On improved accelerated sequential estimation of the mean of an inverse Gaussian distribution

Joshi, N. J.; Bapat, Sudeep R.

doi:10.1080/03610926.2020.1854304

Cited by 5 publications

(3 citation statements)

References 21 publications

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“…Also, one may look to construct some multistage sampling designs, namely three-stage sampling (Chaturvedi et al ., 2019a, b, 2020) and accelerated sequential sampling (Joshi et al. , 2021; Joshi and Bapat, 2022) for the present estimation problem. However, these multistage techniques have their own roots, merits and demerits.…”

Section: Discussionmentioning

confidence: 99%

Optimal estimation of reliability parameter for inverse Pareto distribution with application to insurance data

Joshi,

Bapat,

Sengupta

2024

IJQRM

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PurposeThe purpose of this paper is to develop optimal estimation procedures for the stress-strength reliability (SSR) parameter R = P(X > Y) of an inverse Pareto distribution (IPD).Design/methodology/approachWe estimate the SSR parameter R = P(X > Y) of the IPD under the minimum risk and bounded risk point estimation problems, where X and Y are strength and stress variables, respectively. The total loss function considered is a combination of estimation error (squared error) and cost, utilizing which we minimize the associated risk in order to estimate the reliability parameter. As no fixed-sample technique can be used to solve the proposed point estimation problems, we propose some “cost and time efficient” adaptive sampling techniques (two-stage and purely sequential sampling methods) to tackle them.FindingsWe state important results based on the proposed sampling methodologies. These include estimations of the expected sample size, standard deviation (SD) and mean square error (MSE) of the terminal estimator of reliability parameters. The theoretical values of reliability parameters and the associated sample size and risk functions are well supported by exhaustive simulation analyses. The applicability of our suggested methodology is further corroborated by a real dataset based on insurance claims.Originality/valueThis study will be useful for scenarios where various logistical concerns are involved in the reliability analysis. The methodologies proposed in this study can reduce the number of sampling operations substantially and save time and cost to a great extent.

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Section: Discussionmentioning

confidence: 99%

Optimal estimation of reliability parameter for inverse Pareto distribution with application to insurance data

Joshi,

Bapat,

Sengupta

2024

IJQRM

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“…Similar procedures to deal with some other estimation problems have been developed and studied by numerous authors. To cite a few, one may refer to Son and Hamdy (1990), Hamdy and Son (1991), Chaturvedi and Tomer (2003), Chaturvedi et al (2019a,b), Joshi and Bapat (2020a), Mukhopadhyay and Khariton (2020), Zhuang and Bhattacharjee (2021), Joshi et al (2021) and the references therein.…”

Section: Introductionmentioning

confidence: 99%

A class of accelerated sequential procedures with applications to estimation problems for some distributions useful in reliability theory

Joshi

Bapat²,

Shukla

2021

CSAM

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This paper deals with developing a general class of accelerated sequential procedures and obtaining the associated second-order approximations for the expected sample size and 'regret' (difference between the risks of the proposed accelerated sequential procedure and the optimum fixed sample size procedure) function. We establish that the estimation problems based on various lifetime distributions can be tackled with the help of the proposed class of accelerated sequential procedures. Extensive simulation analysis is presented in support of the accuracy of our proposed methodology using the Pareto distribution and a real data set on carbon fibers is also analyzed to demonstrate the practical utility. We also provide the brief details of some other inferential problems which can be seen as the applications of the proposed class of accelerated sequential procedures.

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“…An R package has also been developed by Leiva et al (2008) for a general class of IG models. Moreover, for an overview of the recent developments on sequential and multi-stage estimation of the parameter(s) of an IG distribution, one may refer to Chaturvedi (1985Chaturvedi ( , 1986, Bapat (2018), Chaturvedi et al (1991Chaturvedi et al ( , 2019Chaturvedi et al ( , 2020a, Joshi and Bapat (2020).…”

Section: Introductionmentioning

confidence: 99%

Sequential Estimation of an Inverse Gaussian Mean with Known Coefficient of Variation

2021

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This paper deals with developing sequential procedures for estimating the mean of an inverse Gaussian (IG) distribution when the population coefficient of variation (CV) is known. We considerthe minimum risk and bounded risk point estimation problems respectively. Moreover, we make use of a weighted squared-error loss function and aim to control the associated risk functions. Instead of the usual estimator, i.e., the sample mean, Searls J. Amer. Stat. Assoc. 50, 1225-1226(1964 estimator is utilized for the purpose of estimation. Second-order approximations are also obtained under both estimation set-ups. We establish that Searls' estimator dominates the usual estimator (sample mean) under proposed sequential sampling procedures. An extensive simulation analysis is carried out to validate the theoretical findings and real data illustrations are also provided to show the practical utility of our proposed sequential stopping strategies.

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On improved accelerated sequential estimation of the mean of an inverse Gaussian distribution

Cited by 5 publications

References 21 publications

Optimal estimation of reliability parameter for inverse Pareto distribution with application to insurance data

Optimal estimation of reliability parameter for inverse Pareto distribution with application to insurance data

A class of accelerated sequential procedures with applications to estimation problems for some distributions useful in reliability theory

Sequential Estimation of an Inverse Gaussian Mean with Known Coefficient of Variation

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