A New Flexible Logarithmic-X Family of Distributions with Applications to Biological Systems

Table 1

The results of conducting a simulation using the NFLog-Wei distribution utilizing sets I and II.

	Est.	Set I: , , and			Set II:, , and
		MLE	MSE	Bias	MLE	MSE	Bias
25		1.359714	3.352142	0.959714	1.470587	1.916907	0.070586
		2.558740	2.272587	0.258740	4.107370	1.019913	0.507369
		3.932950	1.830509	0.432950	4.536813	0.659791	−0.263187
50		1.261625	2.610044	0.861625	1.324459	1.355837	−0.075540
		2.527184	2.103823	0.227184	4.074657	0.827990	0.474657
		3.854091	1.742594	0.354091	4.428739	0.809154	−0.371261
75		1.249921	2.380179	0.849921	1.304567	1.105549	−0.095432
		2.373155	1.660890	0.073155	4.027904	0.720244	0.427903
		3.903062	1.633956	0.403062	4.434167	0.722466	−0.365833
100		1.121601	1.880341	0.721601	1.311440	1.055909	−0.088560
		2.409936	1.568806	0.109935	3.990797	0.645796	0.390796
		3.827443	1.488893	0.327443	4.464805	0.678206	−0.335194
200		0.937715	1.208062	0.537715	1.268340	0.643048	−0.131660
		2.367964	1.106299	0.067963	3.910828	0.469170	0.310828
		3.755479	1.181334	0.255478	4.493781	0.563858	−0.306218
300		0.846743	0.925916	0.446743	1.229159	0.517821	−0.170841
		2.330760	0.853094	0.030759	3.896567	0.414911	0.296567
		3.718240	0.963105	0.218240	4.481787	0.556714	−0.318213
400		0.820652	0.786768	0.420652	1.249808	0.489246	−0.150192
		2.268908	0.698790	−0.031091	3.869472	0.370287	0.269471
		3.744079	0.849120	0.244079	4.507406	0.504602	−0.292593
500		0.726767	0.635959	0.326767	1.240931	0.413434	−0.159069
		2.321649	0.575961	0.021649	3.834327	0.293431	0.234327
		3.652565	0.701084	0.152564	4.531517	0.424718	−0.268482
600		0.666051	0.491945	0.266051	1.280216	0.402240	−0.119784
		2.309838	0.453986	0.009838	3.803557	0.258676	0.203557
		3.629989	0.587730	0.129989	4.559654	0.384078	−0.240346
700		0.701362	0.504666	0.301362	1.299725	0.378063	−0.100275
		2.256093	0.430943	−0.043907	3.790054	0.250775	0.190053
		3.694393	0.588829	0.194392	4.590190	0.345656	−0.209809
800		0.642816	0.378790	0.242816	1.270926	0.336466	−0.129073
		2.255541	0.350091	−0.044459	3.789066	0.208206	0.189066
		3.658857	0.464875	0.158856	4.586876	0.324176	−0.213124
900		0.652121	0.396530	0.252121	1.307186	0.327404	−0.092814
		2.257956	0.353270	−0.042043	3.755260	0.186083	0.155260
		3.668265	0.508969	0.168265	4.618437	0.274431	−0.181562
1000		0.597530	0.304498	0.197530	1.296956	0.316957	−0.123043
		2.292465	0.316204	−0.017534	3.791939	0.188118	0.171938
		3.518328	0.415432	0.118328	4.600692	0.302786	−0.199307