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Three-stage estimation procedures for the negative exponential distributions. (English) Zbl 0629.62034
Authors’ abstract: Fixed width confidence interval estimation problems for location parameters of negative exponential populations have been studied. Three-stage sampling procedures have been developed for both the one- and two-sample situations. The discussions are primarily concerned with second order expansions of various characteristics of the proposed procedures including those for the achieved coverage probability in either problem. Some simulated results are also presented to indicate the usefulness of the procedures for moderate sample sizes.
Reviewer: K.Inada

62F25 Parametric tolerance and confidence regions
62F10 Point estimation
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[1] Basu AP (1971) On a sequential rule for estimating the location parameter of an exponential distribution. Naval Res Logist Qr 18:329–337 · Zbl 0227.62049
[2] Ghosh M, Mukhopadhyay N (1981) Consistency and asymptotic efficiency of two-stage and sequential estimation procedures. Sankhya, Ser A 43: 220–227 · Zbl 0509.62069
[3] Ghurye SG (1958) Note on sufficient statistics and two-stage procedures. Ann Math Statist 29:155–166 · Zbl 0087.34104
[4] Hall P (1981) Asymptotic theory of triple sampling for sequential estimation of a mean. Ann Math Statist 29:1229–1238 · Zbl 0478.62068
[5] Johnson NL, Kotz S (1970) Continuous univariate distributions, vol 2. John Wiley & Sons, Inc, New York · Zbl 0213.21101
[6] Lombard F, Swanepoel JWH (1978) On finite and infinite confidence sequences. S Afr Statist J 12:1–24 · Zbl 0389.62035
[7] Mauromoustakos A (1984) A three-stage estimation procedure for the negative exponential. Masters Report, Department of Statistics, Oklahoma State University, Stillwater · Zbl 0629.62034
[8] Mukhopadhyay N (1974) Sequential estimation of location parameter in exponential distributions. Calcutta Statist Assoc Bul 23:85–95 · Zbl 0342.62058
[9] Mukhopadhyay N (1980) A consistent and asymptotically efficient two-stage procedure to construct fixed width confidence intervals for the mean. Metrika 27:281–284 · Zbl 0449.62028
[10] Mukhopadhyay N (1982a) Stein’s two-stage procedure and exact consistency. Scandinavian Actuarial J:110–122 · Zbl 0493.62072
[11] Mukhopadhyay N (1982b) A study of the asymptotic regret while estimating the location of an exponential distribution. Calcutta Statist Assoc Bul 31:207–213 · Zbl 0516.62077
[12] Mukhopadhyay N, Hamdy HI (1984) On estimating the difference of location parameters of two negative exponential distributions. Canadian J Statist 12:67–76 · Zbl 0543.62061
[13] Swanepoel JWH, van Wyk JWJ (1981) Fixed width confidence intervals for the truncation parameter of an unknown distribution function. S Afr Statist J 15:161–166 · Zbl 0472.62087
[14] Swanepoel JWH, van Wyk JWJ (1982) Fixed width confidence intervals for the location parameter of an exponential distribution. Commun In Statist Ser A 11:1279–1289 · Zbl 0559.62030
[15] Swanepoel JWH, van Wyk JWJ (1984) Small sample performance of confidence intervals for a truncation parameter. S Afr Statist J (to appear) · Zbl 0544.62031
[16] Zelen M (1966) Application of exponential models to problems in cancer research. J Roy Statist Soc 129:368–398
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