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Table 2 Monte Carlo RMSEs and bias values of the entropy estimators VE ( m,n ) and AE ( m,n ) for the exponential distribution, H(f) = 1

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 −0.552032 0.677001 −0.495449 0.631471 −0.430553 0.505229 −0.376361 0.461201
  2 −0.442683 0.571820 −0.323532 0.483573 −0.337494 0.404667 −0.220406 0.315220
  3 −0.435444 0.561640 −0.265713 0.443276 −0.332760 0.401125 −0.159787 0.276197
  4 −0.451545 0.575390 −0.221689 0.424404 −0.348029 0.420617 −0.121584 0.266664
  5 −0.469437 0.597761 −0.179844 0.413541 −0.366628 0.445977 −0.080667 0.266812
20 1 −0.414064 0.490107 −0.384516 0.464796 −0.357765 0.398661 −0.333540 0.376843
  2 −0.285717 0.376086 −0.232518 0.338830 −0.234959 0.280262 −0.176512 0.232710
  3 −0.260773 0.351341 −0.175461 0.298406 −0.213397 0.261261 −0.125059 0.194705
  4 −0.256116 0.352810 0.141143 0.279706 −0.210620 0.259248 −0.098056 0.179990
  5 −0.262412 0.358638 0.118697 0.271887 −0.214122 0.265246 −0.072456 0.172661
  6 −0.265650 0.360325 0.090043 0.263318 −0.218028 0.272315 −0.048075 0.168086
  7 −0.266934 0.365008 −0.067175 0.260090 −0.224596 0.282196 −0.023128 0.173677
  8 −0.273952 0.377519 −0.041928 0.258647 −0.232629 0.293062 −0.000531 0.176806
  9 −0.280123 0.381968 −0.021108 0.262708 −0.236125 0.302083 0.027269 0.190739
  10 −0.285183 0.391290 0.004497 0.267634 −0.238413 0.310922 0.044912 0.203657
30 1 −0.367058 0.423423 −0.346283 0.406311 −0.332526 0.361491 −0.313657 0.343784
  2 −0.233677 0.306086 −0.198867 0.280012 −0.203455 0.236001 −0.163180 0.203230
  3 −0.202277 0.281503 −0.145618 0.241162 −0.170859 0.207468 −0.111717 0.161754
  4 −0.194424 0.275072 −0.115163 0.224526 −0.160246 0.199410 −0.084854 0.145930
  5 −0.191705 0.272356 −0.095073 0.217468 −0.159714 0.200465 −0.059819 0.134539
  6 −0.186870 0.272196 −0.070590 0.208597 −0.158702 0.202869 −0.043778 0.132887
  7 −0.191094 0.275374 −0.058550 0.205261 −0.161705 0.206226 −0.027194 0.130283
  8 −0.195662 0.280589 −0.036080 0.200329 −0.164468 0.212265 −0.010631 0.136358
  9 −0.196983 0.282040 −0.021144 0.202056 −0.165511 0.217222 −0.006685 0.138626
  10 −0.197171 0.283394 −0.005890 0.204787 −0.167152 0.220237 0.024904 0.145306
  11 −0.198853 0.286241 0.008492 0.207709 −0.173076 0.229318 0.039837 0.154215
  12 −0.204089 0.293653 0.022622 0.213445 −0.171555 0.232740 0.055108 0.163320
  13 −0.202908 0.298108 0.049154 0.220522 −0.176996 0.240454 0.070977 0.176787
  14 −0.205700 0.300842 0.061987 0.226574 −0.176922 0.244541 0.093001 0.193377
  15 −0.210699 0.305809 0.081431 0.238902 −0.177959 0.248760 0.109754 0.205539