A Goodness of Fit Test for Non-Gaussian Distributions with Unknown Location and Scale Parameters

TL;DR

This paper develops and compares goodness-of-fit tests for non-Gaussian distributions with unknown parameters, demonstrating improved power and computational methods through simulation studies.

Contribution

It introduces a new goodness-of-fit test with better statistical power and computational techniques for non-Gaussian distributions with unknown location and scale.

Findings

The proposed test outperforms existing tests in power.

Simulation results confirm the effectiveness of the new test.

The paper provides computational methods for the test implementation.

Abstract

This paper studies computational aspects of an asymptotically distribution-free goodness-of-fit test for non-Gaussian distributions based on the Khmaladze martingale transformation when the location and scale parameters of the distribution are unknown. On top of that, we propose another goodness-of-fit test better than existing one in terms of a statistical power. Simulation studies demonstrate that the proposed test compares favorably with the existing test.