Bootstrap confidence intervals of CNpk for type-II generalized log-logistic distribution

Rao, G. Srinivasa; Rosaiah, K.; Prasad, Svsvsv

doi:10.1007/s40092-019-0320-z

Cited by 3 publications

(3 citation statements)

References 17 publications

(15 reference statements)

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“…The data represents runoff amounts at Jug Bridge, Maryland by Chhikara and Folks [18] as one of the data sets which were used to describe the Birnbaum–Saunders distribution. The data set is also cited by Gadde et al [19] . The data are as follows; 0.17, 1.19, 0.23, 0.33, 0.39, 0.39, 0.40, 0.45, 0.52, 0.56, 0.59, 0.64, 0.66, 0.70, 0.76, 0.77, 0.78, 0.95, 0.97, 1.02, 1.12, 1.24, 1.59, 1.74, 2.92.…”

Section: Applicationmentioning

confidence: 99%

A new Lindley-Burr XII power series distribution: model, properties and applications

Makubate

Gabanakgosi

Chipepa

et al. 2021

Heliyon

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A new generalized class of distributions called the Lindley-Burr XII Power Series (LBXIIPS) distribution is proposed and explored. This new class of distributions contain some special cases such as Lindley-Burr XII Poisson (LBXIIP), Lindley-Burr XII Logarithmic (LBXIIL), Lindley-Burr XII Binomial (LBXIIB) and their sub-models among others. Some structural properties of the new distribution including moments, probability weighted moments, distribution of the order statistics and entropy are derived. Maximum likelihood estimation technique is used to estimate the model parameters. A simulation study to examine the bias and mean square error of the maximum likelihood estimators is presented and finally, an application to a real data set in order to illustrate the usefulness of the new distribution is given.

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Section: Applicationmentioning

confidence: 99%

A new Lindley-Burr XII power series distribution: model, properties and applications

Makubate

Gabanakgosi

Chipepa

et al. 2021

Heliyon

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“…It should be noted that the CI proposed by Luceño 18 has an error in asymptotic theory of statistics and we, therefore, provide a corrected version of the same CI. Second, we obtain the nonparametric BCIs using both the BCI approaches by Franklin and Wasserman 30 and the modified BCI approaches by Park et al 28 For other references on the BCI approaches, the readers are referred to the references, [33][34][35][36][37][38][39] among others. Third, we compare the powers of the two approaches using the relation between CIs and hypothesis testing.…”

Section: Introductionmentioning

confidence: 99%

“…Second, we obtain the nonparametric BCIs using both the BCI approaches by Franklin and Wasserman 30 and the modified BCI approaches by Park et al 28 . For other references on the BCI approaches, the readers are referred to the references, 33–39 among others. Third, we compare the powers of the two approaches using the relation between CIs and hypothesis testing.…”

Section: Introductionmentioning

confidence: 99%

Confidence intervals of the process capability index Cpc$C_{pc}$ revisited via modified bootstrap technique and ROC curves

Ouyang

Dey²,

Byun

et al. 2023

Quality & Reliability Eng

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We consider the process capability index (PCI), a widely used quality‐related statistic used to assess the quality of products and performance of monitored processes in various industries. It is widely known that the conventional PCIs perform well when the quality process being monitored has a normal distribution. Unfortunately, using the indices to evaluate a non‐normally distributed process often leads to inaccurate results. In this article, we consider a new PCI, , that can be used in both normal and non‐normal scenarios. The objective of this article is threefold: (i) We provide a corrected form of the confidence interval for . (ii) We compare the performance of three nonparametric bootstrap confidence intervals (BCIs) for . Specifically, the standard bootstrap, percentile bootstrap, and bias‐corrected percentile bootstrap. Under various distributional assumptions such as the normal, chi‐square, Student t, Laplace, and two‐parameter exponential distributions, the estimated coverage probabilities and average width of the confidence intervals and BCIs for are compared. (iii) The power of the respective bootstrap approaches is evaluated by using the equivalence relation between confidence interval construction and two‐sided hypothesis testing. We also provide the receiver operating characteristic curves to evaluate their performance. Finally, as an illustrative example, an actual data set related to groove dimensions (in inches) measured from a manufacturing process of ignition keys is re‐analyzed to illustrate the utility of the proposed methods.

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Research Data and Method Selection

2020

Engineering Research

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Bootstrap confidence intervals of CNpk for type-II generalized log-logistic distribution

Cited by 3 publications

References 17 publications

A new Lindley-Burr XII power series distribution: model, properties and applications

A new Lindley-Burr XII power series distribution: model, properties and applications

Confidence intervals of the process capability index Cpc$C_{pc}$ revisited via modified bootstrap technique and ROC curves

Research Data and Method Selection

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