Recurrence Relations for Marginal and Joint Moment Generating Functions of Topp-Leone Generated Exponential Distribution based on Record Values and its Characterization

Anwar, Zaki; Gupta, Neetu; Khan, Masood Alam; Azhad, Qazi J.

doi:10.22237/jmasm/1571545660

Cited by 5 publications

(2 citation statements)

References 13 publications

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“…For excellent understanding of records, one may refer to books written by Ahsanullah [11], Ahsanullah [12], and Arnold [13]. For application of record values in various disciplines, one may refer to Minimol and Thomas [14], Ahsanullah [15], itekhan2016umvu, Bdair and Raqab [16], MirMostafaee et al [17], Ahsanullah and Nevzorov [18], Arshad and Jamal [19], Arshad and Baklizi [20], Anwar [21], and Arshad and Jamal [22]. Now we discuss the mathematical definition of records and its distribution.…”

Section: Introductionmentioning

confidence: 99%

Statistical Inference for Topp–Leone-generated Family of Distributions Based on Records

Arshad¹,

Azhad²

2019

JSTA

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In this paper, we consider a general family of distributions generated by Topp-Leone distribution (known as TL family of distributions) proposed by Rezaei et al. [1]. We consider the problem of estimation of the shape parameter, scale parameter, and reliability function based on record data from TL family of distributions. We derive the maximum likelihood estimator (MLE) for shape parameter, scale parameter, and reliability function. We have also obtained UMVUE (uniformly minimum-variance unbiased estimator) for reliability function when scale parameter is known. A Bayesian study is carried out under symmetric and asymmetric loss functions in order to find the Bayes estimators for unknown parameters and reliability function. Further, we have predicted future record values using Bayesian approach. A numerical comparison of various estimators is also reported.

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Section: Introductionmentioning

confidence: 99%

Statistical Inference for Topp–Leone-generated Family of Distributions Based on Records

Arshad¹,

Azhad²

2019

JSTA

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“…. , r n ) is the observed value of R. For a sufficient reading of record values see the books: Ahsanullah (1995) and Arnold et al (1998) and for their applications, recent research papers: Belaghi et al (2015), Kizilaslan and Nadar (2016), Singh et al (2017), Arshad and Jamal (2018), Arshad and Baklizi (2018), Anwar et al (2019), Arshad and Jamal (2019c) and Arshad and Jamal (2019b). Statistical research on stress-strength reliability based on record values is growing and various authors have derived results based on such problems.…”

Section: Introductionmentioning

confidence: 99%

Multicomponent stress strength reliability estimation for Pareto distribution based on upper record values

Jamal,

Arshad,

Khandelwal

2019

Preprint

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In this article, inferences about the multicomponent stress strength reliability are drawn under the assumption that strength and stress follow independent Pareto distribution with different shapes (α 1 , α 2 ) and common scale parameter θ. The maximum likelihood estimator, Bayes estimator under squared error and Linear exponential loss function, of multicomponent stress-strength reliability are constructed with corresponding highest posterior density interval for unknown θ. For known θ, uniformly minimum variance unbiased estimator and asymptotic distribution of multicomponent stress-strength reliability with asymptotic confidence interval is discussed. Also, various Bootstrap confidence intervals are constructed. A simulation study is conducted to numerically compare the performances of various estimators of multicomponent stress-strength reliability. Finally, a real life example is presented to show the applications of derived results in real life scenarios.

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Statistical inference of reliability in multicomponent stress strength model for pareto distribution based on upper record values

Azhad

Arshad

Khandelwal

2021

International Journal of Modelling and Simulation

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Recurrence Relations for Marginal and Joint Moment Generating Functions of Topp-Leone Generated Exponential Distribution based on Record Values and its Characterization

Cited by 5 publications

References 13 publications

Statistical Inference for Topp–Leone-generated Family of Distributions Based on Records

Statistical Inference for Topp–Leone-generated Family of Distributions Based on Records

Multicomponent stress strength reliability estimation for Pareto distribution based on upper record values

Statistical inference of reliability in multicomponent stress strength model for pareto distribution based on upper record values

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