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Table 3 Monte Carlo RMSEs and bias values of the entropy estimators VE ( m,n ) and AE ( m,n ) for the standard normal distribution, H(f) = 1.419

From: Goodness-of-fit testing for the inverse Gaussian distribution based on new entropy estimation using ranked set sampling and double ranked set sampling

n m SRS RSS
   VE (m,n) AE (m,n) VE (m,n) AE (m,n)
   Bias RMSE Bias RMSE Bias RMSE Bias RMSE
10 1 −0.598925 0.676499 −0.538428 0.623068 −0.484489 0.549750 −0.429406 0.502967
  2 −0.521455 0.591007 −0.409842 0.496627 −0.422169 0.471157 −0.308706 0.375690
  3 −0.563002 0.623188 −0.386562 0.468471 −0.462240 0.504378 −0.291133 0.353844
  4 −0.610651 0.663364 0.388846 0.469519 −0.523019 0.557792 −0.292810 0.351636
  5 −0.671777 0.719069 −0.382242 0.461612 −0.584483 0.614209 −0.294820 0.349472
20 1 −0.435480 0.483459 −0.402721 0.452976 −0.382986 0.420310 −0.354315 0.393878
  2 −0.327145 0.375798 −0.267005 0.324501 −0.275716 0.313472 −0.218758 0.264068
  3 −0.317948 0.364927 −0.230598 0.292997 −0.268657 0.304811 −0.181588 0.230636
  4 −0.327070 0.372436 −0.214227 0.279269 −0.285331 0.318855 −0.168035 0.219922
  5 −0.352658 0.395796 −0.205782 0.272804 −0.305555 0.337744 −0.160392 0.213700
  6 0.375996 0.416964 −0.203268 0.269194 −0.335066 0.365185 −0.162263 0.216405
  7 −0.404050 0.442997 −0.200951 0.269828 −0.363782 0.391748 −0.162648 0.217866
  8 −0.439618 0.475094 −0.203704 0.270603 −0.395221 0.421583 −0.163443 0.217711
  9 −0.467134 0.500777 0.211872 0.276695 −0.428042 0.451680 −0.169841 0.224475
  10 −0.496926 0.527456 −0.209085 0.275281 −0.454818 0.477152 −0.171572 0.224804
30 1 −0.378860 0.413455 −0.359097 0.394766 −0.343626 0.370512 −0.328056 0.355718
  2 −0.259105 0.299687 −0.221750 0.266138 −0.226914 0.255947 −0.189446 0.223276
  3 −0.236758 0.277238 −0.177599 0.229027 −0.204698 0.234358 −0.147274 0.186797
  4 −0.234369 0.275867 −0.158560 0.213972 −0.204765 0.234413 −0.125487 0.169031
  5 −0.244288 0.283027 −0.148610 0.206988 −0.214434 0.243683 −0.117590 0.165087
  6 −0.255248 0.293332 −0.139542 0.200072 −0.227340 0.255901 −0.111407 0.161770
  7 −0.269724 0.305134 −0.132038 0.196792 −0.241325 0.268228 −0.105796 0.158654
  8 −0.285713 0.321039 −0.129915 0.193509 −0.254983 0.282376 −0.102504 0.157726
  9 −0.304064 0.337563 −0.131105 0.198239 −0.274697 0.301420 −0.103392 0.160749
  10 −0.320051 0.352764 −0.130086 0.196928 −0.295057 0.319933 −0.101392 0.160593
  11 −0.339131 0.369866 −0.127890 0.196985 −0.314201 0.339141 −0.102034 0.161378
  12 −0.361226 0.392070 −0.130212 0.197655 −0.333173 0.356224 −0.103026 0.163577
  13 −0.382347 0.410463 0.129885 0.199488 −0.353582 0.375170 −0.105978 0.165825
  14 −0.400618 0.428008 −0.131518 0.199794 −0.375752 0.397462 −0.109190 0.168154
  15 −0.423597 0.449968 −0.134062 0.200285 −0.394363 0.414605 −0.108705 0.167780