Abstract
Inequalities for comparing the binomial distribution function/operating characteristic function with value 0.5 have been established long ago. It is a trivial task to infer from these inequalities bounds for the 50 percentage point of the binomial operating characteristic function. However, it is also possible to use these inequalities to establish good bounds for the median of the binomial distribution function. By a relation of binomial distribution function/operating characteristic function and negative binomial distribution function/operating characteristic function we can get bounds for the respective parameters of negative binomial distribution, too.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Göb R (1991) α-optimale Stichprobenpläne zur Fehlerprüfung von Warenpartien. Thesis, Universität Würzburg 1991
Göb R (1992) Type A Operating Characteristic Functions of Defects Sampling Plans. Metrika 39:139–153
Johnson NL, Kotz S (1969) Discrete Distributions. Houghton Mifflin Company, Boston
Patel J, Kapadia CH, Owen DB (1976) Handbook of Statistical Distributions, Marcel Dekker, New York/Basel
Uhlmann W (1966) Vergleich der hypergeometrischen mit der Binomial-Verteilung. Metrika 10: 145–158
Uhlmann W (1970) Kostenoptimale Prüfpläne, Tabellen, Praxis and Theorie eines Verfahrens der statistichen Qualitätskontrolle. Physica Verlag, Würzburg/Wien
Uhlmann W (1982) Statistische Qualitätskontrolle. 2nd ed. Teubner Verlag, Stuttgart
van de Ven R, Weber NC (1993) Bounds for the Median of the Negative Binomial Distribution. Metrika 40:185–189
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Göb, R. Bounds for median and 50 percetage point of binomial and negative binomial distribution. Metrika 41, 43–54 (1994). https://doi.org/10.1007/BF01895303
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01895303