Simulation estimation of goodness-of-fit test for right skewed distributions

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Asian Network for Scientific Information
Objective: This study derives a goodness-of-fit test based on chi-square statistic using simulation and examines the values of the χ2 test statistic behavior with the level of skewness for two different distributions, namely chi-square and inverse Gaussian. Methodology: For this purpose, simulation estimation was conducted to generate random numbers from different skewed distributions. Different sample sizes and skewness values were considered and the corresponding values of the χ2 test statistic were derived. Results: The results show a statistically significant evidence for an inverse relationship between the value of χ2 test and the level of skewness for all distributions, i.e. the value of χ2 test statistic decreases as the value of skewness increases and vice versa. The research results also show that the method, estimation by simulation, produces an estimator which is shown to have asymptotic assumed distribution with large sample size. Conclusion: These results are relevant to theories in which shape and skewness measure can be used to determine the validity of the assumed right skewed distribution to fit the data well. The results also have practical implications for portfolio managers who are managing funds to optimize risk-adjusted performance and individual investors who prefer positive skewness in rates of return. © 2017 Rafida M. Elobaid and Elgilani Elshareif.
This article is licensed under Creative Commons License and full text is openly accessible in CUD Digital Repository. The version of the scholarly record of this article is published in Asian Journal of Scientific Research (2017), accessible online through this link
Chi-square test statistic, Goodness-of-fit test, Inverse Gaussian distribution, Right skewed distributions, Shape parameter, Simulation, Skewness measure, χ2 distribution
Elobaid, R. M., & Elshareif, E. (2017). Simulation estimation of goodness-of-fit test for right skewed distributions. Asian Journal of Scientific Research, 10(1), 56–59.