Truncated Power-Normal Distribution with Application to Non-Negative Measurements

Castillo, Nabor O.; Gallardo, Diego I.; Bolfarine, Heleno; Gómez, Héctor W.

doi:10.3390/e20060433

Cited by 8 publications

(4 citation statements)

References 31 publications

(33 reference statements)

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“…Definition 2 is mainly due to the authors of reference [24], and it has been applied in industry [25]. The normalization of probability on interval was verified independently after Definition 2.…”

Section: Intervals With Symmetric Truncated Normal Density Functionmentioning

confidence: 99%

Reasoning Method Based on Intervals with Symmetric Truncated Normal Density

Hou

Liu

et al. 2021

Symmetry

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Error parameters are inevitable in systems. In formal verification, previous reasoning methods seldom considered the probability information of errors. In this article, errors are described as symmetric truncated normal intervals consisting of the intervals and symmetric truncated normal probability density. Furthermore, we also rigorously prove lemmas and a theorem to partially simplify the calculation process of truncated normal intervals and independently verify the formulas of variance and expectation of symmetric truncated interval given by some scholars. The mathematical derivation process or verification codes are provided for most of the key formulas in this article. Hence, we propose a new reasoning method that combines the probability information of errors with the previous statistical reasoning methods. Finally, an engineering example of the reasoning verification of train acceleration is provided. After simulating the large-scale cases, it is shown that the simulation results are consistent with the theoretical reasoning results. This method needs more calculation, while it is more effective in detecting non-error’s fault factors than other error reasoning methods.

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Section: Intervals With Symmetric Truncated Normal Density Functionmentioning

confidence: 99%

Reasoning Method Based on Intervals with Symmetric Truncated Normal Density

Hou

Liu

et al. 2021

Symmetry

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show abstract

“…Ref. [15] studied a truncated power-normal distribution that has the truncation point of zero. They studied the probabilistic properties along with the maximum likelihood and moments estimation methods.…”

Section: Introductionmentioning

confidence: 99%

Inference for the Process Performance Index of Products on the Basis of Power-Normal Distribution

et al. 2021

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The process performance index (PPI) can be a simple metric to connect the conforming rate of products. The properties of the PPI have been well studied for the normal distribution and other widely used lifetime distributions, such as the Weibull, Gamma, and Pareto distributions. Assume that the quality characteristic of product follows power-normal distribution. Statistical inference procedures for the PPI are established. The maximum likelihood estimation method for the model parameters and PPI is investigated and the exact Fisher information matrix is derived. We discuss the drawbacks of using the exact Fisher information matrix to obtain the confidence interval of the model parameters. The parametric bootstrap percentile and bootstrap bias-corrected percentile methods are proposed to obtain approximate confidence intervals for the model parameters and PPI. Monte Carlo simulations are conducted to evaluate the performance of the proposed methods. One example about the flow width of the resist in the hard-bake process is used for illustration.

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“…Another alternative to model skewed data is using the family of power-symmetric distributions (see Pewsey et al [4]) of which the most widely used is the power-normal (PN) distribution. Some references where this family is discussed are Lehmann [5], Durrans [6], Gupta and Gupta [7], Castillo et al [8], among others. In a series of papers by Martínez-Flórez et al ( [9][10][11][12][13]) extensions and applications of the PN distribution can be found.…”

Section: Introductionmentioning

confidence: 99%

A Parametric Quantile Regression Model for Asymmetric Response Variables on the Real Line

et al. 2020

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In this paper, we introduce a novel parametric quantile regression model for asymmetric response variables, where the response variable follows a power skew-normal distribution. By considering a new convenient parametrization, these distribution results are very useful for modeling different quantiles of a response variable on the real line. The maximum likelihood method is employed to estimate the model parameters. Besides, we present a local influence study under different perturbation settings. Some numerical results of the estimators in finite samples are illustrated. In order to illustrate the potential for practice of our model, we apply it to a real dataset.

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Truncated Power-Normal Distribution with Application to Non-Negative Measurements

Cited by 8 publications

References 31 publications

Reasoning Method Based on Intervals with Symmetric Truncated Normal Density

Reasoning Method Based on Intervals with Symmetric Truncated Normal Density

Inference for the Process Performance Index of Products on the Basis of Power-Normal Distribution

A Parametric Quantile Regression Model for Asymmetric Response Variables on the Real Line

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