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 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.

The use of Wald's sequential probability ratio test to develop composite three-decision sampling plans

1985 ◽  
Vol 15 (2) ◽  
pp. 326-330
Author(s):  
Gary W. Fowler
Keyword(s):  
Monte Carlo ◽  
Negative Binomial ◽  
Sequential Sampling ◽  
Ratio Test ◽  
Sample Number ◽  
Sampling Plans ◽  
Probability Ratio ◽  
Sequential Probability ◽  
Error Probabilities ◽  
Decision Boundaries

Many sequential sampling plans used in forest sampling are composite three-decision plans based on the simultaneous use of two of Wald's sequential probability ratio tests (SPRTs). Wald's operating characteristic (OC) and average sample number (ASN) equations for each SPRT are used to describe the properties of the composite sampling plan. Wald's equations are only approximate because of "overshooting" of the decision boundaries of the SPRTs and the two SPRTs operate simultaneously in the composite plan. Wald's and Monte Carlo OC and ASN functions were developed for (i) two SPRTs used to develop a three-decision composite plan and (ii) the three-decision composite plan based on the negative binomial distribution. Wald's equations, in general, overestimate the true error probabilities and underestimate the true ASN for a given SPRT. Wald's equations are less accurate in describing the properties of the three-decision plan. Monte Carlo functions are more accurate than Wald's functions. Recommendations are made regarding the choice between Wald's and Monte Carlo functions. A Monte Carlo procedure to modify the decision boundaries of the plan to yield actual error probabilities approximately equal to the desired error probabilities is suggested.

scholarly journals The VPRT: A Sequential Testing Procedure Dominating the SPRT

1993 ◽  
Vol 9 (3) ◽  
pp. 431-450 ◽  
Author(s):  
Noel Cressie ◽  
Peter B. Morgan
Keyword(s):  
Sample Size ◽  
Decision Problem ◽  
Sequential Analysis ◽  
Testing Procedure ◽  
Sequential Probability Ratio Test ◽  
Ratio Test ◽  
Sequential Decision ◽  
Probability Ratio ◽  
Sampling Cost ◽  
Sequential Probability

Under more general assumptions than those usually made in the sequential analysis literature, a variable-sample-size-sequential probability ratio test (VPRT) of two simple hypotheses is found that maximizes the expected net gain over all sequential decision procedures. In contrast, Wald and Wolfowitz [25] developed the sequential probability ratio test (SPRT) to minimize expected sample size, but their assumptions on the parameters of the decision problem were restrictive. In this article we show that the expected net-gain-maximizing VPRT also minimizes the expected (with respect to both data and prior) total sampling cost and that, under slightly more general conditions than those imposed by Wald and Wolfowitz, it reduces to the one-observation-at-a-time sequential probability ratio test (SPRT). The ways in which the size and power of the VPRT depend upon the parameters of the decision problem are also examined.

The impact of misspecification of the negative binomial shape parameter in sequential sampling plans

1986 ◽  
Vol 16 (3) ◽  
pp. 608-611 ◽  
Author(s):  
W. G. Warren ◽  
Pin Whei Chen
Keyword(s):  
Operating Characteristic ◽  
Shape Parameter ◽  
Negative Binomial ◽  
Sequential Sampling ◽  
Forest Pests ◽  
Sample Number ◽  
Sampling Plans ◽  
Average Sample Number ◽  
The Impact ◽  
Average Sample

Standard sequential sampling plans for determining whether infestations of forest pests have attained critical levels are commonly based on the assumption that the counts follow a negative binomial distribution for which the shape parameter, k, which must be specified, may be difficult to estimate and may well be unstable. This paper studies the effect of misspecification of this parameter on the operating characteristic and average sample number functions of a sequential sampling plan. It appears that slight underestimation of the shape parameter can improve the operating characteristic at little cost, i.e., with only small increase in the average sample number.

Accuracy of sequential sampling plans based on Wald's sequential probability ratio test

1983 ◽  
Vol 13 (6) ◽  
pp. 1197-1203 ◽  
Author(s):  
Gary W. Fowler
Keyword(s):  
Monte Carlo ◽  
Sequential Sampling ◽  
Sequential Probability Ratio Test ◽  
Ratio Test ◽  
Type I ◽  
Sample Number ◽  
Sampling Plans ◽  
Probability Ratio ◽  
Sequential Probability ◽  
Relative Errors

Monte Carlo operating characteristic (OC) and average sample number (ASN) functions were compared with Wald's OC and ASN equations for sequential sampling plans based on Wald's sequential probability ratio test (SPRT) using the binomial, negative binomial, normal, and Poisson distributions. This comparison showed that the errors inherent in Wald's equations as a result of "overshooting" the decision boundaries of the SPRT can be large. Relative errors increased for the OC and ASN equations as the difference between the null (θ0)) and alternative (θ1) test parameter values increased. Relative errors also increased for the ASN equation as the probabilities of type I (α) and type II (β) errors increased. For discrete distributions, the relative errors also increased as θ0 increased with θ1/θ0 fixed. Wald's equations, in general, overestimate the true error probabilities and underestimate the true ASN. For the values of θ0, θ1, α, and β used in many sequential sampling plans in forestry, Wald's equations may not be adequate. For those cases where the errors in Wald's equations are important compared with the other errors associated with the sampling plan, two alternative Monte Carlo OC and ASN functions are proposed.

scholarly journals Spectrum Sensing in Cognitive Radio Using Combined Sequential Energy Detector and Cyclostationary Feature Detector

2016 ◽  
Vol 2 (1) ◽  
pp. 31
Author(s):  
Santosh Poudel ◽  
Heroe Wijanto ◽  
Fiky Y. Suratman
Keyword(s):  
Random Variable ◽  
Energy Detection ◽  
Energy Detector ◽  
Ratio Test ◽  
Feature Detector ◽  
Sample Number ◽  
Low Snr ◽  
Sequential Probability ◽  
Very High ◽  
Average Sample

In the following research, we derive a detector which is based on sequential probability ratio test (SPRT) and it uses Energy Detector (ED) which is followed by Cyclostationary Feature Detector (CFD). ED is a blind sensing technique and it is easy to implement while conceptually simple. However, it is highly affected by interference and noise uncertainties. Therefore, CFD is applied for fine sensing as research has shown that Cyclostationary Feature Detector is more suitable than the energy detection when noise uncertainties are unknown. Our method is novel in trying to derive a sequential Energy Detector and combine it with Cyclostationary Feature Detector for low SNR region where average sample number (ASN) as a random variable may take very high value to achieve a desired performance level for sequential Energy Detector. For this sequential Energy Detector is terminated after it reaches certain cut-off sample number, making it truncated sequential Energy Detector.

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.

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