◽  
Author(s):  
Camilla Calì ◽  
Maria Longobardi ◽  
Claudio Macci ◽  
Barbara Pacchiarotti
Keyword(s):  
Random Variables ◽  
Asymptotic Results ◽  
Linear Combinations ◽  
Exponential Random Variables

Asymptotic results for weighted means of linear combinations of independent Poisson random variables

Stochastics ◽  
2019 ◽  
Vol 92 (4) ◽  
pp. 497-518
Author(s):  
Rita Giuliano ◽  
Claudio Macci ◽  
Barbara Pacchiarotti
Keyword(s):  
Random Variables ◽  
Asymptotic Results ◽  
Linear Combinations ◽  
Weighted Means

scholarly journals Some inequalities of linear combinations of independent random variables: II

Bernoulli ◽  
2013 ◽  
Vol 19 (5A) ◽  
pp. 1776-1789 ◽  
Author(s):  
Xiaoqing Pan ◽  
Maochao Xu ◽  
Taizhong Hu
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Linear Combinations

scholarly journals SOME UNIFIED RESULTS ON COMPARING LINEAR COMBINATIONS OF INDEPENDENT GAMMA RANDOM VARIABLES

2012 ◽  
Vol 26 (3) ◽  
pp. 393-404 ◽  
Author(s):  
Subhash Kochar ◽  
Maochao Xu
Keyword(s):  
Random Variables ◽  
Stochastic Orders ◽  
Sufficient Condition ◽  
Linear Combinations

In this paper, a new sufficient condition for comparing linear combinations of independent gamma random variables according to star ordering is given. This unifies some of the newly proved results on this problem. Equivalent characterizations between various stochastic orders are established by utilizing the new condition. The main results in this paper generalize and unify several results in the literature including those of Amiri, Khaledi, and Samaniego [2], Zhao [18], and Kochar and Xu [9].

scholarly journals Distribution of Minimal Path Lengths when Edge Lengths are Independent Heterogeneous Exponential Random Variables

2012 ◽  
Vol 49 (3) ◽  
pp. 895-900
Author(s):  
Sheldon M. Ross
Keyword(s):  
Joint Distribution ◽  
Shortest Paths ◽  
Random Variables ◽  
Simulated Data ◽  
Minimal Path ◽  
Exponential Random Variables ◽  
Path Lengths

We find the joint distribution of the lengths of the shortest paths from a specified node to all other nodes in a network in which the edge lengths are assumed to be independent heterogeneous exponential random variables. We also give an efficient way to simulate these lengths that requires only one generated exponential per node, as well as efficient procedures to use the simulated data to estimate quantities of the joint distribution.

Marshall–Olkin distributions, subordinators, efficient simulation, and applications to credit risk

2017 ◽  
Vol 49 (2) ◽  
pp. 481-514 ◽  
Author(s):  
Yunpeng Sun ◽  
Rafael Mendoza-Arriaga ◽  
Vadim Linetsky
Keyword(s):  
Credit Risk ◽  
Random Variables ◽  
Exponential Distributions ◽  
Efficient Simulation ◽  
Failure Times ◽  
Independent Unit ◽  
Exponential Random Variables ◽  
Credit Portfolio ◽  
Multivariate Exponential ◽  
Passage Times

Abstract In the paper we present a novel construction of Marshall–Olkin (MO) multivariate exponential distributions of failure times as distributions of the first-passage times of the coordinates of multidimensional Lévy subordinator processes above independent unit-mean exponential random variables. A time-inhomogeneous version is also given that replaces Lévy subordinators with additive subordinators. An attractive feature of MO distributions for applications, such as to portfolio credit risk, is its singular component that yields positive probabilities of simultaneous defaults of multiple obligors, capturing the default clustering phenomenon. The drawback of the original MO fatal shock construction of MO distributions is that it requires one to simulate 2n-1 independent exponential random variables. In practice, the dimensionality is typically on the order of hundreds or thousands of obligors in a large credit portfolio, rendering the MO fatal shock construction infeasible to simulate. The subordinator construction reduces the problem of simulating a rich subclass of MO distributions to simulating an n-dimensional subordinator. When one works with the class of subordinators constructed from independent one-dimensional subordinators with known transition distributions, such as gamma and inverse Gaussian, or their Sato versions in the additive case, the simulation effort is linear in n. To illustrate, we present a simulation of 100,000 samples of a credit portfolio with 1,000 obligors that takes less than 18 seconds on a PC.

On the Sequential Detection Problem

1989 ◽  
Vol 38 (3-4) ◽  
pp. 129-146
Author(s):  
Uttam Bandyopadhyay
Keyword(s):  
Infinite Sequence ◽  
Random Variables ◽  
Stopping Rule ◽  
Independent Random Variables ◽  
Sequential Detection ◽  
Detection Problem ◽  
Asymptotic Results ◽  
Rule Based ◽  
Unknown Point ◽  
Cumulative Sums

In this paper, for an infinite sequence of independent random variables, we have considered the problem of estimation of an unknown point ( q) where a change in the distribution of the random variables occurs. Attaching suitable scores for the observed values. of the random variables, a stopping rule based on the cumulative sums of these scores has been proposed. Some asymptotic results useful for studying the performance of the proposed procedure havo beon obtained.

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