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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.