Table 1 MSEs of ratio estimators for ${\lambda }_{2}$=0.03.

From: Combination of memory type ratio and product estimators under extended EWMA statistic with application to wheat production

$\lambda_{1}$		$0.1$		$0.15$		$0.25$		$0.5$		$0.75$		$1$
$\rho$	$n$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}$
0.05	10	0.0054	0.0040	0.0084	0.0071	0.0142	0.0131	0.0341	0.0332	0.0609	0.0606	0.1023	0.1023
	20	0.0026	0.0023	0.0041	0.0035	0.0072	0.0067	0.0171	0.0168	0.0308	0.0307	0.0511	0.0511
	30	0.0018	0.0013	0.0027	0.0023	0.0050	0.0045	0.0112	0.0110	0.0204	0.0204	0.0344	0.0344
	50	0.0010	0.0008	0.0016	0.0014	0.0030	0.0026	0.0068	0.0067	0.0121	0.0121	0.0203	0.0203
	200	0.0002	0.0002	0.0004	0.0003	0.0007	0.0006	0.0017	0.0016	0.0030	0.0030	0.0050	0.0050
	500	0.0001	0.0000	0.0001	0.0001	0.0003	0.0002	0.0006	0.0006	0.0012	0.0012	0.0020	0.0020
0.25	10	0.0050	0.0038	0.0076	0.0065	0.0133	0.0123	0.0314	0.0307	0.0563	0.0561	0.0951	0.0951
	20	0.0024	0.0018	0.0039	0.0033	0.0067	0.0062	0.0159	0.0155	0.0282	0.0281	0.0471	0.0471
	30	0.0016	0.0012	0.0025	0.0021	0.0044	0.0041	0.0105	0.0102	0.0189	0.0188	0.0314	0.0314
	50	0.0009	0.0007	0.0015	0.0012	0.0027	0.0024	0.0062	0.0061	0.0112	0.0112	0.0186	0.0186
	200	0.0002	0.0001	0.0004	0.0003	0.0006	0.0006	0.0015	0.0015	0.0028	0.0028	0.0046	0.0046
	500	0.0000	0.0000	0.0001	0.0001	0.0002	0.0002	0.0006	0.0006	0.0011	0.0011	0.0018	0.0018
0.50	10	0.0043	0.0032	0.0067	0.0056	0.0118	0.0109	0.0281	0.0276	0.0503	0.0501	0.0833	0.0833
	20	0.0021	0.0015	0.0034	0.0029	0.0060	0.0055	0.0147	0.0137	0.0252	0.0251	0.0418	0.0418
	30	0.0015	0.0011	0.0023	0.0019	0.0040	0.0037	0.0092	0.0090	0.0167	0.0166	0.0279	0.0279
	50	0.0008	0.0006	0.0013	0.0011	0.0024	0.0022	0.0056	0.0054	0.0100	0.0099	0.0168	0.0168
	200	0.0002	0.0001	0.0003	0.0002	0.0006	0.0005	0.0014	0.0013	0.0025	0.0025	0.0041	0.0041
	500	0.0000	0.0000	0.0001	0.0001	0.0002	0.0002	0.0005	0.0005	0.0009	0.0009	0.0016	0.0016
0.75	10	0.0040	0.0030	0.0058	0.0049	0.0104	0.0096	0.0247	0.0242	0.0443	0.0441	0.0750	0.0750
	20	0.0020	0.0015	0.0030	0.0026	0.0053	0.0049	0.0124	0.0121	0.0220	0.0220	0.0370	0.0370
	30	0.0013	0.0009	0.0020	0.0017	0.0035	0.0032	0.0081	0.0079	0.0148	0.0147	0.0245	0.0245
	50	0.0007	0.0005	0.0011	0.0010	0.0020	0.0019	0.0050	0.0048	0.0088	0.0087	0.0146	0.0146
	200	0.0002	0.0001	0.0003	0.0002	0.0005	0.0004	0.0012	0.0012	0.0022	0.0022	0.0036	0.0036
	500	0.0000	0.0000	0.0001	0.0001	0.0002	0.0001	0.0005	0.0004	0.0008	0.0008	0.0014	0.0014
0.95	10	0.0034	0.0025	0.0053	0.0045	0.0094	0.0087	0.0219	0.0215	0.0399	0.0397	0.0662	0.0662
	20	0.0031	0.0012	0.0027	0.0023	0.0047	0.0043	0.0109	0.0107	0.0197	0.0197	0.0327	0.0327
	30	0.0011	0.0008	0.0018	0.0015	0.0031	0.0029	0.0073	0.0071	0.0131	0.0130	0.0219	0.0219
	50	0.0007	0.0005	0.0010	0.0009	0.0018	0.0017	0.0043	0.0042	0.0079	0.0079	0.0131	0.0131
	200	0.0001	0.0001	0.0002	0.0002	0.0004	0.0004	0.0010	0.0010	0.0019	0.0019	0.0032	0.0032
	500	0.0000	0.0000	0.0001	0.0000	0.0001	0.0001	0.0004	0.0004	0.0008	0.0007	0.0013	0.0013

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Table 1 MSEs of ratio estimators for \({\lambda }_{2}\)=0.03.

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\(\lambda_{1}\)		\(0.1\)		\(0.15\)		\(0.25\)		\(0.5\)		\(0.75\)		\(1\)
\(\rho\)	\(n\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}\)
0.05	10	0.0054	0.0040	0.0084	0.0071	0.0142	0.0131	0.0341	0.0332	0.0609	0.0606	0.1023	0.1023
	20	0.0026	0.0023	0.0041	0.0035	0.0072	0.0067	0.0171	0.0168	0.0308	0.0307	0.0511	0.0511
	30	0.0018	0.0013	0.0027	0.0023	0.0050	0.0045	0.0112	0.0110	0.0204	0.0204	0.0344	0.0344
	50	0.0010	0.0008	0.0016	0.0014	0.0030	0.0026	0.0068	0.0067	0.0121	0.0121	0.0203	0.0203
	200	0.0002	0.0002	0.0004	0.0003	0.0007	0.0006	0.0017	0.0016	0.0030	0.0030	0.0050	0.0050
	500	0.0001	0.0000	0.0001	0.0001	0.0003	0.0002	0.0006	0.0006	0.0012	0.0012	0.0020	0.0020
0.25	10	0.0050	0.0038	0.0076	0.0065	0.0133	0.0123	0.0314	0.0307	0.0563	0.0561	0.0951	0.0951
	20	0.0024	0.0018	0.0039	0.0033	0.0067	0.0062	0.0159	0.0155	0.0282	0.0281	0.0471	0.0471
	30	0.0016	0.0012	0.0025	0.0021	0.0044	0.0041	0.0105	0.0102	0.0189	0.0188	0.0314	0.0314
	50	0.0009	0.0007	0.0015	0.0012	0.0027	0.0024	0.0062	0.0061	0.0112	0.0112	0.0186	0.0186
	200	0.0002	0.0001	0.0004	0.0003	0.0006	0.0006	0.0015	0.0015	0.0028	0.0028	0.0046	0.0046
	500	0.0000	0.0000	0.0001	0.0001	0.0002	0.0002	0.0006	0.0006	0.0011	0.0011	0.0018	0.0018
0.50	10	0.0043	0.0032	0.0067	0.0056	0.0118	0.0109	0.0281	0.0276	0.0503	0.0501	0.0833	0.0833
	20	0.0021	0.0015	0.0034	0.0029	0.0060	0.0055	0.0147	0.0137	0.0252	0.0251	0.0418	0.0418
	30	0.0015	0.0011	0.0023	0.0019	0.0040	0.0037	0.0092	0.0090	0.0167	0.0166	0.0279	0.0279
	50	0.0008	0.0006	0.0013	0.0011	0.0024	0.0022	0.0056	0.0054	0.0100	0.0099	0.0168	0.0168
	200	0.0002	0.0001	0.0003	0.0002	0.0006	0.0005	0.0014	0.0013	0.0025	0.0025	0.0041	0.0041
	500	0.0000	0.0000	0.0001	0.0001	0.0002	0.0002	0.0005	0.0005	0.0009	0.0009	0.0016	0.0016
0.75	10	0.0040	0.0030	0.0058	0.0049	0.0104	0.0096	0.0247	0.0242	0.0443	0.0441	0.0750	0.0750
	20	0.0020	0.0015	0.0030	0.0026	0.0053	0.0049	0.0124	0.0121	0.0220	0.0220	0.0370	0.0370
	30	0.0013	0.0009	0.0020	0.0017	0.0035	0.0032	0.0081	0.0079	0.0148	0.0147	0.0245	0.0245
	50	0.0007	0.0005	0.0011	0.0010	0.0020	0.0019	0.0050	0.0048	0.0088	0.0087	0.0146	0.0146
	200	0.0002	0.0001	0.0003	0.0002	0.0005	0.0004	0.0012	0.0012	0.0022	0.0022	0.0036	0.0036
	500	0.0000	0.0000	0.0001	0.0001	0.0002	0.0001	0.0005	0.0004	0.0008	0.0008	0.0014	0.0014
0.95	10	0.0034	0.0025	0.0053	0.0045	0.0094	0.0087	0.0219	0.0215	0.0399	0.0397	0.0662	0.0662
	20	0.0031	0.0012	0.0027	0.0023	0.0047	0.0043	0.0109	0.0107	0.0197	0.0197	0.0327	0.0327
	30	0.0011	0.0008	0.0018	0.0015	0.0031	0.0029	0.0073	0.0071	0.0131	0.0130	0.0219	0.0219
	50	0.0007	0.0005	0.0010	0.0009	0.0018	0.0017	0.0043	0.0042	0.0079	0.0079	0.0131	0.0131
	200	0.0001	0.0001	0.0002	0.0002	0.0004	0.0004	0.0010	0.0010	0.0019	0.0019	0.0032	0.0032
	500	0.0000	0.0000	0.0001	0.0000	0.0001	0.0001	0.0004	0.0004	0.0008	0.0007	0.0013	0.0013