Tolerance intervals in statistical software and robustness under model misspecification

Cho, Kyung Serk; Tony Ng, Hon Keung

doi:10.1186/s40488-021-00123-2

Journal of Statistical Distributions and Applications

Table 11 Performance of tolerance intervals based on Laplace distribution when the true distribution is normal (G: Laplace; F: Normal)

From: Tolerance intervals in statistical software and robustness under model misspecification

		n = 10	n = 25	n = 50	n = 100	n = 10	n = 25	n = 50	n = 100
		ρ= 0.9				ρ= 0.95
α = 0.01	\(\hat {\alpha }\)	0.0000	0.0001	0.0000	0.0000	0.0000	0.0001	0.0000	0.0000
	\(\hat {\rho }\)	1.0000	0.9988	0.9941	0.9852	1.0000	0.9999	0.9995	0.9982
	\(\hat {s}\)	0.0004	0.0036	0.0060	0.0078	0.0001	0.0009	0.0010	0.0016
α= 0.05	\(\hat {\alpha }\)	0.0011	0.0011	0.0005	0.0000	0.0006	0.0003	0.0000	0.0000
	\(\hat {\rho }\)	0.9983	0.9925	0.9851	0.9755	0.9997	0.9990	0.9979	0.9961
	\(\hat {s}\)	0.0087	0.0111	0.0114	0.0111	0.0033	0.0031	0.0028	0.0029
α= 0.1	\(\hat {\alpha }\)	0.0090	0.0041	0.0020	0.0002	0.0045	0.0012	0.0003	0.0000
	\(\hat {\rho }\)	0.9932	0.9858	0.9784	0.9694	0.9985	0.9977	0.9965	0.9945
	\(\hat {s}\)	0.0194	0.0168	0.0146	0.0129	0.0080	0.0053	0.0041	0.0038
α= 0.2	\(\hat {\alpha }\)	0.0418	0.0181	0.0059	0.0010	0.0232	0.0054	0.0011	0.0000
	\(\hat {\rho }\)	0.9798	0.9745	0.9689	0.9615	0.9945	0.9948	0.9939	0.9922
	\(\hat {s}\)	0.0367	0.0244	0.0186	0.0150	0.0171	0.0088	0.0061	0.0049
		ρ = 0.99				ρ = 0.995
α = 0.01	\(\hat {\alpha }\)	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
	\(\hat {\rho }\)	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000
	\(\hat {s}\)	0.0000	0.0001	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
α = 0.05	\(\hat {\alpha }\)	0.0003	0.0001	0.0000	0.0000	0.0002	0.0001	0.0000	0.0000
	\(\hat {\rho }\)	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000
	\(\hat {s}\)	0.0005	0.0003	0.0001	0.0000	0.0002	0.0001	0.0000	0.0000
α = 0.1	\(\hat {\alpha }\)	0.0010	0.0003	0.0000	0.0000	0.0008	0.0003	0.0000	0.0000
	\(\hat {\rho }\)	0.9999	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000
	\(\hat {s}\)	0.0015	0.0005	0.0001	0.0001	0.0008	0.0002	0.0000	0.0000
α = 0.2	\(\hat {\alpha }\)	0.0078	0.0006	0.0000	0.0000	0.0047	0.0003	0.0000	0.0000
	\(\hat {\rho }\)	0.9996	0.9999	0.9999	0.9999	0.9999	1.0000	1.0000	1.0000
	\(\hat {s}\)	0.0037	0.0009	0.0002	0.0001	0.0021	0.0004	0.0000	0.0000

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