Statistical Estimation: Fixed Sample Size Theory

2014 ◽  
pp. 275-320
Keyword(s):  
Sample Size ◽  
Statistical Estimation ◽  
Fixed Sample Size ◽  
Fixed Sample

Stopping rules for proofreading

1989 ◽  
Vol 26 (02) ◽  
pp. 304-313 ◽  
Author(s):  
T. S. Ferguson ◽  
J. P. Hardwick
Keyword(s):  
Sample Size ◽  
Optimal Stopping ◽  
Random Number ◽  
Poisson Model ◽  
Stopping Rule ◽  
Stopping Rules ◽  
Binomial Model ◽  
Fixed Sample Size ◽  
Fixed Sample ◽  
Optimal Stopping Rule

A manuscript with an unknown random numberMof misprints is subjected to a series of proofreadings in an effort to detect and correct the misprints. On thenthproofreading, each remaining misprint is detected independently with probabilitypn– 1. Each proofreading costs an amountCP> 0, and if one stops afternproofreadings, each misprint overlooked costs an amountcn> 0. Two models are treated based on the distribution ofM.In the Poisson model, the optimal stopping rule is seen to be a fixed sample size rule. In the binomial model, the myopic rule is optimal in many important cases. A generalization is made to problems in which individual misprints may have distinct probabilities of detection and distinct overlook costs.

Fixed-Sample Size Sampling Plan

2008 ◽  
pp. 1464-1464
Author(s):  
E. S. Krafsur ◽  
R. D. Moon ◽  
R. Albajes ◽  
O. Alomar ◽  
Elisabetta Chiappini ◽  
...  
Keyword(s):  
Sample Size ◽  
Sampling Plan ◽  
Fixed Sample Size ◽  
Fixed Sample

New exact Bayesian prediction of the range for the exponential lifetime based on fixed and random sample sizes

2017 ◽  
Vol 6 (1-2) ◽  
pp. 169
Author(s):  
A. H. Abd Ellah
Keyword(s):  
Sample Size ◽  
Random Sample ◽  
Real Data ◽  
Predictive Distribution ◽  
Data Sets ◽  
Life Testing ◽  
Random Sample Size ◽  
Fixed Sample Size ◽  
Fixed Sample ◽  
Special Case

We consider the problem of predictive interval for the range of the future observations from an exponential distribution. Two cases are considered, (1) Fixed sample size (FSS). (2) Random sample size (RSS). Further, I derive the predictive function for both FSS and RSS in closely forms. Random sample size is appeared in many application of life testing. Fixed sample size is a special case from the case of random sample size. Illustrative examples are given. Factors of the predictive distribution are given. A comparison in savings is made with the above method. To show the applications of our results, we present some simulation experiments. Finally, we apply our results to some real data sets in life testing.

scholarly journals Modified chain regression type estimator for population mean in the presence of non- response

2015 ◽  
Vol 3 (2) ◽  
pp. 165
Author(s):  
Brij Khare ◽  
Habib Rehman
Keyword(s):  
Sample Size ◽  
Empirical Studies ◽  
Fixed Cost ◽  
Second Phase ◽  
Population Mean ◽  
Fixed Sample Size ◽  
Fixed Sample ◽  
Phase Sample ◽  
Available Information

<p>A modified chain regression type estimator for  population mean in the presence of non-response have been proposed replacing Hansen &amp; Hurwitz (1946) estimator for population mean by Searls (1964) type improved estimator and using Hansen &amp; Hurwitz (1946) estimator for  based on available information comparing to the study character  in the second phase sample. The expressions for MSE for fixed sample size   and also fixed cost   have been obtained. The empirical studies show that the proposed estimator is more efficient than the relevant estimators in the case of fixed sample size as well as for fixed cost.</p>

Optimal Sampling for Identifying a Cluster: An Application in Sorting

1993 ◽  
Vol 7 (3) ◽  
pp. 387-407
Author(s):  
Shmuel Gal ◽  
Dafna Sheinwald
Keyword(s):  
Sample Size ◽  
Sequential Sampling ◽  
A Priori ◽  
Optimal Sampling ◽  
Truncation Point ◽  
Fixed Sample Size ◽  
Fixed Sample ◽  
A Priori Distribution ◽  
Sampling Procedures ◽  
The Cost

We consider the following problem. For a given population of m items, we have to make a decision whether or not the population includes a relatively large cluster of identical items. This decision affects the effectiveness of a subsequent computational process, depending on the actual existence of the cluster and its size. To make a good decision, we use a statistical sample which should indicate the existence of a cluster and find a representative thereof. This paper describes the optimal sampling technique to be used in such a case, given the cost of the sampling and the potential gain in speed of the subsequent process. The optimal fixed sample size is specified, as well as the optimal sequential sampling, along with characterizing the dependence of the cost function on the truncation point.For the case that the a priori distribution of the cluster proportion is known, we present formulae by which the optimal sampling procedures can be easily calculated. For the common situation in which the a priori distribution is not known, we present, in the case of a fixed sample size, a tight upper bound for the sample size, which is independent of the a priori distribution, and for the case of the sequential sampling, we present an approximately optimal truncation point, which is also independent of the a priori distribution.The situation described arose in connection with choosing the best sorting method, an application that will be described in full detail. The most interesting practical result is that for our application truncating the sequential procedure at 35 observations, out of a population of 25,000–30,000 items, guarantees that in our sorting application we are always within 2.1% of the optimal cost independently of the a priori distribution.

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