Estimators for a Poisson parameter using ranked set sampling

Barnett, Vic; Barreto, Maria Cecília Mendes

doi:10.1080/02664760120076616

Cited by 15 publications

(8 citation statements)

References 11 publications

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“…One exception is a paper by Barnett and Barreto (2001) who use the RSS methodology to estimate a Poisson parameter. In a more recent paper Lacayo et al (2002) discuss a RSS proportion estimator.…”

Section: Introductionmentioning

confidence: 97%

On Estimating a Population Proportion via Ranked Set Sampling

Terpstra

2004

Biometrical J

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SummaryThis paper explores the use of the rank set sampling (RSS) protocol as it pertains to the estimation of a population proportion. The maximum likelihood estimator (MLE) and the sample proportion, both based on the RSS data, are discussed and their corresponding asymptotic distributions are derived. Based on these results the MLE is found to be uniformly more efficient than the sample proportion. Nevertheless, both estimators are more efficient than the simple random sample proportion. The greatest gains in efficiency are obtained at the center of the parameter space. Finally, these results remain valid in the presence of judgment error.

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Section: Introductionmentioning

confidence: 97%

On Estimating a Population Proportion via Ranked Set Sampling

Terpstra

2004

Biometrical J

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“…Nevertheless, some results pertaining to discrete random variables are beginning to emerge. For example, Barnett and Barreto [11] have successfully applied RSS to the estimation of Poisson parameters. Furthermore, Terpstra and Nelson [12] have shown that RSS can e ectively be used to estimate population proportions.…”

Section: Introductionmentioning

confidence: 99%

Concomitant‐based rank set sampling proportion estimates

Terpstra

Liudahl

2004

Statistics in Medicine

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This paper discusses the rank set sampling (RSS) protocol as it pertains to the estimation of a population proportion. The ranking process is based on a concomitant variable. The concomitant-based RSS estimate is asymptotically normal so standard inference procedures can still be implemented. This is illustrated using a real data set from the medical literature. The performance of the estimator is studied in terms of relative efficiency. Generally speaking, the concomitant-based RSS estimator is more efficient than the proportion of successes in a simple random sample. The greatest gains in efficiency are obtained when the correlation between the Bernoulli and concomitant variable is large in absolute value.

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“…The unbiased linear estimator for the Poisson process mean using RSS data can be written as (cf. Barnett and Barreto)

{\overset{true^}{μ}}_{R S S j} = \frac{γ_{n}}{n} true {true\sum}_{i = 1}^{n} X_{((), i : n) j},

where

γ_{n} = ((), 1 true/ n) true {true\sum}_{i = 1}^{n} γ_{(i : n)}

is correction constant chosen to minimize

normalV normala normalr ((), {\overset{μ}{true}}_{R S S j})

, the variance of i th order statistic for the i th sample of a subgroup size n . In this study, γ n is found to be approximately unity, γ n ≈ 1.…”

Section: Designing Poisson Ewma Control Chartsmentioning

confidence: 99%

“…In this study, γ n is found to be approximately unity, γ n ≈ 1. Barnett and Barreto defined the minimum variance of

{\overset{true^}{μ}}_{R S S}

normalV normala normalr ((), {\overset{μ}{true}}_{R S S}) = \frac{λ ((), true {true\sum}_{i = 1}^{n} α_{(i : n)}^{2} true/ β_{(i : n)})}{((), true {true\sum}_{i = 1}^{n} 1 true/ β_{(i : n)}) ((), true {true\sum}_{i = 1}^{n} α_{(i : n)}^{2} true/ β_{(i : n)}) - {(\sum_{i = 1}^{n} α_{((), i : n)} / β_{((), i : n)})}^{2}} .

where α ( i : n ) and β ( i : n ) are, respectively, the mean and variance of reduced ordered variables

η_{((), i : n) j} = ((), X_{((), i : n) j} - μ) true/ \sqrt{μ}

.…”

Section: Designing Poisson Ewma Control Chartsmentioning

confidence: 99%

A New EWMA Control Chart for Monitoring Poisson Observations

Abujiya

Riaz

2016

Quality & Reliability Eng

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Quality control charts based on exponentially weighted moving average (EWMA) has been widely used for monitoring continuous process data. However, many quality characteristics of interest are in the form of counts for nonconformities and are often monitored by a Poisson model. In this article, we introduce a new design structure for the Poisson EWMA charts for monitoring Poisson processes. The proposed scheme is based on a well-structured sampling technique, ranked set sampling instead of the traditional simple random sampling. Using Monte Carlo simulations, we compute the run length properties of the new Poisson EWMA chart and compare their relative performance with the existing schemes for monitoring increases and decreases at the Poisson rate. It is found that the new scheme significantly improves the classical procedures for detecting changes in the Poisson processes. Finally, we illustrate the practical application of the proposed scheme through numerical example.

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Estimators for a Poisson parameter using ranked set sampling

Cited by 15 publications

References 11 publications

On Estimating a Population Proportion via Ranked Set Sampling

On Estimating a Population Proportion via Ranked Set Sampling

Concomitant‐based rank set sampling proportion estimates

A New EWMA Control Chart for Monitoring Poisson Observations

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