The Slash Truncated Moyal Distribution: Its Properties and Applications

In this paper, we propose a new extension of the Moyal distribution to extend its applicability to positive-valued and heavy-tailed data that are widely observed in real-world applications, called the Slash Truncated Moyal distribution. The model is constructed by combining the concepts of a truncation and a slash type extension. The truncation is applied to obtain a positive valued random variable, and the slash extension is derived using the stochastic representation of the ratio of two independent random variables: the truncated Moyal distribution and a power of the standard uniform distribution. In our study, we derive various important properties of the proposed distribution such as moment-generating function, moments, skewness, and kurtosis. Moreover, we derive its parameter estimation via the maximum likelihood estimation method and investigate its performance via a simulation study. The results of our analysis indicate that the proposed distribution offers greater flexibility in terms of kurtosis than the original Moyal distribution and other modified models. Finally, the proposed distribution is applied to two real applications in medical sciences. The empirical results, compared with the original Moyal distribution, other modified Moyal distributions, and widely used heavy-tailed distributions, clearly demonstrate the superior goodness-of-fit of the proposed Slash Truncated Moyal distribution over competing distributions, highlighting its effectiveness and practical relevance.