Parameter estimation of Cambanis-type bivariate uniform distribution with Ranked Set Sampling

Koshti, Rohan D.; Kamalja, Kirtee K.

doi:10.1080/02664763.2019.1709808

Cited by 13 publications

(5 citation statements)

References 21 publications

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“…2) and assuming p to be known, the BLUE Note: We also studied extreme RSS schemes as studied by Koshti and Kamalja [22] , and found that usual RSS estimator of scale parameter overperforms these estimators. Hence, we do not report the details of extreme RSS scheme here.…”

Section: The Mean Vector and The Dispersion Matrix Ofmentioning

confidence: 97%

“…In the literature, a number of studies can be found where efficient estimation of parameters of different bivariate distribution is done using RSS and modified RSS schemes. Some work in this direction is by Al-Saleh and Al-Ananbeh [17] , Chacko and Thomas [18] , Chacko [19] , Lesitha et al [20] , Lesitha and Thomas [8] , Kamalja and Koshti [21] , Koshti and Kamalja [22] , Tahmasebi and Jafari [23] , etc.…”

Section: Introductionmentioning

confidence: 99%

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Efficient Estimation of a Scale Parameter of Bivariate Lomax Distribution by Ranked Set Sampling

Koshti

Kamalja

2021

Calcutta Statistical Association Bulletin

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Ranked set sampling (RSS) is an efficient technique for estimating parameters and is applicable whenever ranking on a set of sampling units can be done easily by a judgment method or based on an auxiliary variable. In this paper, we assume [Formula: see text]to have bivariate Lomax distribution where a study variable [Formula: see text]is difficult and/or expensive to measure and is correlated with an auxiliary variable [Formula: see text] which is readily measurable. The auxiliary variable is used to rank the sampling units. In this article, we propose an estimator for the scale parameter of bivariate Lomax distribution using some of the modified RSS schemes. Efficiency comparison of the proposed estimators is performed numerically as well as graphically. A simulation study is also performed to demonstrate the performance of the proposed estimators. Finally, we implement the results to real-life datasets. AMS classification codes: 62D05, 62F07, 62G30

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Section: The Mean Vector and The Dispersion Matrix Ofmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Efficient Estimation of a Scale Parameter of Bivariate Lomax Distribution by Ranked Set Sampling

Koshti

Kamalja

2021

Calcutta Statistical Association Bulletin

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“…4. Simulation from CTBU (α 1 , α 2 , α 3 , θ 1 , θ 2 ) distribution Koshti and Kamalja [19] developed a Matlab function for simulating random pairs of observations from the CT BU(α 1 , α 2 , α 3 , θ 1 , θ 2 ) distribution when α 1 is set to 0. Following their approach, we have developed a R function, rctbu(α 1 , α 2 , α 3 , θ 1 , θ 2 , n), to generate random samples of size n from the CT BU(α 1 , α 2 , α 3 , θ 1 , θ 2 ) distribution.…”

Section: Moment Estimation Of Parameters Of Ctbu Distributionmentioning

confidence: 99%

“…Notably, Nair et al [22] have explored the distributional characteristics, nature of dependence, reliability properties, and applications of the Cambanis family, showcasing its superiority in improving dependence coefficients compared to the Morgenstern family. Koshti and Kamalja [19] obtained the estimator for scale parameter associated with study variable for Cambanis-type bivariate uniform distribution (CTBU) based on different ranked set sampling schemes. Alawady et.…”

Section: Introductionmentioning

confidence: 99%

Cambanis-type Bivariate Uniform Distribution: Properties and Moment Estimation

Koshti,

Kamalja

2024

Computational Journal of Mathematical and Statistical Sciences

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The families of distributions are crucial in statistical modeling, offering a versatile foundation for a variety of applications. The development of bivariate distributions with specific marginal distributions and correlation coefficients is of considerable interest due to its wide-ranging relevance in real-world situations. The range of correlation between variables is an important characterization of the family. The variety of methods of construction of bivariate/multivariate distributions are developed in the literature. The Cambanis family is an important class of multivariate distributions with a wide range of correlation than the traditional families. In this paper, we consider a Cambanis-type bivariate uniform distribution and develop key statistical properties of the Cambanis-type bivariate uniform distribution. We obtain moment estimators of parameters for Cambanis-type bivariate uniform distribution. To evaluate the performance of the estimators, we develop an algorithm to simulate samples from the Cambanis-type bivariate uniform distribution and implement it in the R software. We perform a simulation study to present the performance of moment estimator.

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“…More specifically, they utilized the Wilcoxon signed-rank statistic defined earlier and proposed a new edition of the EWMA signedrank monitoring scheme by implementing ranked set sampling. For some recent advances on the ranked set sampling procedure, the interested reader is referred to Koshti and Kamalja (2021) or Frey and Zhang (2021), while some comprehensive details about the above-mentioned sampling scheme are provided by Hettmansperger (1995), Kvam and Samaniego (1994) or Dell and Clutter (1972). Their proposed chart seems to be more capable for tracking down plausible changes in the underlying distribution, when it is compared to other existing nonparametric EWMA schemes.…”

Section: Nonparametric Ewma Control Charts Based On Wilcoxon Signed-rank Statisticmentioning

confidence: 99%

Nonparametric EWMA-Type Control Charts for Monitoring Industrial Processes: An Overview

Triantafyllou¹,

Ram²

2021

Int J Math, Eng, Manag Sci

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In the present paper we provide an up-to-date overview of nonparametric Exponentially Weighted Moving Average (EWMA) control charts. Due to their nonparametric nature, such memory-type schemes are proved to be very useful for monitoring industrial processes, where the output cannot match to a particular probability distribution. Several fundamental contributions on the topic are mentioned, while recent advances are also presented in some detail. In addition, some practical applications of the nonparametric EWMA-type control charts are highlighted, in order to emphasize their crucial role in the contemporary online statistical process control.

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Parameter estimation of Cambanis-type bivariate uniform distribution with Ranked Set Sampling

Cited by 13 publications

References 21 publications

Efficient Estimation of a Scale Parameter of Bivariate Lomax Distribution by Ranked Set Sampling

Efficient Estimation of a Scale Parameter of Bivariate Lomax Distribution by Ranked Set Sampling

Cambanis-type Bivariate Uniform Distribution: Properties and Moment Estimation

Nonparametric EWMA-Type Control Charts for Monitoring Industrial Processes: An Overview

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