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Table 1 Monte Carlo RMSEs and bias values of the entropy estimators VE ( m,n ) and AE ( m,n ) for the uniform distribution , H(f) = 0

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 −0.519826 0.569537 −0.046482 0.521035 −0.396308 0.443439 −0.343522 0.396739
  2 −0.415135 0.452358 −0.298609 0.350332 −0.304078 0.329233 −0.189664 0.228762
  3 −0.422613 0.453818 −0.249056 0.298944 −0.327681 0.343991 −0.154894 0.186380
  4 −0.458940 0.487054 −0.229082 0.281422 −0.371538 0.383103 −0.143218 0.171767
  5 −0.502063 0.527918 −0.215077 0.270468 −0.425903 0.436521 −0.137821 0.168029
20 1 −0.393900 0.418346 −0.366867 0.392622 −0.343340 0.365754 −0.314244 0.338695
  2 −0.271880 0.290818 −0.212993 0.236696 −0.217937 0.233026 −0.162729 0.183187
  3 −0.253931 0.270200 −0.168961 0.192998 −0.205321 0.216879 −0.117939 0.136570
  4 −0.260596 0.274678 −0.144016 0.167779 −0.214042 0.222524 −0.100304 0.118284
  5 −0.276800 0.288985 −0.133179 0.157805 −0.235141 0.242179 −0.091608 0.108584
  6 −0.299321 0.310256 −0.125960 0.150733 −0.258899 0.264554 −0.085981 0.101365
  7 −0.322084 0.332301 −0.121244 0.146386 −0.285310 0.290156 −0.084733 0.099613
  8 −0.348254 0.357901 −0.118562 0.144786 −0.314138 0.318471 −0.083482 0.098588
  9 −0.374620 0.383864 −0.116399 0.143986 −0.343410 0.347711 −0.083926 0.099430
  10 −0.402840 0.411741 −0.117057 0.145063 −0.371780 0.375737 −0.848235 0.101014
30 1 −0.352853 0.368369 −0.334631 0.351096 −0.319230 0.333509 −0.300423 0.316118
  2 −0.223356 0.235685 −0.184969 0.199765 −0.190866 0.201625 −0.152577 0.165665
  3 −0.197719 0.208362 −0.141411 0.156683 −0.165182 0.173360 −0.106329 0.119047
  4 −0.196240 0.205882 −0.118803 0.133958 −0.162899 0.169841 −0.087046 0.099566
  5 −0.202003 0.210395 −0.105711 0.120861 −0.172441 0.178293 −0.078599 0.088072
  6 −0.213804 0.221385 −0.097719 0.113216 −0.185622 0.190458 −0.069898 0.081972
  7 −0.226688 0.233521 −0.092957 0.109089 −0.200036 0.204048 −0.066053 0.077716
  8 −0.242599 0.248992 −0.089259 0.105818 −0.217704 0.221309 −0.064713 0.076188
  9 −0.259471 0.265356 −0.087074 0.103535 −0.235661 0.238850 −0.062931 0.073734
  10 −0.276934 0.282548 −0.085151 0.102071 −0.254437 0.257257 −0.062044 0.072402
  11 −0.295302 0.300725 −0.841357 0.101314 −0.273700 0.276336 −0.062243 0.072977
  12 −0.313803 0.319255 −0.083206 0.102002 −0.293398 0.295911 −0.062262 0.072981
  13 −0.332279 0.337432 −0.082858 0.101944 −0.311978 0.341101 −0.063754 0.074987
  14 −0.351090 0.356205 −0.082540 0.101854 −0.332096 0.334518 −0.063579 0.075100
  15 −0.370555 0.375518 −0.082665 0.102618 −0.352077 0.354327 −0.064127 0.075825