More efficient approaches to the exponentiated half-logistic distribution based on record values

Seo, Jung-In; Kang, Suk-Bok

doi:10.1186/s40064-016-3047-y

SpringerPlus

Table 1 MSEs(biases) and \(95\,\%\) CIs for \(\lambda \)

From: More efficient approaches to the exponentiated half-logistic distribution based on record values

\(\lambda \)	k	MSE(bias)			c	MSE(bias)	CI based on
\(\lambda \)	k	\(\hat{\lambda }\)	\(\hat{\lambda }_p \left( \hat{\theta }_p \right) \)	\(\hat{\lambda }_B \left( \hat{\theta }_{MAP} \right) \)	c	\(\hat{\lambda }_{HB} \left( \hat{\theta }_{HMAP} \right) \)	\(\hat{\lambda }\)	\(W \left( \theta ^* \right) \)
2	10	0.357 (0.239)	0.175 (0.005)	0.260 (0.115)	5	0.170 (−0.003)	0.977	0.954
					100	0.173 (−0.004)
					500	0.173 (−0.004)
	12	0.230 (0.180)	0.135 (0.003)	0.179 (0.086)	5	0.132 (−0.002)	0.972	0.951
					100	0.135 (−0.002)
					500	0.135 (−0.002)
	14	0.151 (0.139)	0.100 (−0.003)	0.123 (0.065)	5	0.099 (−0.002)	0.971	0.949
					100	0.100 (−0.002)
					500	0.100 (−0.002)
	16	0.121 (0.119)	0.085 (−0.003)	0.101 (0.056)	5	0.084 (−0.001)	0.970	0.950
					100	0.085 (−0.001)
					500	0.085 (−0.001)
4	10	0.771 (0.330)	0.270 (0.020)	0.427 (0.178)	5	0.228 (−0.004)	0.972	0.954
					100	0.229 (−0.005)
					500	0.229 (−0.005)
	12	0.406 (0.230)	0.189 (0.012)	0.266 (0.126)	5	0.172 (−0.005)	0.968	0.951
					100	0.172 (−0.005)
					500	0.172 (−0.005)
	14	0.208 (0.167)	0.120 (0.001)	0.157 (0.089)	5	0.115 (−0.003)	0.968	0.950
					100	0.115 (−0.003)
					500	0.115 (−0.003)
	16	0.151 (0.136)	0.096 (0.000)	0.119 (0.072)	5	0.094 (−0.002)	0.966	0.949
					100	0.094 (−0.002)
					500	0.094 (−0.002)
6	10	1.923 (0.454)	0.468 (0.046)	0.624 (0.227)	5	0.294 (0.004)	0.975	0.954
					100	0.294 (0.004)
					500	0.294 (0.004)
	12	0.783 (0.298)	0.289 (0.027)	0.383 (0.159)	5	0.224 (0.002)	0.968	0.951
					100	0.224 (0.002)
					500	0.224 (0.002)
	14	0.306 (0.204)	0.153 (0.008)	0.208 (0.110)	5	0.141 (−0.001)	0.967	0.950
					100	0.141 (−0.001)
					500	0.141 (−0.001)
	16	0.195 (0.159)	0.113 (0.003)	0.146 (0.086)	5	0.108 (−0.001)	0.966	0.950
					100	0.108 (−0.001)
					500	0.108 (−0.001)
8	10	5.376 (0.604)	0.871 (0.079)	0.769 (0.264)	5	0.355 (0.009)	0.975	0.952
					100	0.355 (0.009)
					500	0.355 (0.009)
	12	1.522 (0.377)	0.452 (0.047)	0.488 (0.188)	5	0.279 (0.006)	0.967	0.951
					100	0.279 (0.006)
					500	0.279 (0.006)
	14	0.458 (0.247)	0.202 (0.018)	0.268 (0.130)	5	0.171 (−0.003)	0.964	0.950
					100	0.171 (−0.003)
					500	0.171 (−0.003)
	16	0.254 (0.186)	0.134 (0.009)	0.176 (0.099)	5	0.124 (−0.003)	0.962	0.950
					100	0.124 (−0.003)
					500	0.124 (−0.003)

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