A New Goodness-of-Fit Test Based on the Laplace Statistic for a Large Class of NHPP Models

ABSTRACT

Nonhomogeneous Poisson processes (NHPP) provide many models for hardware and software reliability analysis. In order to get an appropriate NHPP model, goodness-of-Fit (GOF for short) tests have to be carried out. For the power-law processes, lots of GOF tests have been developed. For other NHPP models, only the Conditional Probability Integral Transformation (CPIT) test has been proposed. However, the CPIT test is less powerful and cannot be applied to some NHPP models. This article proposes a general GOF test based on the Laplace statistic for a large class of NHPP models with intensity functions of the form αλ(t, β). The simulation results show that this test is more powerful than CPIT test.     

A review of model selection procedures relevant to the weibull distribution

A number of goodness-of-fit and model selection procedures related to the Weibull distribution are reviewed. These procedures include probability plotting, correlation type goodness-of-fit tests, and chi-square goodness-of-fit tests. Also the Kolmogorow-Smirniv, Kuiper, and Cramer-Von Mises test statistics for completely specified hypothesis based on censored data are reviewed, and these test statistics based on complete samples for the unspecified parameters case are considered. Goodness-of-fit tests based on sample spacings, and a goodness-of-fit test for the Weibull process, is also discussed.

Model selection procedures for selecting between a Weibull and gamma model, a Weibull and lognormal model, and for selecting from among all three models are considered. Also tests of exponential versus Weibull and Weibull versus generalized gamma are mentioned.     

Coverage probabilities of nonparametric simultaneous confidence bands for a survival function

Simultaneous confidence bands provide a useful adjunct to the popular Kaplan–Meier product limit estimator for a survival function, particularly when results are displayed graphically. They allow an assessment of the magnitude of sampling errors and provide a graphical view of a formal goodness-of-fit test. In this paper we evaluate a modified version of Nair's (1981) simultaneous confidence bands. The modification is based on a logistic transformation of the Kaplan–Meier estimator. We show that the modified bands have some important practical advantages.     

A Symposium on Unemployment Statistics

Separate Poisson distributions were evaluated via several hypotheses tests for each of the 16 teams in the National Hockey League using 1973–74 goals for and goals against both home and away. After examining independence of goals for and goals against, they in turn were used to explain order of finish for the 16 teams. The results were quite surprising.     

A compound Rayleigh survival model and its application to randomly censored data

Received: May 5, 1999; revised version: June 15, 2000     

Normalized spacings and goodness-of-fit tests

This paper presents a number of goodness-of-fit tests based on normalized spacings. These tests can be used in the presence of unknown location and scale parameters. We considered the problems of testing for the normal, logistic and extreme-value distributions. An extensive Monte Carlo study is presented to compare the powers of some normality tests. Another Monte Carlo study on the powers of some extreme-value tests is also given. The power results show that our proposed tests are powerful against a wide range of alternatives