The heavy-tailed chi-square model: properties, estimation and application to wind speed data

Abstract

In this article, we introduced an extension of the chi-square distribution by employing a slash-type methodology that enhanced the weight of the right tail, thereby producing a heavy-tailed distribution. We explored two different representations of the proposed distribution and examined several of its key properties, such as the mode, cumulative distribution function, reliability and hazard functions, moments, and the skewness and kurtosis coefficients. Additionally, we demonstrated that the classical chi-square distribution was a special case of our proposed model. Parameter estimation was carried out using both the method of moments and the maximum likelihood estimation, the latter via the expectation-maximization (EM) algorithm. A simulation study was conducted to evaluate the performance of parameter recovery. Finally, we applied the new distribution to a wind speed dataset, showing that it provided a good fit, particularly in the presence of extreme values.