Operating Characteristic and Average Sample Number of Binary and Multi-Hypothesis Sequential Probability Ratio Test

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.

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

Canadian Journal of Forest Research ◽

10.1139/x89-138 ◽

1989 ◽

Vol 19 (7) ◽

pp. 911-916 ◽

Cited By ~ 14

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.).

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

Canadian Journal of Forest Research ◽

10.1139/x83-158 ◽

1983 ◽

Vol 13 (6) ◽

pp. 1197-1203 ◽

Cited By ~ 3

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.

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On the Operating Characteristic Function for the Exponential Family

Calcutta Statistical Association Bulletin ◽

10.1177/0008068319860310 ◽

1986 ◽

Vol 35 (3-4) ◽

pp. 203-206

Author(s):

D.M. Walker ◽

N.C. Weber

Keyword(s):

Characteristic Function ◽

Exponential Family ◽

Operating Characteristic ◽

Sequential Probability Ratio Test ◽

Ratio Test ◽

Probability Ratio ◽

Operating Characteristic Function ◽

Sequential Probability

This note investigates the behaviour of the function h( θ) used in Wald's approximation to the operating characteristic function of a sequential probability ratio test for testing a parameter in an exponential family density.

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Operating Characteristic and Expected Sample Size of a Sequential Probability Ratio Test for the Simple Exponential Distribution

Calcutta Statistical Association Bulletin ◽

10.1177/0008068319650105 ◽

1965 ◽

Vol 14 (1-2) ◽

pp. 65-73 ◽

Cited By ~ 6

Author(s):

M. Raghavachari

Keyword(s):

Sample Size ◽

Exponential Distribution ◽

Operating Characteristic ◽

Sequential Probability Ratio Test ◽

Ratio Test ◽

Probability Ratio ◽

Expected Sample Size ◽

Simple Alternative ◽

Sequential Probability Ratio Tests ◽

Sequential Probability

Summary For the problem of testing the simple hypothesis H : θ = θ1 against the simple alternative K : θ = θ2 with θ2 > θ1 , where θ is the unknown parameter of the simple exponential distribution, the familar Wald's Sequential Probability ratio test may be adopted. It is shown in the present paper that for a class of sequential probability ratio tests, exact expressions for the operating characteristic and the expected sample size can be given. The nature of the expected sample size function and the effect of Walo's approximations to the stopping bounds of the sequential probability ratio test are also studied.

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