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

Sangnawakij, Patarawan

doi:10.14416/j.appsci.2021.02.002

Cited by 4 publications

(2 citation statements)

References 16 publications

(25 reference statements)

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“…The probability model of PS distribution can be utilized to analyze data that contains both zero and positive values with low occurrence probabilities within a predefined time or area range (Sangnawakij, 2021). However, probability models can become truncated when a range of possible values for the variables is either disregarded or impossible to observe.…”

Section:  +mentioning

confidence: 99%

"Confidence Intervals using Bootstrap Methods for the Parameter of the zero-truncated Poisson-Shanker Distribution and their Application"

Kaskasamkul,

Panichkitkosolkul

2023

JASET.KMUTNB

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Count data with non-zero values can be modeled using the zero-truncated Poisson-Shanker distribution in a variety of situations. However, the confidence interval estimation for the parameter has not yet been examined. In this paper, confidence interval estimation based on percentile bootstrap, simple bootstrap, biased-corrected and accelerated bootstrap, and bootstrap-t methods was examined in terms of coverage probability, lower and upper error rate, and average interval length through Monte Carlo simulation. The simulation results indicate that attaining the nominal confidence level using the bootstrap methods were not possible for small sample sizes, regardless of the other settings. Furthermore, in cases when the sample size was large, there was no significant difference observed in the performances of the all methods. In several scenarios, the bias-corrected and accelerated bootstrap method exhibited superior performance compared to the other methods. Last, we used the bootstrap methods to calculate the confidence interval for the parameter of the zero-truncated Poisson-Shanker distribution via three numerical examples, and the results of these examples matched those from the simulation study.

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Section:  +mentioning

confidence: 99%

"Confidence Intervals using Bootstrap Methods for the Parameter of the zero-truncated Poisson-Shanker Distribution and their Application"

Kaskasamkul,

Panichkitkosolkul

2023

JASET.KMUTNB

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“…where e is a constant approximately equal to 2.71828 and  is the mean number of events within a given interval of time or space. This probability model can be used to analyze data containing zeros and positive values that have low occurrence probabilities within a predefined time or area range (Sangnawakij, 2021). However, probability models can become truncated when a range of possible values for the variables is either disregarded or impossible to observe.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric Bootstrap Confidence Intervals for the Population Mean of a Zero-Truncated Poisson-Lindley Distribution and Their Application

Suriyakat,

Panichkitkosolkul

2023

JCST

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Recently, the zero-truncated Poisson-Lindley distribution has been proposed for studying count data containing non-zero values. However, the nonparametric bootstrap confidence interval estimation of the population mean has not yet been studied. In this study, confidence interval estimation based on percentile, simple, and biased-corrected bootstrap methods was compared in terms of coverage probability and average interval length via Monte Carlo simulation. The true values of parameter () were set as 0.25, 0.5, 1, 1.5, and 2, and the population means are approximate 7.7586, 4.0909, 2.4000, 1.8817, and 1.6364, respectively. The bootstrap samples (=1,000) of size were generated from the original sample, and each simulation was repeated 1,000 times. The results indicate that attaining the nominal confidence level using the bootstrap confidence intervals was impossible for small sample sizes regardless of the other settings. Moreover, when the sample size was large, the performance of the nonparametric bootstrap confidence intervals was not substantially different. Overall, the bias-corrected bootstrap confidence interval outperformed the others, even for small sample sizes. Last, the nonparametric bootstrap confidence intervals were used to calculate the confidence interval for the population mean of the zero-truncated Poisson-Lindley distribution via two numerical examples, the results of which match those from the simulation study.

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On the Normal Approximations to the Method of Moments Point Estimators of the Parameter and Mean of the Zero-Truncated Poisson Distribution

Ngamkham,

Panta

2023

Lobachevskii J Math

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

Cited by 4 publications

References 16 publications

"Confidence Intervals using Bootstrap Methods for the Parameter of the zero-truncated Poisson-Shanker Distribution and their Application"

"Confidence Intervals using Bootstrap Methods for the Parameter of the zero-truncated Poisson-Shanker Distribution and their Application"

Nonparametric Bootstrap Confidence Intervals for the Population Mean of a Zero-Truncated Poisson-Lindley Distribution and Their Application

On the Normal Approximations to the Method of Moments Point Estimators of the Parameter and Mean of the Zero-Truncated Poisson Distribution

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