A methodology based on the Birnbaum–Saunders distribution for reliability analysis applied to nano-materials

Leiva, Víctor; Ruggeri, Fabrizio; Saulo, Helton; Vivanco, Juan

doi:10.1016/j.ress.2016.08.024

Cited by 25 publications

(9 citation statements)

References 36 publications

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“…In a recent paper, Mohammadi et al have discussed the modeling of wind speed and wind power distributions by a BS distribution. Also, in the reliability analysis of nanomaterials, Leiva et al have recently made use of the BS lifetime distribution. Garcia‐Papani et al have considered a spatial modeling of the BS distribution and applied it to agricultural engineering data.…”

Section: Concluding Remarks and Further Readingmentioning

confidence: 99%

Birnbaum‐Saunders distribution: A review of models, analysis, and applications

Balakrishnan

Kundu

2018

Appl Stoch Models Bus & Ind

106

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Birnbaum and Saunders introduced a two-parameter lifetime distribution to model the fatigue life of a metal, subject to cyclic stress. Since then, extensive work has been done on this model providing different interpretations, constructions, generalizations, inferential methods, and extensions to bivariate, multivariate, and matrix-variate cases. More than 200 papers and one research monograph have already appeared describing all these aspects and developments. In this paper, we provide a detailed review of all these developments and, at the same time, indicate several open problems that could be considered for further research. KEYWORDSBayes estimators, EM algorithm, Fisher information matrix, hazard function, length-biased distribution, moments and inverse moments, probability density function, stochastic orderings, TP 2 property 4

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Section: Concluding Remarks and Further Readingmentioning

confidence: 99%

Birnbaum‐Saunders distribution: A review of models, analysis, and applications

Balakrishnan

Kundu

2018

Appl Stoch Models Bus & Ind

106

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“…The data correspond to the hardness (in MPa) of a bone cement called Palacos R, treated with low‐loadings of mesoporous silica nanoparticles, and were obtained from the work of Leiva et al We consider n = 16 observations under treatment 0.2%‐COOH, and the data are 169.38, 168.68, 175.28, 163.34, 162.35, 160.55, 193.66, 174.58, 171.75, 168.03, 173.60, 173.44, 180.79, 177.54, 177.57, and 176.47. The readers are referred to the work of Leiva et al for a detailed description about the real data. The ML estimates of α and β are

\overset{α}{true} = 0.04443

and

\overset{β}{true} = 172.76763

, respectively.…”

Section: A Simple Real Data Illustrationmentioning

confidence: 99%

Discussion of “Birnbaum‐Saunders distribution: A review of models, analysis, and applications”

Lemonte

Cordeiro

2018

Appl Stoch Models Bus & Ind

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“…The BS distribution originates from material fatigue and has interesting properties, doing it widely studied. Some of its recent applications range across fields different to engineering, such as business, environment, finance, industry and medicine, which have been conducted by an international, transdisciplinary group of researchers; see Jin and Kawczak (2003), Bhatti (2010), Lio et al (2010), Castillo et al (2011), Saulo et al (2013), Leiva et al (2015Leiva et al ( , 2016bLeiva et al ( , 2017, Wanke and Leiva (2015), Garcia-Papani et al (2016), Marchant et al (2016b), and Leao et al (2017). The BSACD model proposed by Bhatti (2010) is constructed in terms of a conditional median duration, rather than an ACD model in the sense of Engle and Russell (1998) based on the mean.…”

Section: Introductionmentioning

confidence: 99%

Birnbaum–Saunders autoregressive conditional duration models applied to high-frequency financial data

et al. 2017

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Modern financial markets now record the precise time of each stock trade, along with price and volume, with the aim of analysing the structure of the times between trading events -leading to a big data problem. In this paper, we propose and compare two Birnbaum-Saunders autoregressive conditional duration models specified in terms of time-varying conditional median and mean durations. These models provide a novel alternative to the existing autoregressive conditional duration models due to their flexibility and ease of estimation. Influence diagnostic tools are developed to allow goodness-of-fit assessment and to detect departures from assumptions, including the presence of outliers and influential cases. Both global and local influence tools are considered based on the parameter estimates under different perturbation schemes. A thorough Monte Carlo study is presented to evaluate the performance of the maximum likelihood estimators, and the forecasting ability of the models is assessed using the traditional and density forecast evaluation techniques. The Monte Carlo study suggests that the parameter estimators are asymptotically unbiased, consistent and normally distributed. Finally, a full analysis of a real-world financial transaction data set, from the German DAX in 2016, is presented to illustrate the proposed approach and to compare the fitting and forecasting performances with existing models in the literature. One case related to the duration time is identified as potentially influential, but its removal does not change resulting inferences demonstrating the robustness of the proposed approach. Fitting and forecasting performances favor the proposed models and, in particular, the median-based approach gives additional protection against outliers, as expected.

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A methodology based on the Birnbaum–Saunders distribution for reliability analysis applied to nano-materials

Cited by 25 publications

References 36 publications

Birnbaum‐Saunders distribution: A review of models, analysis, and applications

Birnbaum‐Saunders distribution: A review of models, analysis, and applications

Discussion of “Birnbaum‐Saunders distribution: A review of models, analysis, and applications”

Birnbaum–Saunders autoregressive conditional duration models applied to high-frequency financial data

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