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Bounded length sequential intervals
Lapšanská, Alica ; Hušková, Marie (advisor) ; Hlávka, Zdeněk (referee)
The Bachelor's thesis concerns the construction of bounded length sequential intervals with predetermined confidence. This paper analyses some methods, which solve this problem. In the first part we deal with a special case of random sample from normal population. For a known variance we use knowledge from nonsequential theory of interval estimation. We describe Stein's two-stage procedure for an unknown variance. Furthermore, we determine expected value of total sample range for various interval lengths. The second part generally considers a random sample from population with unknown finite variance. We present modified Stein's procedure and sequential Wald's procedure. Finally using simulation, we endeavor to find out a distribution of random variable, which corresponds to the sample range in case of unknown variance. We do this for all of the three mentioned procedures.
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Two-step statistical procedures
Rusá, Šárka ; Hušková, Marie (advisor) ; Jurečková, Jana (referee)
Title: Two-step statistical procedures Author: Šárka Rusá Department: Department of Probability and Mathematical Statistics Supervisor: prof. RNDr. Marie Hušková, DrSc., Department of Probability and Mathematical Statistics Abstract: The Bachelor thesis deals with specific sequential confidence inter- val estimation and hypothesis testing. Initially, we limit ourselves to the study of a random sample selected from a Normal population. Chapter 1 is devoted to the construction of a fixed-width confidence interval for the mean given by Stein's two-step procedure for an unknown variance. In Chapter 2 with the use of a theorem proven in Chapter 1 it is possible to test a hypothesis for a mean value while the type II error remains independent of the variance. In the third chapter we present a modification of Stein's procedure, whose motivation consists in the reduction in the mean of the final sample size. The generalization of the modified procedure, which is applicable to distributions with an unknown finite non-zero variance, is treated in Chapter 4. In Chapters 1 and 4 we will simulate the distribution of the random variable which determines the final sample size. Keywords: Sequential estimation, Stein's two-step procedure, fixed-width confidence intervals.
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Two-step statistical procedures
Rusá, Šárka ; Hušková, Marie (advisor) ; Jurečková, Jana (referee)
Title: Two-step statistical procedures Author: Šárka Rusá Department: Department of Probability and Mathematical Statistics Supervisor: prof. RNDr. Marie Hušková, DrSc., Department of Probability and Mathematical Statistics Abstract: The Bachelor thesis deals with specific sequential confidence inter- val estimation and hypothesis testing. Initially, we limit ourselves to the study of a random sample selected from a Normal population. Chapter 1 is devoted to the construction of a fixed-width confidence interval for the mean given by Stein's two-step procedure for an unknown variance. In Chapter 2 with the use of a theorem proven in Chapter 1 it is possible to test a hypothesis for a mean value while the type II error remains independent of the variance. In the third chapter we present a modification of Stein's procedure, whose motivation consists in the reduction in the mean of the final sample size. The generalization of the modified procedure, which is applicable to distributions with an unknown finite non-zero variance, is treated in Chapter 4. In Chapters 1 and 4 we will simulate the distribution of the random variable which determines the final sample size. Keywords: Sequential estimation, Stein's two-step procedure, fixed-width confidence intervals.
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Bounded length sequential intervals
Lapšanská, Alica ; Hušková, Marie (advisor) ; Hlávka, Zdeněk (referee)
The Bachelor's thesis concerns the construction of bounded length sequential intervals with predetermined confidence. This paper analyses some methods, which solve this problem. In the first part we deal with a special case of random sample from normal population. For a known variance we use knowledge from nonsequential theory of interval estimation. We describe Stein's two-stage procedure for an unknown variance. Furthermore, we determine expected value of total sample range for various interval lengths. The second part generally considers a random sample from population with unknown finite variance. We present modified Stein's procedure and sequential Wald's procedure. Finally using simulation, we endeavor to find out a distribution of random variable, which corresponds to the sample range in case of unknown variance. We do this for all of the three mentioned procedures.
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