Bayesian inference of Unit Gompertz distribution based on dual generalized order statistics

Arshad, Mohd Anuar; Azhad, Qazi J.; Gupta, Neetu; Pathak, Ashutosh

doi:10.1080/03610918.2021.1943441

Cited by 13 publications

(8 citation statements)

References 28 publications

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“…For detailed discussion about the order and record statistics and their application, the readers refer Chandler (1952), Arnold et al (1992), Arnold et al (1998), Ahsanullah (1995), David and Nagaraja (2003), Khan and Arshad (2016), Arshad and Baklizi (2019), , , Arshad et al (2021), Azhad et al (2021). Let X 1 , X 2 , .…”

Section: Order Statistics and Record Statisticsmentioning

confidence: 99%

A New Nadarajah-Haghighi Distribution with Applications

Kumar,

Chakraborty,

Arshad

et al. 2024

Preprint

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We propose a new Nadarajah-Haghighi (NH) distribution by applying the record transmutation function to the NH distribution for enhanced flexibility in data modeling. We discuss the shape of the probability density function and hazard function. Furthermore, we obtain quantile function, moments and moment generating function of the distribution. Moreover, we study various estimators for the parameters, such as maximum likelihood estimators, ordinary least squares and weighted least squares estimators, Anderson-Darling estimators, and Cram´er-von Mises estimators. The biases and mean squared errors of these estimators are thoroughly examined through Monte Carlo simulation studies. To demonstrate the practical application of the proposed distribution, two real data analysis are considered. The results highlight the effectiveness of the proposed distribution in modeling real-life data, with the model exhibiting superior fitting performance compared to other competing models.

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Section: Order Statistics and Record Statisticsmentioning

confidence: 99%

A New Nadarajah-Haghighi Distribution with Applications

Kumar,

Chakraborty,

Arshad

et al. 2024

Preprint

Self Cite

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“…More details about Bayesian computation methods can refer to Albert. 22 For more research on Bayes method, Arshad et al, 23 Bai et al, 10 and Azhad et al 24 are recommended.…”

Section: Bayesian Estimationmentioning

confidence: 99%

“…More details about Bayesian computation methods can refer to Albert. 22 For more research on Bayes method, Arshad et al, 23 Bai et al, 10 and Azhad et al 24 are recommended. When selecting the prior distribution of parameters, the conjugate prior distribution is often the first choice.…”

Section: Bayesian Estimationmentioning

confidence: 99%

Inference for cumulative risk model under step-stress experiments and its application in nanocrystalline data

Qiao

Gui

2022

Proceedings of the Institution of Mechanical Engineers, Part O:

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With the popularity of step-stress accelerated life testing, researchers are exploring more possibilities for models that relate the life distributions under different stress levels. Cumulative risk model assumes that the effects of stress changes have a lag period before they are fully observed, which guarantees the continuity of the hazard rate function. This paper studies the cumulative risk model for Lomax distribution with step-stress experiments. For maximum likelihood estimation, Newton-Rapson method is adopted to get point estimates. Meanwhile, the asymptotic normality of the maximum likelihood estimator is used to obtain asymptotic confidence intervals. For Bayesian estimation, point estimates and highest posterior density credible intervals under squared error loss function with informative prior and non-informative prior are derived using Metropolis-Hastings method and Metropolis-Hastings within Gibbs algorithm. To evaluate the effects of stress change time and the length of lag period, as well as the performance of different methods, numerical simulations are conducted. Then a real nanocrystalline data set is analyzed.

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“…For more details, the readers are advised to see, Chandler (1952), Arnold et al (1992Arnold et al ( , 1998, Ahsanullah (1995), David and Nagaraja. (2003), Khan and Arshad (2016), Arshad and Baklizi (2019), Jamal (2019a, 2019b), Arshad et al (2021), Azhad et al (2021). Let X 1 , X 2 , .…”

Section: Order and Record Statisticsmentioning

confidence: 99%

Record-Based Transmuted Generalized Linear Exponential Distribution with Increasing, Decreasing and Bathtub Shaped Failure Rates

Arshad¹,

Khetan²,

Kumar³

et al. 2021

Preprint

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The linear exponential distribution is a generalization of the exponential and Rayleigh distributions. This distribution is one of the best models to fit data with increasing failure rate (IFR). But it does not provide a reasonable fit for modeling data with decreasing failure rate (DFR) and bathtub shaped failure rate (BTFR). To overcome this drawback, we propose a new record-based transmuted generalized linear exponential (RTGLE) distribution by using the technique of Balakrishnan and He (2021). The family of RTGLE distributions is more flexible to fit the data sets with IFR, DFR, and BTFR, and also generalizes several well-known models as well as some new record-based transmuted models. This paper aims to study the statistical properties of RTGLE distribution, like, the shape of the probability density function and hazard function, quantile function and its applications, moments and its generating function, order and record statistics, Rényi entropy. The maximum likelihood estimators, least squares and weighted least squares estimators, Anderson-Darling estimators, Cramér-von Mises estimators of the unknown parameters are constructed and their biases and mean squared errors are reported via Monte Carlo simulation study. Finally, the real data set based on failure time illustrates the goodness of fit and applicability of the proposed distribution; hence, suitable recommendations are forwarded.

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Bayesian inference of Unit Gompertz distribution based on dual generalized order statistics

Cited by 13 publications

References 28 publications

A New Nadarajah-Haghighi Distribution with Applications

A New Nadarajah-Haghighi Distribution with Applications

Inference for cumulative risk model under step-stress experiments and its application in nanocrystalline data

Record-Based Transmuted Generalized Linear Exponential Distribution with Increasing, Decreasing and Bathtub Shaped Failure Rates

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