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 5 Performance of tolerance intervals based on Laplace distribution when the true distribution is Laplace (F=G: Laplace)

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	\(\hat {\alpha }\)	0.0001	0.0009	0.0017	0.0022	0.0001	0.0010	0.0021	0.0025
	\(\hat {\rho }\)	0.9995	0.9867	0.9706	0.9543	0.9999	0.9957	0.9890	0.9811
	\(\hat {s}\)	0.0024	0.0128	0.0151	0.0145	0.0009	0.0057	0.0074	0.0078
α= 0.05	\(\hat {\alpha }\)	0.0089	0.0158	0.0153	0.0174	0.0090	0.0172	0.0175	0.0191
	\(\hat {\rho }\)	0.9887	0.9698	0.9552	0.9418	0.9958	0.9881	0.9813	0.9744
	\(\hat {s}\)	0.0199	0.0227	0.0200	0.0170	0.0102	0.0119	0.0110	0.0097
α= 0.1	\(\hat {\alpha }\)	0.0409	0.0436	0.0398	0.0423	0.0414	0.0459	0.0427	0.0470
	\(\hat {\rho }\)	0.9753	0.9586	0.9463	0.9350	0.9896	0.9825	0.9765	0.9706
	\(\hat {s}\)	0.0332	0.0279	0.0225	0.0183	0.0189	0.0156	0.0129	0.0107
α= 0.2	\(\hat {\alpha }\)	0.1219	0.1050	0.0911	0.0985	0.1225	0.1081	0.0952	0.1047
	\(\hat {\rho }\)	0.9538	0.9440	0.9353	0.9268	0.9781	0.9745	0.9703	0.9658
	\(\hat {s}\)	0.0492	0.0338	0.0253	0.0196	0.0307	0.0202	0.0152	0.0119
		ρ = 0.99				ρ = 0.995
α = 0.01	\(\hat {\alpha }\)	0.0001	0.0011	0.0022	0.0029	0.0001	0.0011	0.0023	0.0030
	\(\hat {\rho }\)	1.0000	0.9996	0.9988	0.9975	1.0000	0.9999	0.9995	0.9990
	\(\hat {s}\)	0.0002	0.0009	0.0013	0.0016	0.0001	0.0004	0.0006	0.0008
α = 0.05	\(\hat {\alpha }\)	0.0094	0.0178	0.0182	0.0212	0.0094	0.0178	0.0182	0.0221
	\(\hat {\rho }\)	0.9995	0.9985	0.9974	0.9961	0.9997	0.9993	0.9989	0.9983
	\(\hat {s}\)	0.0027	0.0026	0.0025	0.0023	0.0016	0.0014	0.0013	0.0012
α = 0.1	\(\hat {\alpha }\)	0.0420	0.0471	0.0447	0.0500	0.0423	0.0473	0.0448	0.0512
	\(\hat {\rho }\)	0.9982	0.9974	0.9964	0.9952	0.9991	0.9988	0.9984	0.9978
	\(\hat {s}\)	0.0058	0.0039	0.0032	0.0027	0.0037	0.0022	0.0017	0.0015
α = 0.2	\(\hat {\alpha }\)	0.1222	0.1113	0.0994	0.1091	0.1218	0.1120	0.1003	0.1101
	\(\hat {\rho }\)	0.9954	0.9955	0.9950	0.9941	0.9975	0.9978	0.9976	0.9972
	\(\hat {s}\)	0.0109	0.0058	0.0041	0.0032	0.0073	0.0034	0.0023	0.0018

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