Monte Carlo exact goodness-of-fit tests for nonhomogeneous Poisson processes

Lindqvist, Bo Henry; Rannestad, Bjarte

doi:10.1002/asmb.841

Cited by 6 publications

(4 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, for the accepted samples we conclude from () and () that the resulting conditional sample is

\hat{x} = (t \frac{u_{1}}{\sum_{i = 1}^{n} u_{i}}, t \frac{u_{2}}{\sum_{i = 1}^{n} u_{i}}, \dots, t \frac{u_{n}}{\sum_{i = 1}^{n} u_{i}}) .

It can be verified that () is needed in addition to () in order to have samples from the correct conditional distribution. Still the algorithm is very simple, and simpler than the corresponding algorithms of Lindqvist and Taraldsen (2005) and Lindqvist and Rannestad (2011) that were mentioned above.…”

Section: Examplesmentioning

confidence: 95%

See 1 more Smart Citation

Conditional Monte Carlo revisited

Lindqvist

Erlemann

Taraldsen

2021

Scandinavian J Statistics

Self Cite

View full text Add to dashboard Cite

Conditional Monte Carlo refers to sampling from the conditional distribution of a random vector X given the value T(X) = t for a function T(X). Classical conditional Monte Carlo methods were designed for estimating conditional expectations of functions 𝜙(X) by sampling from unconditional distributions obtained by certain weighting schemes. The basic ingredients were the use of importance sampling and change of variables.In the present paper we reformulate the problem by introducing an artificial parametric model in which X is a pivotal quantity, and next representing the conditional distribution of X given T(X) = t within this new model. The approach is illustrated by several examples, including a short simulation study and an application to goodness-of-fit testing of real data. The connection to a related approach based on sufficient statistics is briefly discussed.

show abstract

“…Finally, for the accepted samples we conclude from () and () that the resulting conditional sample is

\hat{x} = (t \frac{u_{1}}{\sum_{i = 1}^{n} u_{i}}, t \frac{u_{2}}{\sum_{i = 1}^{n} u_{i}}, \dots, t \frac{u_{n}}{\sum_{i = 1}^{n} u_{i}}) .

Section: Examplesmentioning

confidence: 95%

“…The resulting method is, however, surprisingly complicated. A Gibbs sampling method was devised by Lindqvist and Rannestad (2011), apparently being much quicker than the former method, and much easier to implement.…”

Section: Examplesmentioning

confidence: 99%

Conditional Monte Carlo revisited

Lindqvist

Erlemann

Taraldsen

2021

Scandinavian J Statistics

Self Cite

View full text Add to dashboard Cite

show abstract

“…For minimal repairs, GoF tests for NHPPs have to be used. Such tests have been proposed for instance by Park and Kim, 14 Gaudoin, 15 Crétois et al., 16 Zhao and Wang 17 and Lindqvist and Rannestad 18 among others.…”

Section: Introductionmentioning

confidence: 99%

“…Reviews on GoF tests for these distributions are, respectively, presented in Henze and Meintanis 12 and Krit et al 13 For minimal repairs, GoF tests for NHPPs have to be used. Such tests have been proposed for instance by Park and Kim, 14 Gaudoin, 15 Crétois et al, 16 Zhao and Wang 17 and Lindqvist and Rannestad 18 among others.…”

Section: Introductionmentioning

confidence: 99%

Imperfect repair models: Sequential goodness‐of‐fit testing based on predictive performances

El‐Aroui

Gaudoin

2022

Quality & Reliability Eng

View full text Add to dashboard Cite

Imperfect repair (IR) modelling has attracted a lot of attention during the last decades. To assess and predict repairable systems' reliability, analysts have to choose among a plethora of models: renewal processes, non-homogeneous Poisson processes (NHPPs), Brown-Proschan, Kijima, ARA, ARI, Quasi-Renewal (QR), Trend-Renewal and so forth. Choosing an appropriate model for a given failures, dataset is an important practical issue. The fit of an IR model can be assessed using goodness-of-fit (GoF) tests but very few have been proposed and a good fit to past data does not guarantee good reliability predictions. This work proposes general GoF tests for IR models based on sequential (or on-line) assessment of times-to-failures forecasts. The suggested predictive-sequential (or prequential) GoF tests have a low computational complexity and a common test statistic for several IR models. These tests have been proved to be asymptotically distribution-free (ADF) for renewal and power-law processes (PLPs). Our numerical simulations and preliminary theoretical results highly suggest that this ADF property still holds for several other IR models. The prequential tests are much easier to use than the already known bootstrap tests, and a simulation study shows that they are also slightly more powerful. The simulations also show that the prequential tests are powerful to identify classes of similar appropriate models but are much less powerful to distinguish models belonging to the same class. A comparison of MTTF estimates show that models from the same class give close reliability predictions and that the tests are able to reject models which would yield to dramatic errors in reliability predictions.

show abstract

Goodness-of-fit tests in the multi-state Markov model

Kong

2017

Reliability Engineering & System Safety

View full text Add to dashboard Cite

Monte Carlo exact goodness-of-fit tests for nonhomogeneous Poisson processes

Cited by 6 publications

References 21 publications

Conditional Monte Carlo revisited

Conditional Monte Carlo revisited

Imperfect repair models: Sequential goodness‐of‐fit testing based on predictive performances

Goodness-of-fit tests in the multi-state Markov model

Contact Info

Product

Resources

About