A Novel Method for Developing Efficient Probability Distributions with Applications to Engineering and Life Science Data

Table 1

MSE and bias of MLE.

Parameters	N	MSE ()	MSE ()	Bias ()	Bias ()
α = 5.557197; β = 7.558804	50	2.067219	0.9272915	0.5047117	0.2639728
	70	0.9708544	0.7031859	0.3088091	0.2101214
	100	0.7753223	0.372835	0.2578149	0.1197992
α = 6.457197; β = 3.558804	50	2.026492	0.2259845	0.4415551	0.1637077
	70	1.550174	0.1505096	0.4327197	0.1085847
	100	0.8022496	0.1029645	0.1910671	0.03691258
α = 5.457197; β = 3.558804	50	1.190428	0.2059653	0.4247818	2.342903
	70	0.8619716	0.1373483	0.2461313	2.341802
	100	0.4419579	0.08574337	0.04261996	2.333286
α = 6.457197; β = 2.558804	50	2.518832	0.09526091	0.7185321	0.1320379
	70	1.728531	0.09429495	0.4747864	0.07025322
	100	0.8006676	0.04351014	0.1573213	0.01418112
α = 4.557197; β = 4.558804	50	0.9564051	0.2857103	0.2557071	0.1324175
	70	0.3593258	0.2089236	0.08780059	0.04002267
	100	0.2750382	0.14968	0.02739781	0.01301724
α = 6.557197; β = 1.558804	50	3.244032	0.04392251	0.5185741	0.03279788
	70	1.495698	0.02470381	0.3520218	0.02578572
	100	0.9790736	0.01922724	0.09188152	0.02093735
α = 5.557197; β = 7.558804	50	2.067219	0.9272915	0.5047117	0.2639728
	70	0.9708544	0.7031859	0.3088091	0.2101214
	100	0.7753223	0.372835	0.2578149	0.1197992
α = 2.557197; β = 7.558804	50	0.1693338	1.094077	0.1063671	0.3148875
	70	0.08930482	0.4333755	0.08538295	0.1227512
	100	0.06259663	0.3701105	0.02511625	0.03947369