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Simultaneous monitoring of origin and scale in left-bounded processes via depth

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  • Ignacio Cascos

    (Universidad Carlos III)

Abstract

A novel notion of depth for the origin and scale of a distribution with left-bounded support, like those modelling lifetime data, is presented. This origin-scale depth, evaluated on parameter estimates, serves as plotting statistic of a Shewhart-type chart for rational samples of a fixed size for which three variations are considered: a nonparametric version, built without distributional assumptions, and parametric and semiparametric versions, built for shifted exponential processes (paradigmatic model governed by origin and scale parameters). An EWMA scheme based on the rank induced by the origin-scale depth is also presented and, together with the Shewhart-type chart, compared with other existing monitoring proposals. The new proposals are competitive when the reference distribution is a shifted exponential one, while outperform them for other reference distributions.

Suggested Citation

  • Ignacio Cascos, 2021. "Simultaneous monitoring of origin and scale in left-bounded processes via depth," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(4), pages 649-673, December.
    • Handle: RePEc:spr:alstar:v:105:y:2021:i:4:d:10.1007_s10182-021-00401-z
    DOI: 10.1007/s10182-021-00401-z
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    References listed on IDEAS

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    1. Cascos, Ignacio & López-Díaz, Miguel, 2016. "On the uniform consistency of the zonoid depth," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 394-397.
    2. Shih-Chou Kao, 2010. "Normalization of the origin-shifted exponential distribution for control chart construction," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(7), pages 1067-1087.
    3. Cascos, Ignacio & López-Díaz, Miguel, 2012. "Trimmed regions induced by parameters of a probability," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 306-318.
    4. R. van Zyl & A. J. van der Merwe, 2019. "Bayesian process monitoring schemes for the two-parameter exponential distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(7), pages 1766-1797, April.
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