Assessing the Impact of Square Root Transformation on Weibull-Distributed Error Component of a Multiplicative Error Model
Onyemachi Chris Uchechi · Science Journal of Applied Mathematics and Statistics · 2021
This paper aims at determining if the assumed fundamental structure of the error component (unit mean and constant variance) is maintained after the square root transformation of a Weibull-distributed error component of a multiplicative model and also to investigate what happens to variance of the transformed and untransformed in terms of equality and non-equality. Considering the possibility that the error component of a Multiplicative Error Model (MEM) can be a Weibull distribution (W (σ, n)); σ and n are shape and scale parameters respectively) and the need for data transformation as a popular remedial measure to stabilize the variance of a data set prior to statistical modeling, this paper investigates the impact of the square root transformation on the mean and variance of a Weibull-distributed error component of a MEM. The mean and variance of W (σ, n) and those of the square root transformed distributions are calculated for σ= 6, 7,.., 99, 100 with the corresponding values of n for which the mean of the untransformed distribution is equal to one. The fitted MEM (2,0) under the square root transformation gave a better fit than the original fitted MEM (2,0). The paper concludes that the square-root transformation would yield better results as they reveal constancy in variance when using MEM with a Weibull-distributed error component and where data transformation is deemed necessary to stabilize the variance of the data set.