Sequential fixed-width confidence interval for the rth power of the exponential scale parameter: Two-stage and sequential sampling procedures

2018 ◽  
Vol 37 (3) ◽  
pp. 293-310 ◽  
Author(s):  
Reihaneh Lalehzari ◽  
Eisa Mahmoudi ◽  
Ashkan Khalifeh
Keyword(s):  
Confidence Interval ◽  
Scale Parameter ◽  
Sequential Sampling ◽  
Two Stage ◽  
Sampling Procedures ◽  
Width Confidence Interval

On Fixed width Confidence Interval Estimation of the Common Mean in Symmetric Multivariate Normal Distribution

2019 ◽  
Vol 71 (2) ◽  
pp. 113-120
Author(s):  
Uttam Bandyopadhyay ◽  
Pritam Sarkar
Keyword(s):  
Confidence Interval ◽  
Sequential Sampling ◽  
Interval Estimation ◽  
Multivariate Normal ◽  
Common Mean ◽  
Multivariate Normal Mean ◽  
Normal Mean ◽  
The Common ◽  
Sampling Procedures ◽  
Width Confidence Interval

This article deals with purely and accelerated sequential sampling procedures to find fixed-width confidence interval of completely symmetric multivariate normal mean. Procedures are studied asymptotically and are evaluated numerically. AMS 2000 subject classification: 62F25 62H12

scholarly journals Multistage Estimation of the Scale Parameter of Rayleigh Distribution with Simulation

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1925 ◽  
Author(s):  
Ali Yousef ◽  
Emad E. H. Hassan ◽  
Ayman A. Amin ◽  
Hosny I. Hamdy
Keyword(s):  
Confidence Interval ◽  
Scale Parameter ◽  
Sequential Sampling ◽  
Interval Estimation ◽  
Rayleigh Distribution ◽  
Sampling Procedure ◽  
Optimal Decision ◽  
Large Sample Size ◽  
Asymptotic Results ◽  
Confidence Interval Estimation

This paper discusses the sequential estimation of the scale parameter of the Rayleigh distribution using the three-stage sequential sampling procedure proposed by Hall (Ann. Stat.1981, 9, 1229–1238). Both point and confidence interval estimation are considered via a unified optimal decision framework, which enables one to make the maximum use of the available data and, at the same time, reduces the number of sampling operations by using bulk samples. The asymptotic characteristics of the proposed sampling procedure are fully discussed for both point and confidence interval estimation. Since the results are asymptotic, Monte Carlo simulation studies are conducted to provide the feel of small, moderate, and large sample size performance in typical situations using the Microsoft Developer Studio software. The procedure enjoys several interesting asymptotic characteristics illustrated by the asymptotic results and supported by simulation.

scholarly journals Fixed-width confidence interval for a lognormal mean

2002 ◽  
Vol 29 (3) ◽  
pp. 143-153 ◽  
Author(s):  
Makoto Aoshima ◽  
Zakkula Govindarajulu
Keyword(s):  
Confidence Interval ◽  
Asymptotic Properties ◽  
Sequential Procedure ◽  
Two Stage ◽  
Accelerated Sequential Procedure ◽  
Width Confidence Interval

We consider the problem of constructing a fixed-width confidence interval for a lognormal mean. We give a Birnbaum and Healy type two-stage procedure to construct such a confidence interval. We discuss some asymptotic properties of the procedure. A three-stage procedure and an accelerated sequential procedure are also given for the comparison of efficiency among these three multistage methodologies.

Fixed Width Confidence Interval ofP(X

2003 ◽  
Vol 22 (1-2) ◽  
pp. 75-93 ◽  
Author(s):  
Uttam Bandyopadhyay ◽  
Radhakanta Das ◽  
Atanu Biswas
Keyword(s):  
Confidence Interval ◽  
Sequential Sampling ◽  
Sampling Scheme ◽  
Width Confidence Interval

The Stability of Weed Seedling Population Models and Parameters in Eastern Nebraska Corn (Zea mays) and Soybean (Glycine max) Fields

Weed Science ◽  
1995 ◽  
Vol 43 (4) ◽  
pp. 604-611 ◽  
Author(s):  
Gregg A. Johnson ◽  
David A. Mortensen ◽  
Linda J. Young ◽  
Alex R. Martin
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Sequential Sampling ◽  
Mean Value ◽  
Distribution Model ◽  
Ratio Test ◽  
Weed Species ◽  
Sampling Procedures ◽  
Grass Weed

Intensive field surveys were conducted in eastern Nebraska to determine the frequency distribution model and associated parameters of broadleaf and grass weed seedling populations. The negative binomial distribution consistently fit the data over time (1992 to 1993) and space (fields) for both the inter and intrarow broadleaf and grass weed seedling populations. The other distributions tested (Poisson with zeros, Neyman type A, logarithmic with zeros, and Poisson-binomial) did not fit the data as consistently as the negative binomial distribution. Associated with the negative binomial distribution is akparameter.kis a nonspatial aggregation parameter related to the variance at a given mean value. Thekparameter of the negative binomial distribution was consistent across weed density for individual weed species in a given field except for foxtail spp. populations. Stability of thekparameter across field sites was assessed using the likelihood ratio test There was no stable or commonkvalue across field sites and years for all weed species populations. The lack of stability inkacross field sites is of concern, because this parameter is used extensively in the development of parametric sequential sampling procedures. Becausekis not stable across field sites,kmust be estimated at the time of sampling. Understanding the variability in it is critical to the development of parametric sequential sampling strategies and understanding the dynamics of weed species in the field.

scholarly journals Multistage Estimation of the Rayleigh Distribution Variance

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2084
Author(s):  
Ali Yousef ◽  
Ayman A. Amin ◽  
Emad E. Hassan ◽  
Hosny I. Hamdy
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
Interval Estimation ◽  
Sequential Estimation ◽  
Rayleigh Distribution ◽  
Point Estimation ◽  
Asymptotic Results ◽  
Squared Error Loss Function ◽  
Estimation Problems ◽  
Width Confidence Interval

In this paper we discuss the multistage sequential estimation of the variance of the Rayleigh distribution using the three-stage procedure that was presented by Hall (Ann. Stat. 9(6):1229–1238, 1981). Since the Rayleigh distribution variance is a linear function of the distribution scale parameter’s square, it suffices to estimate the Rayleigh distribution’s scale parameter’s square. We tackle two estimation problems: first, the minimum risk point estimation problem under a squared-error loss function plus linear sampling cost, and the second is a fixed-width confidence interval estimation, using a unified optimal stopping rule. Such an estimation cannot be performed using fixed-width classical procedures due to the non-existence of a fixed sample size that simultaneously achieves both estimation problems. We find all the asymptotic results that enhanced finding the three-stage regret as well as the three-stage fixed-width confidence interval for the desired parameter. The procedure attains asymptotic second-order efficiency and asymptotic consistency. A series of Monte Carlo simulations were conducted to study the procedure’s performance as the optimal sample size increases. We found that the simulation results agree with the asymptotic results.

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