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The Effect of Inverse Transformation on the Unit Mean and Constant Variance Assumptions of a Multiplicative Error Model Whose Error Component has a Gamma Distribution.

机译:逆变换对其误差分量具有伽马分布的乘法误差模型的单位均值和恒定方差假设的影响。

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In this paper, the effect of inverse transformation on the unit mean and constant variance assumptions of a multiplicative error model whose error component is Gamma distributed was studied. From the results of the study, it was discovered that the unit mean assumption is violated after inverse transformation. The mean and variance of the inverse-transformed gamma error component were found to be smaller than those of the untransformed error. Furthermore this decrease in mean, was modeled and was found to increase per unit increase in ?, the shape parameter while that of the variance was found to decrease per unit increase in the shape parameter and their relationships (predictive equations) were determined. Finally, it was discovered that in order to achieve the unit mean condition after inverse transformation, the condition is unavoidable, where ? and ? are respectively the shape and location parameters of the Gamma distribution, otherwise inverse transformation would not be successful.
机译:本文研究了逆变换对误差分量为Gamma分布的乘法误差模型的单位均值和常数方差假设的影响。根据研究结果,发现逆变换后违反了单位均值假设。发现逆变换的伽马误差分量的均值和方差小于未变换的伽马误差分量的均值和方差。此外,对这种均值下降进行了建模,发现形状参数每单位增加而增加,而形状参数方差每单位增加而减少,并确定了它们的关系(预测方程)。最后,发现为了获得逆变换后的单位均值条件,该条件不可避免。和?分别是Gamma分布的形状和位置参数,否则逆变换将不会成功。

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