Estimating tail probabilities in queues via extremal statistics

2000 ◽  
pp. 135-158 ◽  
Author(s):  
P. Glynn ◽  
A. Zeevi
Keyword(s):  
Tail Probabilities

scholarly journals Multivariate Tail Probabilities: Predicting Regional Pertussis Cases in Washington State

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 675
Author(s):  
Xuze Zhang ◽  
Saumyadipta Pyne ◽  
Benjamin Kedem
Keyword(s):  
Disease Modeling ◽  
Empirical Distribution ◽  
Density Ratio ◽  
Washington State ◽  
Ratio Model ◽  
Multiple Sources ◽  
Tail Probabilities ◽  
Data Set ◽  
Density Ratio Model ◽  
Regional Prediction

In disease modeling, a key statistical problem is the estimation of lower and upper tail probabilities of health events from given data sets of small size and limited range. Assuming such constraints, we describe a computational framework for the systematic fusion of observations from multiple sources to compute tail probabilities that could not be obtained otherwise due to a lack of lower or upper tail data. The estimation of multivariate lower and upper tail probabilities from a given small reference data set that lacks complete information about such tail data is addressed in terms of pertussis case count data. Fusion of data from multiple sources in conjunction with the density ratio model is used to give probability estimates that are non-obtainable from the empirical distribution. Based on a density ratio model with variable tilts, we first present a univariate fit and, subsequently, improve it with a multivariate extension. In the multivariate analysis, we selected the best model in terms of the Akaike Information Criterion (AIC). Regional prediction, in Washington state, of the number of pertussis cases is approached by providing joint probabilities using fused data from several relatively small samples following the selected density ratio model. The model is validated by a graphical goodness-of-fit plot comparing the estimated reference distribution obtained from the fused data with that of the empirical distribution obtained from the reference sample only.

scholarly journals Efficient simulation of tail probabilities of sums of correlated lognormals

2009 ◽  
Vol 189 (1) ◽  
pp. 5-23 ◽  
Author(s):  
Søren Asmussen ◽  
José Blanchet ◽  
Sandeep Juneja ◽  
Leonardo Rojas-Nandayapa
Keyword(s):  
Tail Probabilities ◽  
Efficient Simulation
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