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Table 4 Monte Carlo RMSEs and bias values of the entropy estimators VE ( m,n ) and AE ( m,n ) for the uniform distribution with H(f) = 0 and exponential distribution with H(f) = 1 using DRSS

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 Uniform distribution and H f = 0 Exponential distribution and H f = 1
   VE (m,n) AE (m,n) VE (m,n) AE (m,n)
   Bias RMSE Bias RMSE Bias RMSE Bias RMSE
10 1 −0.327408 0.369593 −0.267924 0.318205 −0.365854 0.425279 −0.305667 0.379121
  2 −0.260621 0.278731 −0.145388 0.176159 −0.288898 0.340618 −0.173991 0.251460
  3 −0.296104 0.306116 −0.122180 0.144286 −0.300393 0.351750 −0.128545 0.223802
  4 −0.346305 0.352712 −0.115995 0.134276 −0.322839 0.377437 −0.089495 0.215854
  5 −0.404121 0.409902 −0.116805 0.135411 −0.335248 0.399189 −0.047170 0.219634
20 1 −0.308453 0.329353 −0.279902 0.302719 −0.329105 0.363241 −0.298237 0.335475
  2 −0.189231 0.202666 −0.132076 0.151177 −0.204908 0.240316 −0.150759 0.196279
  3 −0.182095 0.191163 −0.095961 0.112229 −0.191216 0.228320 −0.104346 0.163293
  4 −0.197693 0.204342 −0.082268 0.096978 −0.190904 0.229986 −0.075338 0.179771
  5 −0.220876 0.225845 −0.077708 0.091093 −0.197900 0.239789 −0.052175 0.145269
  6 −0.247733 0.251580 −0.075071 0.086966 −0.207032 0.251002 −0.026183 0.146832
  7 −0.275808 0.278919 −0.074331 0.085055 −0.209883 0.258152 −0.012044 0.152682
  8 −0.303823 0.306608 −0.073793 0.084202 −0.218701 0.271560 0.014201 0.161180
  9 −0.333903 0.336495 −0.075306 0.086127 −0.223692 0.278728 0.035069 0.173654
  10 −0.363272 0.365731 −0.075514 0.086480 −0.228126 0.290431 0.061574 0.189857
30 1 −0.298092 0.312767 −0.278830 0.293698 −0.308011 0.331033 −0.289677 0.314515
  2 −0.170745 0.180210 −0.133715 0.146379 −0.182416 0.207785 −0.143418 0.174632
  3 −0.146113 0.153646 −0.088998 0.100564 −0.152039 0.180708 −0.094799 0.136371
  4 −0.149143 0.154886 −0.072297 0.083848 −0.145325 0.176699 −0.071094 0.123270
  5 −0.159888 0.164564 −0.063874 0.074562 −0.146632 0.179028 −0.049250 0.114227
  6 −0.174419 0.178204 −0.060394 0.070784 −0.149443 0.184598 −0.030887 0.113500
  7 −0.191854 0.194940 −0.058041 0.067650 −0.150245 0.188158 −0.046556 0.115023
  8 −0.209886 0.212509 −0.056421 0.065369 −0.153441 0.194332 −0.001239 0.120306
  9 −0.229010 0.231261 −0.056053 0.064628 −0.157250 0.199936 0.012716 0.124585
  10 −0.248006 0.249993 −0.056843 0.064868 −0.162854 0.208891 0.029477 0.133242
  11 −0.267506 0.269188 −0.056931 0.064430 −0.163540 0.213175 0.045951 0.145582
  12 −0.287408 0.289018 −0.056982 0.064673 −0.167660 0.221482 0.063602 0.155340
  13 −0.307160 0.308699 −0.058363 0.066130 −0.171024 0.225764 0.079779 0.169499
  14 −0.327370 0.328890 −0.058038 0.065797 −0.170880 0.232977 0.096359 0.182124
  15 −0.346997 0.348439 −0.059523 0.067623 −0.169873 0.235173 0.115563 0.198755