Classical and Bayesian Estimations on the Kumaraswamy Distribution using Grouped and Un-grouped Data under Difference Loss Functions

Gholizadeh, Ramin; Shirazi, Aliakbar Mastani; Mosalmanza, Samira

doi:10.3923/jas.2011.2154.2162

Cited by 12 publications

(12 citation statements)

References 8 publications

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“…Grag [3] derived the distribution of single order statistics, the joint distribution of two order statistics and the distribution of the product and the quotient of two order statistics when the random variables are independent and identically Kum-distributed. Golizadeh et al [4] obtained non-Bayesian and Bayesian estimation for the parameters of the Kum distribution. Moreover, non-Bayesian and Bayesian approaches are used to obtain point and interval estimation of the shape parameters, the reliability and the hazard rate functions of the Kum distribution based on generalized order statistics [5].…”

Section: Original Research Articlementioning

confidence: 99%

Kumaraswamy Distribution Based on Alpha Power Transformation Methods

Hozaien¹,

Dayian²,

EL-Helbawy³

2021

AJPAS

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In this paper, the alpha power Kumaraswamy distribution, new alpha power transformed Kumaraswamy distribution and new extended alpha power transformed Kumaraswamy distribution are presented. Some statistical properties of the three distributions are derived including quantile function, moments and moment generating function, mean residual life and order statistics. Estimation of the unknown parameters based on maximum likelihood estimation are obtained. A simulation study is carried out. Finally, a real data set is applied.

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Section: Original Research Articlementioning

confidence: 99%

Kumaraswamy Distribution Based on Alpha Power Transformation Methods

Hozaien¹,

Dayian²,

EL-Helbawy³

2021

AJPAS

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“…However, it has a closed-form cumulative distribution function which is invertible and for which the moments do exist. The KumD method was widely applied for testing natural phenomena such as test scores, temperatures and daily hydrological data of rain fall, [9][10][11][12]. After that, Abd Al-Fattah [13] derived the inversion of KumD by using the transformation ; KumD (α ,β ) [8].…”

Section: Inverted Kumaraswamy Distributionmentioning

confidence: 99%

On Estimation of P(Y_1<X<Y_2 ) in Cased Inverse Kumaraswamy Distribution

Hameed

Salman

Kalaf

2020

eijs

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This paper deals with the estimation of the stress strength reliability for a component which has a strength that is independent on opposite lower and upper bound stresses, when the stresses and strength follow Inverse Kumaraswamy Distribution. D estimation approaches were applied, namely the maximum likelihood, moment, and shrinkage methods. Monte Carlo simulation experiments were performed to compare the estimation methods based on the mean squared error criteria.

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“…The distribution is appropriate to natural phenomena whose outcomes are bounded from both sides, such as the individuals' heights, test scores, temperatures and hydrological daily data of rain fall (for more details, see Kumaraswamy [6], Jones [7], Golizadeh et al [8], Sindhu et al [9] and Sharaf El-Deen et al [10]). …”

Section: Introductionmentioning

confidence: 99%

Generalized Inverted Kumaraswamy Distribution: Properties and Application

Iqbal¹,

Tahir²,

Riaz³

et al. 2017

OJS

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The techniques to find appropriate new models for data sets are very popular nowadays among the researchers of this area where existed models in the literature are not suitable. In this paper, a new distribution, generalized inverted Kumaraswamy (GIKum) distribution is introduced. The main aims of this research are to develop a general form of inverted Kumaraswamy (IKum) distribution which is flexible than the IKum distribution and all of its related and sub models. Some properties of GIKum distribution such as measures of central tendency and dispersion, models of stress-strength, limiting distributions, characterization of GIKum distribution and related probability distributions through some specific transformations are derived. The mathematical expressions of reliability function (r.f) and the hazard rate function (hrf) of the GIKum distribution are found and presented through their graphs. The parameters estimation through the maximum likelihood (ML) estimation method is used and the results are applied to the data set of prices of wooden toys of 31 children.

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Classical and Bayesian Estimations on the Kumaraswamy Distribution using Grouped and Un-grouped Data under Difference Loss Functions

Cited by 12 publications

References 8 publications

Kumaraswamy Distribution Based on Alpha Power Transformation Methods

Kumaraswamy Distribution Based on Alpha Power Transformation Methods

On Estimation of P(Y_1<X<Y_2 ) in Cased Inverse Kumaraswamy Distribution

Generalized Inverted Kumaraswamy Distribution: Properties and Application

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