A Method for Estimating and Testing the Distribution Parameters of an Asymmetric Distribution When a Large Number of Moment Estimates Are Available

Akio Torii
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Akio Torii: Chuo University, Institute of Economic Research

Chapter Chapter 2 in Production Efficiency with the Stochastic Management Model, 2026, pp 21-67 from Springer

Abstract: Abstract This chapter presents a method for identifying a distribution shape that can be considered uniform across the entire population, given that the population is divided into several subsets where the distribution shape is the same but the distribution parameters differ for each subset. This method uses the second-, third-, and fourth-order central moments of the samples constituting each subset. The distribution shape under analysis is a convolution of a specific asymmetric distribution and a symmetric normal distribution. The estimation method is described explicitly, and Monte Carlo experiments are conducted for testing specific distributions. These results provide the basis for setting up and performing tests throughout this book.

Date: 2026
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DOI: 10.1007/978-981-95-3501-9_2

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