Graphical procedures and goodness-of-fit tests for the compound poisson-exponential distribution

ABSTRACT

The compound Poisson-exponential distribution is a basic model in risk analysis and stochastic hydrology. Graphical procedures for assessing this distribution are proposed which utilize the residuals from a regression involving the moment generating function. Plots furnished with a 95% simultaneous confidence band are constructed. The band and critical points of the equivalent goodness-of-fit test are found by utilizing asymptotic results and fitted regressions involving the supremum of the standardized residuals, the sample size, and the estimated Poisson mean. Simulation results indicate that the tests have good level stability and appreciable power against competing compound Poisson distributions of a mixed type.

KEYWORDS:

• Poisson-exponential distribution
• Cumulant generating function
• Empirical moment generating function
• Goodness-of-fit tests
• Graphical methods.

Mathematics Subject Classification:

• 62-09, 62F03, 60E10, 62-07