Testing a tolerance hypothesis by means of an information distance

František Rublík

Aplikace matematiky (1990)

  • Volume: 35, Issue: 6, page 458-470
  • ISSN: 0862-7940

Abstract

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In the paper a test of the hypothesis μ + c σ M , μ - c σ m on parameters of the normal distribution is presented, and explicit formulas for critical regions are derived for finite sample sizes. Asymptotic null distribution of the test statistic is investigated under the assumption, that the true distribution possesses the fourth moment.

How to cite

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Rublík, František. "Testing a tolerance hypothesis by means of an information distance." Aplikace matematiky 35.6 (1990): 458-470. <http://eudml.org/doc/15646>.

@article{Rublík1990,
abstract = {In the paper a test of the hypothesis $\mu +c \sigma \le M$, $\mu - c \sigma \ge m$ on parameters of the normal distribution is presented, and explicit formulas for critical regions are derived for finite sample sizes. Asymptotic null distribution of the test statistic is investigated under the assumption, that the true distribution possesses the fourth moment.},
author = {Rublík, František},
journal = {Aplikace matematiky},
keywords = {hypothesis testing; Fisher information matrix; concentration of the statistical population in prescribed tolerance limits; statistical quality control; normal distribution; explicit formulas for critical regions; finite sample sizes; fourth moment; Fisher information matrix; prescribed tolerance limits; quality control; normal distribution; explicit formulas for critical regions; finite sample sizes; asymptotic null distribution; fourth moment},
language = {eng},
number = {6},
pages = {458-470},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Testing a tolerance hypothesis by means of an information distance},
url = {http://eudml.org/doc/15646},
volume = {35},
year = {1990},
}

TY - JOUR
AU - Rublík, František
TI - Testing a tolerance hypothesis by means of an information distance
JO - Aplikace matematiky
PY - 1990
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 35
IS - 6
SP - 458
EP - 470
AB - In the paper a test of the hypothesis $\mu +c \sigma \le M$, $\mu - c \sigma \ge m$ on parameters of the normal distribution is presented, and explicit formulas for critical regions are derived for finite sample sizes. Asymptotic null distribution of the test statistic is investigated under the assumption, that the true distribution possesses the fourth moment.
LA - eng
KW - hypothesis testing; Fisher information matrix; concentration of the statistical population in prescribed tolerance limits; statistical quality control; normal distribution; explicit formulas for critical regions; finite sample sizes; fourth moment; Fisher information matrix; prescribed tolerance limits; quality control; normal distribution; explicit formulas for critical regions; finite sample sizes; asymptotic null distribution; fourth moment
UR - http://eudml.org/doc/15646
ER -

References

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  1. J. Anděl, Matematická statistika, Praha, SNTL 1978. (1978) 
  2. H. Cramér, Mathematical Methods of Statistics, Princeton University Press 1946. (1946) Zbl0063.01014MR0016588
  3. C. R. Rao, Linear Statistical Inference and Its Applications, (Czech translation). Praha, Academia 1978. (1978) 
  4. F. Rublík, On testing hypotheses approximable by cones, Math. Slovaca 39 (1989), 199-213. (1989) Zbl0699.62057MR1018261
  5. F. Rublík, On the two-sided quality control, Apl. Mat. 27 (1982), 87-95. (1982) Zbl0491.62085MR0651047
  6. F. Rublík, Correction to the paper "On the two-sided quality control", Apl. Mat. 34 (1989), 425-428. (1989) MR1026506

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