scholarly journals STATISTICAL ANALYSIS OF PEDAGOGICAL EXPERIMENT IN CASE AN UNKNOWN DISTRIBUTION FUNCTION

2013 ◽  
pp. 44-51
Author(s):  
V. S. Erемееv ◽  
V. V. Кusminov
Keyword(s):  
Distribution Function ◽  
Statistical Analysis ◽  
Unknown Distribution ◽  
Unknown Distribution Function

Asymptotical problems of sequential interval and point estimation

2020 ◽  
Vol 86 (7) ◽  
pp. 72-80
Author(s):  
A. A. Abdushukurov ◽  
G. G. Rakhimova
Keyword(s):  
Distribution Function ◽  
Confidence Intervals ◽  
Wide Class ◽  
Sequential Analysis ◽  
Interval Estimation ◽  
Sequential Estimation ◽  
Point Estimation ◽  
Minimum Risk ◽  
Unknown Distribution ◽  
Unknown Distribution Function

The accuracy of interval estimation systems is usually measured using interval lengths for given covering probabilities. The confidence intervals are the intervals of a fixed width if the length of the interval is determined, i.e., not random, and tends to zero for a given covering probability. We consider two important directions of statistical analysis -sequential interval estimation with confidence intervals of fixed width and sequential point estimation with asymptotically minimum risk. Two statistical models are used to describe the basis problems of sequential interval estimation by confidence intervals of a fixed width and point estimation. A review of data on nonparametric sequential estimation is carried out and new original results obtained by the authors are presented. Sequential analysis is characterized by the fact that the moment of termination of observations (stopping time) is random and is determined depending on the values of the observed data and on the adopted measure of optimality of the constructed statistical estimate. Therefore, to solve the asymptotic problems of sequential estimation, the methods of summation of random variables are used. To prove the asymptotic consistency of the confidence intervals of a fixed width, we used a method based on application of limit theorems for randomly stopped random processes. General conditions of the consistency and efficiency of sequential interval estimation of a wide class of functionals of an unknown distribution function are obtained and verified by sequential interval estimation of an unknown probability density of asymptotically uncorrelated and linear processes. Conditions of the regularity are specified that provide the property of being an estimate with an asymptotically minimum risk for a wide class of estimates and loss functions. Those conditions are verified by sequential point estimation of an unknown distribution function.

scholarly journals Approximation of multivariate distribution functions

2008 ◽  
Vol 58 (5) ◽  
Author(s):  
Margus Pihlak
Keyword(s):  
Distribution Function ◽  
Linear Algebra ◽  
Taylor Expansion ◽  
Simulated Data ◽  
Distribution Functions ◽  
Normal Distribution Function ◽  
Matrix Operation ◽  
Unknown Distribution ◽  
Matrix Integral ◽  
Unknown Distribution Function

AbstractIn the paper the unknown distribution function is approximated with a known distribution function by means of Taylor expansion. For this approximation a new matrix operation — matrix integral — is introduced and studied in [PIHLAK, M.: Matrix integral, Linear Algebra Appl. 388 (2004), 315–325]. The approximation is applied in the bivariate case when the unknown distribution function is approximated with normal distribution function. An example on simulated data is also given.

Robust Sequential Confidence Intervals for the Behrens–Fisher Problem*

1971 ◽  
Vol 20 (1-3) ◽  
pp. 77-82 ◽  
Author(s):  
Malay Ghosh
Keyword(s):  
Distribution Function ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Present Note ◽  
Rank Order ◽  
Sample Problem ◽  
Unknown Distribution ◽  
Two Sample Problem ◽  
Unknown Distribution Function ◽  
Rank Order Statistics

Summary The problem of providing a bounded length (sequential) confidence interval for the median of a symmetric (but otherwise unknown) distribution based on a general class of one-sample rank-order statistics was investigated in (Sen & Ghosh, 1971). The purpose of the present note is to indicate how the techniques developed there can be extended to the two-sample problem. It has been shown that in particular for the Behrens- Fisher situation (see e.g., Høyland, 1965 or Ramchandramurty, 1966), when the proposed procedure is based on the “normal-scores” statistic, under very general conditions on the unknown distribution function (d.f.), it is asymptotically at least as efficient as an analogous procedure suggested in (Robbins, Simons & Starr, 1967) and (Srivastava, 1970).

Order Statistics and Applications

2018 ◽  
pp. 1856-1868
Author(s):  
E. Jack Chen
Keyword(s):  
Distribution Function ◽  
Statistical Analysis ◽  
Order Statistics ◽  
Goodness Of Fit ◽  
Ranking And Selection ◽  
Quantile Estimation ◽  
Cumulative Distribution ◽  
Parametric Statistics ◽  
Goodness Of Fit Hypothesis ◽  
Tests Of Independence

Order statistics refer to the collection of sample observations sorted in ascending order and are among the most fundamental tools in non-parametric statistics and inference. Statistical inference established based on order statistics assumes nothing stronger than continuity of the cumulative distribution function of the population and is simple and broadly applicable. We discuss how order statistics are applied in statistical analysis, e.g., tests of independence, tests of goodness of fit, hypothesis tests of equivalence of means, ranking and selection, and quantile estimation. These order-statistics techniques are key components of many studies.

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