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Abstract

In the examination of the mean parameter of the skewed distributions, testing methods often rely on the central limit theorem and data transformation. Notably, Johnson’s and Chen’s modified ttests offer reliable alternatives by incorporating additional sample moments. This work directs its attention towards the truncated saddlepoint (TS) approximation method, which effectively estimates the right-tail probability of right-skewed continuous distributions using a limited number of sample moments. The TS approximation is employed to derive the p-value in one-sample mean testing. To evaluate its performance, a Monte Carlo simulation study is conducted, comparing the TS approximation at four distinct truncation levels with the traditional t-test and its alternatives. The findings indicate that the fifth-order truncation and Chen’s method exhibit better performance for highly skewed distributions, particularly when the sample size is small. Furthermore, a numerical example is provided to illustrate the practical application of the TS approximation and its competitors.

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