Article2003

Tests for an Epidemic Change in a Sequence of Exponentially Distributed Random Variables

15 citations0/0 files storedBiometrical Journal

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Advanced Statistical Process Monitoring Probability and Statistical Research Statistical Distribution Estimation and Applications

Abstract

Abstract Consider a sequence of independent exponential random variables that is susceptible to a change in the means. We would like to test whether the means have been subjected to an epidemic change after an unknown point, for an unknown duration in the sequence. The likelihood ratio statistic and a likelihood ratio type statistic are derived. The distribution theories and related properties of the test statistics are discussed. Percentage points and powers of the tests are tabulated for selected values of the parameters. The powers of these two tests are then compared to the two statistics proposed by Aly and Bouzar. The tests are applied to find epidemic changes in the set of Stanford heart transplant data and air traffic arrival data.

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References

1997Testing and Locating Variance Changepoints with Application to Stock Prices 2000Parametric Statistical Change Point Analysis 1966Test Procedures for Possible Changes in Parameters of Statistical Distributions Occurring at Unknown Time Points 1986Likelihood Ratio Tests for a Change in the Multivariate Normal Mean 1988Confidence Sets in Change-Point Problems 1985The cusum test of homogeneity with an application in spontaneous abortion epidemiology 1993Tests for Change-Points with Epidemic Alternatives 1990Asymptotic Distributions of Maximum Likelihood Tests for Change in the Mean

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2015Empirical likelihood test in a posteriori change-point nonlinear model 2016Change-point analysis with bathtub shape for the exponential distribution 2022Change point analysis for weighted exponential distribution

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