Analyzing Skewed Data with the Epsilon Skew Gamma Distribution

Examination of skewness makes academics more aware of the importance of accurate statistical analysis. Undoubtedly, most phenomena contain a certain percentage of skewness which resulted to the appearance of what is -called "asymmetry" and, consequently, the importance of the skew normal family . The epsilon skew normal distribution ESN (μ, σ, ε) is one of the probability distributions which provide a more flexible model because the skewness parameter provides the possibility to fluctuate from normal to skewed distribution. Theoretically, the estimation of linear regression model parameters, with an average error value that is not zero, is considered a major challenge due to having difficulties, as no explicit formula to calculate these estimates can be obtained. Practically, values for these estimates can be obtained only by referring to numerical methods. This research paper is dedicated to estimate parameters of the Epsilon Skew Normal General Linear Model (ESNGLM) using an adaptive least squares method, as along with the employment of the ordinary least squares method for estimating parameters of the General Linear Model (GLM). In addition, the coefficient of determination was used as a criterion to compare the models' preference. These methods were applied to real data represented by dollar exchange rates. The Matlab software was applied in this work and the results showed that the ESNGLM represents a satisfactory model.

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“…By equalizing all of the equations (11), (12), (13) and (14) to 0, the estimated formulas for , μ, σ, and ε are as follows:…”

Section: Epsilon Skew Normal General Linear Model (Esnglm)mentioning

confidence: 99%

“…The results showed that a linear equation produces satisfactory results. In 2013, Abdulah and Elsalloukh [13] studied the estimations of Epsilon Skew Gamma (ESΓ) and their application to data distributed in ESΓ [74]. In 2015, Mudholkar et al [3] introduced the M-Gaussian (M-G) distribution for a right-skewed data set.…”

Section: Introductionmentioning

confidence: 99%

Least Squares Estimations for the General Linear Model Parameters with Epsilon Skew Normal Error Term

Nashoor

Abdulah

2020

eijs

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“…A variable transformation

is applied to get the α power of Gamma distribution. Here, the random variables Y and T are independent [ 5 , 29 ] . After applying this transformation on gamma distribution in Equation ( 1 ), we will get the following PDF:

where the parameters

and

[ 29 ].…”

Section: Gamma Distribution: Reparametrization and Abep Distributimentioning

confidence: 99%

“…The proposed distributions are in [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 ] and references therein via using different generating techniques [ 27 ] to get a probability density function (PDF). In these distributions,

-skew form of gamma distribution on the real line was proposed by [ 5 , 6 ]. The deficiency of these functions is that different height and shape of peakedness around location on the real line cannot be modelled separately.…”

Section: Introductionmentioning

confidence: 99%

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Asymmetric Bimodal Exponential Power Distribution on the Real Line

Çankaya

2018

Entropy

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Abstract:The asymmetric bimodal exponential power (ABEP) distribution is an extension of the generalized gamma distribution to the real line via adding two parameters that fit the shape of peakedness in bimodality on the real line. The special values of peakedness parameters of the distribution are a combination of half Laplace and half normal distributions on the real line. The distribution has two parameters fitting the height of bimodality, so capacity of bimodality is enhanced by using these parameters. Adding a skewness parameter is considered to model asymmetry in data. The location-scale form of this distribution is proposed. The Fisher information matrix of these parameters in ABEP is obtained explicitly. Properties of ABEP are examined. Real data examples are given to illustrate the modelling capacity of ABEP. The replicated artificial data from maximum likelihood estimates of parameters of ABEP and other distributions having an algorithm for artificial data generation procedure are provided to test the similarity with real data. A brief simulation study is presented.

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