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. 2022;37(4):1751-1770.
doi: 10.1007/s00180-021-01178-0. Epub 2022 Jan 9.

New classes of tests for the Weibull distribution using Stein's method in the presence of random right censoring

E Bothma  1 , J S Allison  1 , I J H Visagie  1
Affiliations

New classes of tests for the Weibull distribution using Stein's method in the presence of random right censoring

E Bothma et al. Comput Stat. 2022.

Abstract

We develop two new classes of tests for the Weibull distribution based on Stein's method. The proposed tests are applied in the full sample case as well as in the presence of random right censoring. We investigate the finite sample performance of the new tests using a comprehensive Monte Carlo study. In both the absence and presence of censoring, it is found that the newly proposed classes of tests outperform competing tests against the majority of the distributions considered. In the cases where censoring is present we consider various censoring distributions. Some remarks on the asymptotic properties of the proposed tests are included. We present another result of independent interest; a test initially proposed for use with full samples is amended to allow for testing for the Weibull distribution in the presence of censoring. The techniques developed in the paper are illustrated using two practical examples.

Keywords: Goodness-of-fit testing; Hypothesis testing; Random right censoring; Warp-speed bootstrap; Weibull distribution.

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Conflict of interest statement

Conflict of interestThe authors declare that they have no conflict of interest.

References

    1. Allison J, Milošević B, Obradović M, Smuts M (2021) Distribution-free goodness-of-fit tests for the pareto distribution based on a characterization. Comput Stat pp 1–16
    1. Allison J, Santana L. On a data-dependent choice of the tuning parameter appearing in certain goodness-of-fit tests. J Stat Comput Simul. 2015;85(16):3276–3288. doi: 10.1080/00949655.2014.968781. - DOI
    1. Allison JS, Betsch S, Ebner B, Visagie IJH (2019) New weighted L2-type tests for the inverse Gaussian distribution. arXiv preprint arXiv:1910.14119
    1. Allison JS, Huskova M, Meintanis SG. Testing the adequacy of semiparametric transformation models. Test. 2017;27:1–25.
    1. Allison JS, Santana L, Smit N, Visagie IJH (2017) An “apples-to-apples” comparison of various tests for exponentiality. Comput Stat 32(4):1241–1283

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