An extension of the generalized half-normal distribution

Olmos, Neveka M.; Varela, Héctor; Bolfarine, Heleno; Gómez, Héctor W.

doi:10.1007/s00362-013-0546-6

Cited by 25 publications

(26 citation statements)

References 18 publications

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“…In the literature, interesting studies on slash distributions are available considering both theoretical and practical viewpoints. For example, see Gómez et al [21], Genc [22], Punathumparambath [23], Olmos et al [15], Astorga et al [24], Korkmaz [25], Gómez et al [7] and references given in these studies for the univariate slash distribution. Additionally, see, for example, Arslan [26] and Arslan and Genc [27] in the context of multivariate slash distributions.…”

Section: The Slash and α-Monotone Distributionsmentioning

confidence: 99%

“…The α-GlogM distribution also converges to inverse generalized half-normal (invGHN) and inverse half-normal (invHN) distributions as limiting distributions. 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.…”

Section: Introductionmentioning

confidence: 99%

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An α-Monotone Generalized Log-Moyal Distribution with Applications to Environmental Data

Arslan

2021

Mathematics

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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.

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Section: The Slash and α-Monotone Distributionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An α-Monotone Generalized Log-Moyal Distribution with Applications to Environmental Data

Arslan

2021

Mathematics

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“…Cooray and Ananda [11] present the full details of this distribution. Several extensions of the generalised half-normal distribution have been proposed, among others, by Pescim et al [12], Olmos et al [44], Duarte Sanchez et al [45], and Ascitas [46].…”

Section: Conflicts Of Interestmentioning

confidence: 99%

Risk Analysis through the Half-Normal Distribution

2020

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We study the applicability of the half-normal distribution to the probability–severity risk analysis traditionally performed through risk matrices and continuous probability–consequence diagrams (CPCDs). To this end, we develop a model that adapts the financial risk measures Value-at-Risk (VaR) and Conditional Value at Risk (CVaR) to risky scenarios that face only negative impacts. This model leads to three risk indicators: The Hazards Index-at-Risk (HIaR), the Expected Hazards Damage (EHD), and the Conditional HIaR (CHIaR). HIaR measures the expected highest hazards impact under a certain probability, while EHD consists of the expected impact that stems from truncating the half-normal distribution at the HIaR point. CHIaR, in turn, measures the expected damage in the case it exceeds the HIaR. Therefore, the Truncated Risk Model that we develop generates a measure for hazards expectations (EHD) and another measure for hazards surprises (CHIaR). Our analysis includes deduction of the mathematical functions that relate HIaR, EHD, and CHIaR to one another as well as the expected loss estimated by risk matrices. By extending the model to the generalised half-normal distribution, we incorporate a shape parameter into the model that can be interpreted as a hazard aversion coefficient.

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“…Olivares-Pacheco et al [8] introduce slash-Weilbull distribution. Olmos et al [9,10] present slash half normal and slash generalized half normal distributions, respectively. Genc [11] obtains a skew extenstion of the slash distribution is using beta-normal distribution.…”

Section: Introductionmentioning

confidence: 99%