Applied mathematical statistics

 (MATERIALS TO SEMINARS)

Nonparametric Goodness-of-Fit Tests in Testing Simple and Composite Hypotheses

– Goodness-of-fit test, Kolmogorov test, Cramer-Von Mises-Smirnov test, Anderson-Darling test:

ü Distribution models for nonparametric tests for fit in verifying complicated hypotheses and maximum-likelihood estimators. Part 1;

ü Distribution models for nonparametric tests for fit in verifying complicated hypotheses and maximum-likelihood estimators. Part 2;

ü Statistic Distribution Models for Some Nonparametric Goodness-of-Fit Tests in Testing Composite Hypotheses;

ü Models of Statistic Distributions of Nonparametric Goodness-of-Fit Tests in Composite Hypotheses Testing for Double Exponential Law Cases;

ü Construction of Statistic Distribution Models for Nonparametric Goodness-of-Fit Tests in Testing Composite Hypotheses: The Computer Approach

ü Application of the nonparametric goodness-of-fit Tests in testing composite hypotheses;

ü Modeling statistic distributions for nonparametric goodness-of-fit criteria for testing complex hypotheses with respect to the inverse Gaussian law;

ü Inverse Gaussian Model and Its Applications in Reliability and Survival Analysis;

ü Models of Statistic Distributions of Nonparametric Goodness-of-fit Tests in Composite Hypotheses Testing in Case of Generalized Weibull Law;

ü Using nonparametric goodness-of-fit tests to validate accelerated failure time models.

– power of a goodness-of-fit test, Kolmogorov test, Cramer-Von Mises-Smirnov test, Anderson-Darling test,  Pearson test, the Nikulin-Rao-Robson test:

ü Comparative Analysis of the Power of Goodness-of-Fit Tests for Near Competing Hypotheses. I. The Verification of Simple Hypotheses;

ü Comparative analysis of the power of goodness-of-fit tests for near competing hypotheses. II. Verification of complex hypotheses;

ü The power of goodness of fit tests for close alternatives.

– Errors when using nonparametric fitting criteria.

Chi-Square Goodness-of-Fit Tests:

ü Errors and Incorrect Procedures When Utilizing χ² Fitting Criteria.

Homogeneity tests (Smirnov homogeneity test, Lehmann–Rosenblatt homogeneity test):

ü Statistical distribution convergence and homogeneity test power for Smirnov and Lehmann–Rosenblatt tests.

Homogeneity of means tests (Tests to Compare Two Sample Means with Known Variances, Student’s Test for Comparison of Two Sample Means with Unknown but Equal Variances, Test to Compare Two Sample Means with Unknown and Unequal Variances, Fisher’s Test, Mann and Whitney Test, Kruskal–Wallis Test, Robustness of Parametric Tests, Power of tests):

ü Power and robustness of criteria used to verify the homogeneity of means.

Tests of homogeneity of variances:

– tests of homogeneity of variances, Fisher test, Bartlett test, Cochran test, Hartley test, Levene test, power of tests:

ü Application and power of criteria for testing the homogeneity of variances. Part I. Parametric criteria;

ü Bartlett and Cochran tests in measurements with probability laws different from normal;

ü Application of Parametric Homogeneity of Variances Tests under Violation of Classical Assumption;

ü About robustness and power of variance homogeneity tests;

ü Tests For Homogeneity Of Variances Under Violation Of Normality Assumption.

– nonparametric tests of homogeneity of variances, Ansari–Bradley test, Mood test, Siegel–Tukey test, Capon test, Klotz test, power of tests:

ü Application and power of criteria for testing the homogeneity of variances. Part II. Nonparametric criteria;

Anomalous observations, Grubbs test, percentage points:

– Extending the Application of Grubbs-Type Tests in Rejecting Anomalous Measurements.

Abbé independence test:

– The Abbé independence test with deviations from normality.

Software for Simulation and Research of Probabilistic Regularities:

– Software System for Simulation and Research of Probabilistic Regularities and Statistical Data Analysis in Reliability and Quality Control.

Estimation of parameters of laws and testing of hypotheses on censored samples:

– Investigation Of The Estimates Properties And Goodness-Of-Fit Test Statistics From Censored Samples With Computer Modeling Technique;

Research of laws of distribution of functions from random variables:

– Statistical modeling as an effective instrument for investigating the distribution laws of functions of random quantities.