Odd Hyperbolic Cosine Exponential-Exponential (OHC-EE) Distribution

Kharazmi, Omid; Saadatinik, Ali; Jahangard, Shahla

doi:10.1007/s40745-019-00200-z

Cited by 22 publications

(14 citation statements)

References 6 publications

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“…For more detail, we refer to [15][16][17][18]. Next, we provide a Bayesian estimation approach for estimating the parameters of NG-Weibull distribution via analyzing complete sample data.…”

Section: Plos Onementioning

confidence: 99%

New generalized-X family: Modeling the reliability engineering applications

et al. 2021

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As is already known, statistical models are very important for modeling data in applied fields, particularly in engineering, medicine, and many other disciplines. In this paper, we propose a new family to introduce new distributions suitable for modeling reliability engineering data. We called our proposed family a new generalized-X family of distributions. For the practical illustration, we introduced a new special sub-model, called the new generalized-Weibull distribution, to describe the new family’s significance. For the proposed family, we introduced some mathematical reliability properties. The maximum likelihood estimators for the parameters of the new generalized-X distributions are derived. For assessing the performance of these estimators, a comprehensive Monte Carlo simulation study is carried out. To assess the efficiency of the proposed model, the new generalized-Weibull model is applied to the coating machine failure time data. Finally, Bayesian analysis and performance of Gibbs sampling for the coating machine failure time data are also carried out. Furthermore, the measures such as Gelman-Rubin, Geweke and Raftery-Lewis are used to track algorithm convergence.

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“…For more detail, we refer to [15][16][17][18]. Next, we provide a Bayesian estimation approach for estimating the parameters of NG-Weibull distribution via analyzing complete sample data.…”

Section: Plos Onementioning

confidence: 99%

New generalized-X family: Modeling the reliability engineering applications

et al. 2021

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“…Motivated by idea of Alzaatreh et al [2], a new class of statistical distributions is proposed. The new model is constructed by applying Alzaattreh idea to the HCF family of lifetime distributions that recently have seen proposed by Kharazmi and Saadatinik [7]. According to Kharazmi and Saadatinik [7] a random variable X has a HCF distribution if its CDF is given by…”

Section: New General Model and Its Propertiesmentioning

confidence: 99%

“…i. Hyperbolic Cosine-Exponential distribution (HCE)[7]. The two-parameter HCE density function is given byf (x; a, ) = 2a e a e 2a − 1 e − x cosh ( a ( 1 − e − x )) ; x > 0.where a > 0 and > 0.ii.…”

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confidence: 99%

Odd Hyperbolic Cosine-FG Family of Lifetime Distributions

Kharazmi¹,

Saadatinik²,

Alizadeh³

et al. 2019

JSTA

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In the present paper, a new family of lifetime distributions is introduced via odd ratio function, the well-known concept in survival analysis and reliability engineering. Some important properties of the proposed model including survival function, quantile function, hazard function, order statistic are obtained in a general setting. A special case of this new family is taken up by considering exponential and Lindley models as the parent distributions. In addition, estimation of the unknown parameters of the special model will be examined from the perspective of the classic statistics. A simulation study is presented to investigate the bias and mean square error of the maximum likelihood estimators. Moreover, an example of real data set is studied; point and interval estimations of all parameters are obtained by maximum likelihood and bootstrap (parametric and non-parametric) procedures. Finally, the superiority of the proposed model in terms of the parent exponential distribution over other fundamental statistical distributions is shown via the example of real observations.

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“…The modification of trigonometric functions to give new statistical distributions is be-coming a popular technique in the literature, and for examples see [1][2][3][4][5][6]. In Kumar D, et al [1], they transformed the sine function into a new statistical distribution called SS transformation with the following CDF…”

Section: Introductionmentioning

confidence: 99%