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Table 2 The MLEs and goodness-of-fit statistics for the famous Old Faithful Eruption data

From: On generating T-X family of distributions using quantile functions

  Five-parameter NW{C} Mixture-normala Four-parameter NW{C} Beta-normal
MLE (SEb) μ ^ = 1.883 (0.447) μ ^ 1 = 4.273 (0.034) μ ^ = 0.644 (0.288) μ ^ = 3.163 (0.007)
σ ^ = 5.156 (0.645) σ ^ 1 = 0.437 (0.027) σ ^ = 3.756 (0.438) σ ^ = 0.238 (0.001)
c ^ = 2.032 (0.150) μ ^ 2 = 2.019 (0.026) c ^ = 3.899 (0.168) a ^ = 0.083 (0.007)
γ ^ = 1.885 (0.116) σ ^ 2 = 0.236 (0.023) γ ^ = 3.623 (0.031) b ^ = 0.060 (0.004)
δ ^ = 1.343 (0.060) p ^ = 0.652 (0.029)
Log-likelihood -270.0 -276.35 -292.3 -372.566
AIC 550.0 562.7 592.6 753.1
K-S statistic 0.042 0.049 0.075 0.151
p-value 0.712 0.539 0.096 8.908e-06
  1. aMixture normal is defined as pN(μ1, σ1) + (1 - p)N(μ2, σ2); bSE: standard error of the MLE.