The Inverse Moyal Distribution and Its Properties
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Abstract
In this paper, we introduce a new extension of the Moyal distribution, called the inverse Moyal (IMoyal) distribution, for heavy-tailed distribution. We derive its important statistical properties, such as the probability density function, cumulative distribution function, survival function, hazard function, and cumulative hazard function. Furthermore, we provide the formula for maximum likelihood estimation and perform simulation studies to assess its performance. Finally, we apply the IMoyal distribution to two real-world datasets: an automobile insurance premium data and a commercial bank asset data of Thailand. The analyses show that the proposed distribution demonstrates a superior fit to the data compared to existing distributions.
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