The Location-Scale Mixture Exponential Power Distribution: A Bayesian and Maximum Likelihood Approach

Table 1

Estimates of the parameters by choosing 100 samples of sizes 𝑛=50,100,200, and 500 from the LSMEP distribution with 𝜇=1, 𝜎=2, 𝛼=5, and (𝛽,𝑝)=(1.5,1.5),(−3,2.5),(5.5,3.5).

𝑛	𝜇	MSE(𝜇)	𝜎	MSE(𝜎)	𝛼	MSE(𝛼)
			(𝛽,𝑝)=(1.5,1.5)
50	0.8889	0.1437	1.9073	0.0796	4.4925	2.0219
100	0.9095	0.0814	1.9181	0.0445	4.4072	1.6825
200	1.0248	0.0259	1.9685	0.0088	4.7590	0.5509
500	1.0422	0.0230	1.9694	0.0065	4.5369	0.5505
			(𝛽,𝑝)=(−3,2.5)
50	1.0597	0.1671	1.9881	0.0497	5.6578	3.8411
100	1.0795	0.0496	1.9984	0.0137	4.8799	0.3877
200	1.0377	0.0433	2.0086	0.0192	5.3394	2.1051
500	1.0137	0.0309	2.0009	0.0121	5.1260	0.4680
			(𝛽,𝑝)=(5.5,3.5)
50	0.9072	0.0247	1.9727	0.0073	4.8450	1.3445
100	0.9309	0.1365	1.9610	0.0402	4.9806	0.1360
200	0.9520	0.0989	1.9170	0.0624	5.0175	0.8248
500	0.9571	0.0712	1.9982	0.0274	4.8970	0.7012