Average worth estimation of the selected subset of Poisson populations

Al-Mosawi, Riyadh R.; Shanubhogue, Ashok; Vellaisamy, P.

doi:10.1080/02331888.2011.555552

Cited by 2 publications

(4 citation statements)

References 18 publications

(22 reference statements)

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“…. By the independence of the X i 's and (1) , Y (1) ( using Lemma 3.1) 2) , Y (2) , and continuing this process completes the proof.…”

Section: Estimation Based On Two-stage Samplementioning

confidence: 68%

“…It is well-known that X i ∼ bin(n i , θ i ) while X i is no longer binomial. Let θ [1] = max{θ 1 , • • • , θ p } and X (1) = max{X 1 , • • • , X p } and let θ = (θ 1 , . .…”

Section: Introductionmentioning

confidence: 99%

“…, X p ). The population associated with θ [1] is called the best population and in case of ties, we randomly tagged any of the tied populations.…”

Section: Introductionmentioning

confidence: 99%

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Estimating The Average Worth Of A Subset Selected From Binomial Populations

Al-Mosawi¹

2011

J. Math. Computer Sci.

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Suppose X = (X 1 , • • • , X p), (p ≥ 2), where X i represents the mean of a random sample of size n i drawn from binomial bin(1, θ i) population. Assume the parameters θ 1 , • • • , θ p are unknown and the populations bin(1, θ 1), • • • , bin(1, θ p) are independent. A subset of random size is selected using Gupta's (Gupta, S. S. (1965). On some multiple decision(selection and ranking) rules. Technometrics 7,225-245) subset selection procedure. In this paper, we estimate of the average worth of the parameters for the selected subset under squared error loss and normalized squared error loss functions. First, we show that neither the unbiased estimator nor the riskunbiased estimator of the average worth (corresponding to the normalized squared error loss function) exist based on a single-stage sample. Second, when additional observations are available from the selected populations, we derive an unbiased and risk-unbiased estimators of the average worth and also prove that the natural estimator of the average worth is positively biased. Finally, the bias and risk of the natural, unbiased and risk-unbiased estimators are computed and compared using Monti Carlo simulation method.

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“…. By the independence of the X i 's and (1) , Y (1) ( using Lemma 3.1) 2) , Y (2) , and continuing this process completes the proof.…”

Section: Estimation Based On Two-stage Samplementioning

confidence: 68%

Section: Introductionmentioning

confidence: 99%

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Estimating The Average Worth Of A Subset Selected From Binomial Populations

Al-Mosawi¹

2011

J. Math. Computer Sci.

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“…For example, a commercial vehicle operator not only prefers to buy a vehicle with maximum fuel efficiency, but he also wants to estimate the average fuel efficiency of the selected vehicle (see Kumar and Gangopadhyay, 2005). For more applications, discussions and recent references see Kumar and Kar (2001 a,b), Misra et al (2006 a,b), Kumar et al (2009), Al-Mosawi et al (2012), Nematollahi and Motamed-Shariati (2012) and .…”

Section: Introductionmentioning

confidence: 98%

Estimation of the location parameter and the average worth of the selected subset of two parameter exponential populations under LINEX loss function

Nematollahi

Pagheh

2016

Communications in Statistics - Theory and Methods

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Suppose a subset of populations is selected from k exponential populations with unknown location parameters θ 1 , θ 2 , ..., θ k and common known scale parameter σ. We consider the estimation of the location parameter of the selected population and the average worth of the selected subset under an asymmetric LINEX loss function. We show that the natural estimator of these parameters is biased and find the Uniformly Minimum Risk Unbiased (UMRU) estimator of these parameters. In the case of k = 2, we find the minimax estimator of the location parameter of the smallest selected population. Furthermore, we compare numerically the risk of UMRU, minimax and the natural estimators.

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Average worth estimation of the selected subset of Poisson populations

Cited by 2 publications

References 18 publications

Estimating The Average Worth Of A Subset Selected From Binomial Populations

Estimating The Average Worth Of A Subset Selected From Binomial Populations

Estimation of the location parameter and the average worth of the selected subset of two parameter exponential populations under LINEX loss function

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