In the present paper, we introduce a new lifetime distribution based on the general odd hyperbolic cosine-FG model. Some important properties of proposed model including survival function, quantile function, hazard function, order statistic are obtained. In addition estimating unknown parameters of this model will be examined from the perspective of classic and Bayesian statistics. Moreover, an example of real data set is studied; point and interval estimations of all parameters are obtained by maximum likelihood, bootstrap (parametric and non-parametric) and Bayesian procedures. Finally, the superiority of proposed model in terms of parent exponential distribution over other fundamental statistical distributions is shown via the example of real observations.
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.
Kharazmi and Saadatinik [21] introduced a new family of distribution called hyperbolic cosine-F (HCF) distributions. They studied some properties of this model and obtained the estimates of its parameters by different methods. In this paper, it is focused on a special case of HCF family with Weibull distribution as a baseline model. Various properties of the proposed distribution including explicit expressions for the moments, quantiles, moment generating function, failure rate function, mean residual lifetime, order statistics and expression of the entropies are derived. Superiority of this model is proved in some simulations and applications.
A new family of lifetime distributions is introduced via distribution of the upper record values, the well-known concept in survival analysis and reliability engineering. Some important properties of the proposed model including quantile function, hazard function, order statistics are obtained in a general setting. A special case of this new family is proposed by considering the exponential and Weibull distribution as the parent distributions. In addition estimating unknown parameters of specialized distribution is examined from the perspective of the traditional statistics. A simulation study is presented to investigate the bias and mean square error of the maximum likelihood estimators. Moreover, one 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 known distributions is shown via the example of real observations. 2020 Mathematics Subject Classi…cation. 62E15.
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