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

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

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 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
χ^{2} Fitting Criteria.

** **

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

** **

**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: **

__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.__

** **

**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:**

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

**Research of laws of distribution of functions from random variables:**