&lt;b&gt;ON INTERVAL ESTIMATION OF THE POISSON PARAMETER &lt;/b&gt;&lt;b&gt;IN A ZERO-TRUNCATED POISSON DISTRIBUTION &lt;/b&gt;

Daidoji, Kasumi; Iwasaki, Manabu

doi:10.5183/jjscs.1103002_193

Cited by 3 publications

(11 citation statements)

References 18 publications

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“…Simulations were used to confirm the performance of the confidence interval. It was found that the coverage probabilities of the confidence interval proposed by Daidoji & Iwasaki (2012) were lower than the target probability in many cases, especially when the sample sizes were less than 50. Many techniques have been developed to estimate the functions of parameter in the distribution related to the Poisson model.…”

Section: Introductionmentioning

confidence: 99%

“…We know that confidence interval which has a high coverage probability will cover the true parameter value better than that has a low coverage probability. However, as noted in Daidoji & Iwasaki (2012) little papers on interval estimation for the ZTP distribution have been shown. The confidence interval introduced in that paper is also unsatisfactory in terms of coverage probability.…”

Section: Introductionmentioning

confidence: 99%

“…Papers related to parameter estimation in the Poisson distribution with missing zero have been discussed by Dahiya & Gross (1973), Johnson et al (2005), and Nasiri (2011;2015). For interval estimation, Daidoji & Iwasaki (2012) introduced a confidence interval for  in a ZTP distribution. They derived the likelihood function and estimated the variance of the maximum likelihood (ML) estimator for building the confidence interval using the Wald method.…”

Section: Introductionmentioning

confidence: 99%

“…-15 -The rest of this paper is organized as follows. In Section 2, the definition of the ZTP distribution and the confidence interval of Daidoji & Iwasaki (2012) for  are explained. We also derive the likelihood using the adjusted profile function method and introduce the novel confidence interval in Section 2.…”

Section: Introductionmentioning

confidence: 99%

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Confidence interval for the parameter of the zero-truncated Poisson distribution

Sangnawakij¹

2021

j.appsci

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This paper introduces a confidence interval for the parameter in a zero-truncated Poisson distribution. We adjust the profile likelihood method to construct this confidence interval by using a function of parameter as a nuisance. The performance of the proposed estimator is investigated through simulations, and compared with the conventional Wald confidence interval. From the results, the proposed estimator provides a good performance in terms of coverage probability in all cases in the study. It also has the short interval length. The practicality of our approach is confirmed by application to two real datasets, on a choleraepidemic and on mortality rates of infants on an estate.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Confidence interval for the parameter of the zero-truncated Poisson distribution

Sangnawakij¹

2021

j.appsci

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“…Lambert (1992) (Lee, Stevenson, Wang and Yau (2002), Lord, Washington and Ivan (2005)) (Böhning, Dietz and Schlattmann, 2000) (Paul, Jiang, Rai and Balassoriya, 2007) Gardner, Mulvey and Shaw (1995) Daidoji and Iwasaki (2012) ( (Dempster, Laird and Rubin, 1977) ω ω…”

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confidence: 99%

Statistical Inference for the Zero Modification Parameter in Zero-Modified Poisson Models

Daidoji¹,

Iwasaki²,

Yamashita³

2013

Kodo Keiryogaku

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For count data of rare events, a Poisson distribution is most frequently used to model the phenomenon under consideration. However, it is sometimes observed in various applications that the zero count is too many or too few than the count expected under the usual Poisson model. In such cases so-called zero-modified Poisson (ZMP) distributions would be fitted to the observed data. This paper discusses the performance of estimation procedures of the parameter involved in the ZMP distribution. First we attempt to clarify the meaning of the zero-modification parameter in the zero-deflated Poisson (ZDP) distribution in comparison to the zero-inflated Poisson (ZIP) distribution. After reviewing the maximum likelihood estimation procedures for the parameters of ZMP models, a simulation study is conducted to assess the performance of confidence intervals of the zero-modification parameter from the viewpoint of coverage probability. It is found that when sample size is small and the Poisson parameter is small, the performance of interval estimation is not so well. However, for the case of moderate and large sample sizes the coverage probabilities of the confidence intervals are almost equal to the nominal confidence coefficient.

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Bayesian Computation for the Parameters of a Zero-Inflated Cosine Geometric Distribution with Application to COVID-19 Pandemic Data

Junnumtuam¹,

Niwitpong²,

Niwitpong³

2023

Computer Modeling in Engineering &Amp; Sciences

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A new three-parameter discrete distribution called the zero-inflated cosine geometric (ZICG) distribution is proposed for the first time herein. It can be used to analyze over-dispersed count data with excess zeros. The basic statistical properties of the new distribution, such as the moment generating function, mean, and variance are presented. Furthermore, confidence intervals are constructed by using the Wald, Bayesian, and highest posterior density (HPD) methods to estimate the true confidence intervals for the parameters of the ZICG distribution. Their efficacies were investigated by using both simulation and real-world data comprising the number of daily COVID-19 positive cases at the Olympic Games in Tokyo 2020. The results show that the HPD interval performed better than the other methods in terms of coverage probability and average length in most cases studied.

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<b>ON INTERVAL ESTIMATION OF THE POISSON PARAMETER </b><b>IN A ZERO-TRUNCATED POISSON DISTRIBUTION </b>

Cited by 3 publications

References 18 publications

Confidence interval for the parameter of the zero-truncated Poisson distribution

Confidence interval for the parameter of the zero-truncated Poisson distribution

Statistical Inference for the Zero Modification Parameter in Zero-Modified Poisson Models

Bayesian Computation for the Parameters of a Zero-Inflated Cosine Geometric Distribution with Application to COVID-19 Pandemic Data

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