Better performance for right-skewed data using an alternative gamma model

Table 1 Monte Carlo simulation results for the distribution of estimates from 10,000 iterations for the gamma scale (incorrect specification) and gamma shape (correct specification) models

Coefficient	Model	Mean	Standard Deviation	Mean Standard Error	Skewness (p value)	Kurtosis (p value)	Joint test p value^a
\({\theta _x}\)= 2	Scale	2.037	0.393	0.290	0.145 (0.000)	3.064 (0.189)	0.000
\({\theta _x}\)= 2	Shape	2.000	0.166	0.166	-0.016 (0.505)	2.935 (0.182)	0.328
\({\theta _{{x^2}}}\)= 0.05	Scale	0.036	0.163	0.141	-0.120 (0.000)	3.053 (0.272)	0.000
\({\theta _{{x^2}}}\)= 0.05	Shape	0.051	0.069	0.069	0.035 (0.151)	2.926 (0.124)	0.110
\({\theta _{Const}}\)= 1	Scale	0.978	0.210	0.126	-0.158 (0.000)	3.059 (0.228)	0.000
\({\theta _{Const}}\)= 1	Shape	0.998	0.099	0.099	-0.032 (0.188)	3.059 (0.225)	0.202

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