An overview of goodness-of-fit tests for the Poisson distribution

We develop two new classes of tests for the Weibull distribution based on Stein’s method. The proposed tests are applied in the full sample case as well as in the presence of random right censoring. We investigate the finite sample performance of the new tests using a comprehensive Monte Carlo study. In both the absence and presence of censoring, it is found that the newly proposed classes of tests outperform competing tests against the majority of the distributions considered. In the cases where censoring is present we consider various censoring distributions. Some remarks on the asymptotic properties of the proposed tests are included. We present another result of independent interest; a test initially proposed for use with full samples is amended to allow for testing for the Weibull distribution in the presence of censoring. The techniques developed in the paper are illustrated using two practical examples.

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“…( 2018 ), Allison et al. ( 2019 ) as well as Mijburgh and Visagie ( 2020 ). The bootstrap algorithm in Sect.…”

Section: Numerical Resultsmentioning

confidence: 96%

New classes of tests for the Weibull distribution using Stein’s method in the presence of random right censoring

2022

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“…To quantify this discrepancy, we employed goodness-of-fit tests for the Poisson distribution. Several such tests have been developed [ 21 ]. For their simplicity of implementation and interpretation, we used two test statistics, Z and T , based respectively on the first and second, and third and fourth, moments of the empirical distributions [ 21 , 22 ].…”

Section: Resultsmentioning

confidence: 99%

“…Several such tests have been developed [ 21 ]. For their simplicity of implementation and interpretation, we used two test statistics, Z and T , based respectively on the first and second, and third and fourth, moments of the empirical distributions [ 21 , 22 ]. As a brief reminder, the Poisson distribution has mean equal to variance and squared-skewness equal to excess kurtosis.…”

Section: Resultsmentioning

confidence: 99%

Statistical analysis reveals the onset of synchrony in sparse swarms of Photinus knulli fireflies

Sarfati

Gaudette

Cicero³

et al. 2022

J. R. Soc. Interface.

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Flash synchrony within firefly swarms is an elegant but elusive manifestation of collective animal behaviour. It has been observed, and sometimes demonstrated, in a few populations across the world, but exactly which species are capable of large-scale synchronization remains unclear, especially for low-density swarms. The underlying question which we address here is: how does one qualify a collective flashing display as synchronous, given that the only information available is the time and location of flashes? We propose different statistical approaches and apply them to high-resolution stereoscopic video recordings of the collective flashing of Photinus knulli fireflies, hence establishing the occurrence of synchrony in this species. These results substantiate detailed visual observations published in the early 1980s and made at the same experimental site: Peña Blanca Canyon, Coronado National Forest, AZ, USA. We also remark that P. knulli ’s collective flashing patterns mirror those observed in Photinus carolinus fireflies in the Eastern USA, consisting of synchronous flashes in periodic bursts with rapid accretion and quick decay.

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“…Sensor detection probabilities 1, 2, and 3 represent the detection probabilities of the concentration-measurement, ultrasonic, and combined gas-leak detectors, respectively. The Poisson distribution, a probability distribution based on the likelihood of certain events occurring within a specific time period [53][54][55][56], was applied to the combined detector model in our study. Here, 'events' refer to instances where smoke is undetected.…”

Section: Gas-leak Detection Probability Prediction Modelmentioning

confidence: 99%

Comparative Analysis of Ultrasonic and Traditional Gas-Leak Detection Systems in the Process Industries: A Monte Carlo Approach

Lee,

Kim,

Kim

et al. 2023

Processes

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Gas leaks can cause disasters at process sites, including fires and explosions, and thus, effective gas-leak detection systems are required. This study investigated the limitations of conventional detectors and introduced an innovative ultrasonic sensor-based approach for continuous monitoring. A new configuration for a stationary remote ultrasonic gas-leak monitoring system is proposed. The selected material was 1-Butene. The detection probability was assessed through a simulation based on a gas-leak scenario, detailing the selection criteria for leak sites and simulation conditions. Computational fluid-dynamics (CFD) simulations were used to evaluate the detection capability of the existing system, whereas Monte Carlo simulations were used to compare it with the proposed ultrasonic system. The CFD simulation was performed by setting the lower detection limit of the concentration-measurement-type gas detector to 600 ppm, and the leak-detection time was approximately 8.895 s. A Monte Carlo simulation accounting for wind direction showed that the existing system’s average detection probability was 3.41%. By integrating the existing and new systems, the detection probability increased by 96.58% and 3.92% compared with that using only the concentration-measurement and ultrasonic measurement methods, respectively. These rates provide valuable insights for future applications in oil refining and petrochemical industries.

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An overview of goodness-of-fit tests for the Poisson distribution

Cited by 9 publications

References 48 publications

New classes of tests for the Weibull distribution using Stein’s method in the presence of random right censoring

New classes of tests for the Weibull distribution using Stein’s method in the presence of random right censoring

Statistical analysis reveals the onset of synchrony in sparse swarms of Photinus knulli fireflies

Comparative Analysis of Ultrasonic and Traditional Gas-Leak Detection Systems in the Process Industries: A Monte Carlo Approach

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