# zbMATH — the first resource for mathematics

A fixed sample size selection procedure for negative binomial populations. (English) Zbl 0764.62023
Summary: A fixed sample size procedure for selecting the ‘best’ of $$k$$ negative binomial populations is developed. Selection is made in such a way that the probability of correct selection is at least $$P^*$$ whenever the distance between the probabilities of success is at least $$\delta^*$$. The exponent $$r$$ is assumed to be known and the same for all populations. Extensive computer calculations were employed to obtain the exact least favorable configuration. The smallest sample sizes needed to meet specifications $$(P^*,\delta^*)$$ are tabulated for $$r=1(1)5$$; $$\delta^*=0.05(0.05)0.55$$ and $$P^*=0.75,0.80,0.90,0.95,0.98,0.99$$ involving $$k=3(1)6,8,10$$ populations.

##### MSC:
 62F07 Statistical ranking and selection procedures 62Q05 Statistical tables
Full Text:
##### References:
 [1] Bechhofer RE, Kiefer J, Sobel M (1968) Sequential Identification and Ranking Procedures. The Univ of Chicago Press, Chicago · Zbl 0208.44601 [2] Chambers ML, Jarratt P (1964) Use of Double Sampling for Selecting Best Population. Biometrika 51:49–64 · Zbl 0129.11101 [3] Clark SJ, Perry JN (1989) Estimation of the Negative Binomial Parameterk by Maximum Quasi-Likelihood. Biometrics 45:309–316 · Zbl 0715.62048 [4] Gupta SS, Nagel K (1971) In: Gupta SS, Yackel J (eds) On some Contributions to Multiple Decision Theory. Statistical Decision Theory and Related Topics, pp 79–95 [5] Mahamunulu DM (1967) Some Fixed-Sample Ranking and Selection Problems. Ann Math Statist 38:1079–1091 · Zbl 0158.36702 [6] Nagardeolekar MS (1988) Fixed Sample Selection Procedures and an Approximate Kiefer-Weiss Solution for Negative Binomial Populations. Ph D Dissertation, Okla-State Univ., Stillwater, OK [7] Shenton LR, Bowman KO (1967) Remarks on Large Sample Estimators for some Discrete Distributions. Technometrics 9:587–598 [8] Sobel M, Huyett MJ (1957) Selecting the Best one of Several Binomial Populations. Bell Syst Tech J 36:537–576 [9] Williamson E, Brentherton MH (1964) Tables of Logarithmic Series Distribution. Ann Math Statist 35:284–297 · Zbl 0129.33504 [10] Willson LJ, Folks JL, Young JH (1984) Multistage Estimation Compared with Fixed-Sample-Size Estimation of the Negative Binomial Parameterk Biometrics 40:109–117 [11] Quenouille MH (1949) A Relation Between the Logarithmic Poisson and Negative Binomial Series. Biometrics 5:162–164
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.