A generalized skew two-piece skew-normal distribution

Jamalizadeh, Ahad; Arabpour, Alireza

doi:10.1007/s00362-009-0240-x

Cited by 27 publications

(13 citation statements)

References 14 publications

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“…A generalised two‐piece skew normal distribution was introduced by Jamalizadeh et al (), through a standard bivariate normal distribution with correlation ρ . The density in this case is given by

f_{δ, λ, ρ} false(y false) = \frac{c^{*} false(δ, λ, ρ false)}{\sum} ϕ ((), \frac{y - μ}{\sum}) {normalΦ}_{2} ((), \frac{δ false(y - μ false)}{\sum}, \frac{λ false| y - μ false|}{\sum}, ρ), δ, λ, y \in double-struckR,

where

c^{*} false(δ, λ, ρ false) = false(4 π false) {({}, \cos^{- 1} ((), \frac{- false(ρ + δ λ false)}{\sqrt{1 + δ^{2}} \sqrt{1 + λ^{2}}}) + \cos^{- 1} ((), \frac{- false(ρ - δ λ false)}{\sqrt{1 + δ^{2}} \sqrt{1 + λ^{2}}}) + 2 \tan^{- 1} false(λ false))}^{- 1}

and Φ 2 (.,.…”

Section: Quantile‐based Asymmetric Normal Densitiesmentioning

confidence: 99%

On Quantile‐based Asymmetric Family of Distributions: Properties and Inference

Gijbels

Karim

Verhasselt

2019

Int Statistical Rev

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Summary In this paper, we provide a detailed study of a general family of asymmetric densities. In the general framework, we establish expressions for important characteristics of the distributions and discuss estimation of the parameters via method‐of‐moments as well as maximum likelihood estimation. Asymptotic normality results for the estimators are provided. The results under the general framework are then applied to some specific examples of asymmetric densities. The use of the asymmetric densities is illustrated in a real‐data analysis.

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f_{δ, λ, ρ} false(y false) = \frac{c^{*} false(δ, λ, ρ false)}{\sum} ϕ ((), \frac{y - μ}{\sum}) {normalΦ}_{2} ((), \frac{δ false(y - μ false)}{\sum}, \frac{λ false| y - μ false|}{\sum}, ρ), δ, λ, y \in double-struckR,

where

c^{*} false(δ, λ, ρ false) = false(4 π false) {({}, \cos^{- 1} ((), \frac{- false(ρ + δ λ false)}{\sqrt{1 + δ^{2}} \sqrt{1 + λ^{2}}}) + \cos^{- 1} ((), \frac{- false(ρ - δ λ false)}{\sqrt{1 + δ^{2}} \sqrt{1 + λ^{2}}}) + 2 \tan^{- 1} false(λ false))}^{- 1}

and Φ 2 (.,.…”

Section: Quantile‐based Asymmetric Normal Densitiesmentioning

confidence: 99%

On Quantile‐based Asymmetric Family of Distributions: Properties and Inference

Gijbels

Karim

Verhasselt

2019

Int Statistical Rev

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“…The data was collected at the Australian Institute of Sport. It has been previously used and analyzed by (Jamalizadeh et al, 2011;Choudhury and Abdul Matin, 2011;Al-Aqtash et al, 2014). The data is as follows: 148.9, 149.0, 156.0, 156.9, 157.9, 158.9, 162.0, 162.0, 162.5, 163.0, 163.9, 165.0, 166.1, 166.7, 167.3, 167.9, 168.0, 168.6, 169.1, 169.8, 169.9, 170.0, 170.0, 170.3, 170.8, 171.1, 171.4, 171.4, 171.6, 171.7, 172.0, 172.2, 172.3, 172.5, 172.6, 172.7, 173.0, 173.3, 173.3, 173.5, 173.6, 173.7, 173.8, 174.0, 174.0, 174.0, 174.1, 174.1, 174.4, 175.0, 175.0, 175.0, 175.3, 175.6, 176.0, 176.0, 176.0, 176.0, 176.8, 177.0, 177.3, 177.3, 177.5, 177.5, 177.8, 177.9, 178.0, 178.2, 178.7, 178.9, 179.3, 179.5, 179.6, 179.6, 179.7, 179.7, 179.8, 179.9, 180.2, 180.2, 180.5, 180.5, 180.9, 181.0, 181.3, 182.1, 182.7, 183.0, 183.3, 183.3, 184.6, 184.7, 185.0, 185.2, 186.2, 186.3, 188.7, 189.7, 193.4, 195.9. The data is summarized in Table 3 and the performances of the competing distributions are given in Table 4.…”

Section: Data Set Imentioning

confidence: 99%

A Comparative Analysis on the Performance of the Convoluted Exponential Distribution and the Exponential Distribution in Terms of Flexibility

Owoloko¹,

Oguntunde²,

Adejumo³

2016

Journal of Mathematics and Statistics

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Abstract:In this article, the convoluted exponential distribution which was derived as the sum of two independent exponentially distributed random variables was compared with the exponential distribution in terms of flexibility when applied to four real data sets. The idea is to verify if the convoluted exponential distribution would perform better than the exponential distribution in modeling real life situations. Some other basic statistical properties of the convoluted exponential distribution were also identified.

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“…Jamalizadeh et al (2011) used the heights for the 100 female athletes and the hemoglobin concentration levels for the 202 athletes to illustrate the application of a generalized skew two-piece skew-normal distribution. Choudhury and Abdul Matin (2011) also used percentage of the hemoglobin blood cell for the male athletes to illustrate the application of an extended skew 216 generalized normal distribution.…”

Section: Australian Athletes' Datamentioning

confidence: 99%

Gumbel-Weibull Distribution: Properties and Applications

Lee

Al-Aqtash

Famoye

2014

J. Mod. App. Stat. Meth.

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Some properties of the Gumbel-Weibull distribution including the mean deviations and modes are studied. A detailed discussion of regions of unimodality and bimodality is given. The method of maximum likelihood is proposed for estimating the distribution parameters and a simulation is conducted to study the performance of the method. Three tests are given for testing the significance of a distribution parameter. The applications of GumbelWeibull distribution are emphasized. Five data sets are used to illustrate the flexibility of the distribution in fitting unimodal and bimodal data sets.

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A generalized skew two-piece skew-normal distribution

Abstract: Skew-normal distribution, Generalized skew-normal distribution, Two-piece skew-normal distribution, Generalized two-piece skew-normal distribution, Generalized skew two-piece skew-normal distribution, Unimodality and bimodality, Orthant probability,

Cited by 27 publications

References 14 publications

On Quantile‐based Asymmetric Family of Distributions: Properties and Inference

On Quantile‐based Asymmetric Family of Distributions: Properties and Inference

A Comparative Analysis on the Performance of the Convoluted Exponential Distribution and the Exponential Distribution in Terms of Flexibility

Gumbel-Weibull Distribution: Properties and Applications

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