scholarly journals Average Sample Number Function for Pareto Heavy Tailed Distributions

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Boukhalfa El-Hafsi
Keyword(s):  
Heavy Tails ◽  
Analytical Formula ◽  
Large Data ◽  
Stable Distributions ◽  
Distribution Functions ◽  
Ratio Test ◽  
Major Drawback ◽  
Sample Number ◽  
Average Sample Number ◽  
Average Sample

The main purpose of this work is shortly to give the average sample number function after a sequential probability ratio test on the index parameter alpha of stable densities, which we give a mean of the number of data required to take decision in the case , we use the fact that the tails of Levy-stable distributions are asymptotically equivalent to a Pareto law for large data. Stable distributions are a rich class of probability distributions that allow skewness and heavy tails and have many intriguing mathematical properties. The lack of closed formulas for densities and distribution functions for all has been a major drawback to the use of stable distributions by practitioners, but few stable distributions have the analytical formula of their densities functions which are Gauss, Levy, and Cauchy.

scholarly journals Control of Traffic Intensity in Hyperexponential and Mixed Erlang Queueing Systems with a Method Based on SPRT

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Müjgan Zobu ◽  
Vedat Sağlam
Keyword(s):  
Operating Characteristic ◽  
Queueing Systems ◽  
Ratio Test ◽  
Traffic Intensity ◽  
Sample Number ◽  
Average Sample Number ◽  
Phase Type ◽  
Sequential Probability ◽  
Matlab Programming ◽  
Average Sample

The control of traffic intensity is one of the important problems in the study of queueing systems. Rao et al. (1984) developed a method to detect changes in the traffic intensity in queueing systems of the and types based on the Sequential Probability Ratio Test (SPRT). In this paper, SPRT is theoretically investigated for two different phase-type queueing systems which consist of hyperexponential and mixed Erlang. Also, for testing against , Operating Characteristic (OC) and Average Sample Number (ASN) functions are obtained with numerical methods using multipoint derivative equations according to different situations of and type errors. Afterward, numerical illustrations for each model are provided with Matlab programming.

A sequential decision plan for the management of the eastern hemlock looper, Lambdinafiscellariafiscellaria (Lepidoptera: Geometridae), in Newfoundland

1989 ◽  
Vol 19 (7) ◽  
pp. 911-916 ◽  
Author(s):  
E. J. Dobesberger
Keyword(s):  
Negative Binomial ◽  
Eastern Hemlock ◽  
Ratio Test ◽  
Sequential Decision ◽  
Sample Number ◽  
Average Sample Number ◽  
Probability Ratio ◽  
Sequential Probability ◽  
Hemlock Looper ◽  
Average Sample

A sequential decision plan based on Wald's sequential probability ratio test for the negative binomial distribution was derived for eastern hemlock looper (Lambdinafiscellariafiscellaria (Guen.)) egg populations in Newfoundland. An average sample number of not more than six midcrown branches was feasible, and both α and β error rates were defined. Monte Carlo simulation of operating characteristic and average sample number values for static and dynamic K of the negative binomial showed that Wald's sequential probability ratio test was acceptable. More eggs were found on midcrown balsam fir (Abiesbalsamea (L.) Mill.) branches than on other sampling substrates, such as ground mosses (mainly comprising Hylocomiumsplendens (Hedw.) B.S.G., Pleuroziumschreberi (Brid.) Mitt., and Ptiliumcrista-castrensis (Hedw.) De Not.), loose bark from paper birch (Betulapapyrifera Marsh.), and crown lichens (primarily Usnealongissima Ach.).

scholarly journals Design of SkSP-R Variables Sampling Plans

2015 ◽  
Vol 38 (2) ◽  
pp. 413-429 ◽  
Author(s):  
Muhammad Aslam ◽  
Saminathan Balamurali ◽  
Chi-Hyuck Jun ◽  
Batool Hussain
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Problem ◽  
Sampling Plan ◽  
Producer’S Risk ◽  
Sample Number ◽  
Sampling Plans ◽  
Average Sample Number ◽  
Nonlinear Optimization Problem ◽  
Better Than ◽  
Average Sample

In this paper, we present the designing of the skip-lot sampling plan including the re-inspection  called SkSP-R. The plan parameters of the proposed plan are determined through a  nonlinear optimization problem by minimizing the average sample number satisfying both the producer's risk and the consumer's risks. The proposed plan is shown to perform better than the existing sampling plans in terms of the average sample number. The application of the proposed plan is explained with the help of illustrative examples.

scholarly journals Mixed Variables-Attributes Test Plans for Single and Double Acceptance Sampling under Exponential Distribution

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Yan Li ◽  
Xiaolong Pu ◽  
Dongdong Xiang
Keyword(s):  
Exponential Distribution ◽  
Operating Characteristic ◽  
Acceptance Sampling ◽  
Sample Sizes ◽  
Sample Number ◽  
Sampling Plans ◽  
Average Sample Number ◽  
Mixed Variables ◽  
Average Sample

The mixed variables-attributes test plans for single acceptance sampling are proposed to protect “good lots” from attributes aspect and to optimize sample sizes from variables aspect. For the single and double mixed plans, exact formulas of the operating characteristic and average sample number are developed for the exponential distribution. Numerical illustrations show that the mixed sampling plans have some advantages over the variables plans or attributes plans alone.

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