Abstract
Modeling environmental data plays a crucial role in explaining environmental phenomena. In some cases, well-known distributions, e.g., Weibull, inverse Weibull, and Gumbel distributions, cannot model environmental events adequately. Therefore, many authors tried to find new statistical distributions to represent environmental phenomena more accurately. In this paper, an α-monotone generalized log-Moyal (α-GlogM) distribution is introduced and some statistical properties such as cumulative distribution function, hazard rate function (hrf), scale-mixture representation, and moments are derived. The hrf of the α-GlogM distribution can form a variety of shapes including the bathtub shape. The α-GlogM distribution converges to generalized half-normal (GHN) and inverse GHN distributions. It reduces to slash GHN and α-monotone inverse GHN distributions for certain parameter settings. Environmental data sets are used to show implementations of the α-GlogM distribution and also to compare its modeling performance with its rivals. The comparisons are carried out using well-known information criteria and goodness-of-fit statistics. The comparison results show that the α-GlogM distribution is preferable over its rivals in terms of the modeling capability.
Highlights
Modeling environmental data plays a crucial role in explaining environmental phenomena
Gómez et al [1] obtained a general family of skew-symmetric distributions generated by the cumulative distribution function of the normal distribution
The α-monotone generalized log-Moyal (α-generalized form of the log-Moyal (GlogM)) distribution becomes the slash halfnormal (SHN) distribution proposed by Olmos et al [14] and slash generalized half-normal (SGHN) distribution introduced by Olmos et al [15] under the particular transformation of a random variable and parameters settings
Summary
Modeling environmental data plays a crucial role in explaining environmental phenomena. In determining a baseline distribution, the attention is given to the distributions having a lower number of parameters while providing flexibility for modeling purposes In this context, the Moyal distribution, introduced by Moyal in 1955, has drawn the attention of statisticians in recent years, and it has been widely used in physics for many years. Bahti and Ravi [8] introduced a generalized form of the log-Moyal (GlogM) distribution. The Moyal distribution and its extensions/generalizations have been studied by the limited number of studies in the context of statistics. The α-GlogM distribution becomes the slash halfnormal (SHN) distribution proposed by Olmos et al [14] and slash generalized half-normal (SGHN) distribution introduced by Olmos et al [15] under the particular transformation of a random variable and parameters settings.
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