All Stories

  1. Using Vector Representations of Characteristic Functions and Vector Logarithms When Proving Asymptotic Statements

    Article • Stats, February 2026, MDPI AG

    Professor Wolf-Dieter Richter

  2. Inversion of Characteristic Functions Without Imaginary Unit

    Article • January 2026, MDPI AG

    Professor Wolf-Dieter Richter

  3. Using Vector Representations of Characteristic Functions and Vector Logarithms When Proving Asymptotic Statements

    Article • December 2025, MDPI AG

    Professor Wolf-Dieter Richter

  4. Vector Representations of Euler’s Formula and Riemann’s Zeta Function

    Article • Symmetry, September 2025, MDPI AG

    Professor Wolf-Dieter Richter

  5. Quaternions Without Imaginary Quantities or the Vector Representation of Quaternions

    Article • AppliedMath, September 2025, MDPI AG

    Professor Wolf-Dieter Richter

  6. Vector Representations of Euler’s Formula and Riemann’s Zeta Function

    Article • August 2025, MDPI AG

    Professor Wolf-Dieter Richter

  7. Quaternions Without Imaginarities or the Vector Representation of Quaternions

    Article • July 2025, MDPI AG

    Professor Wolf-Dieter Richter

  8. Short Remark on (p1,p2,p3)-Complex Numbers

    Article • Symmetry, December 2023, MDPI AG

    Professor Wolf-Dieter Richter

  9. On the Vector Representation of Characteristic Functions

    Article • Stats, October 2023, MDPI AG

    Professor Wolf-Dieter Richter

  10. Deterministic and Random Generalized Complex Numbers Related to a Class of Positively Homogeneous Functionals

    Article • Axioms, January 2023, MDPI AG

    Professor Wolf-Dieter Richter

  11. On Hyperbolic Complex Numbers

    Article • Applied Sciences, June 2022, MDPI AG

    Professor Wolf-Dieter Richter

  12. On Complex Numbers in Higher Dimensions

    Article • Axioms, January 2022, MDPI AG

    Professor Wolf-Dieter Richter

  13. Complex Numbers Related to Semi-Antinorms, Ellipses or Matrix Homogeneous Functionals

    Article • Axioms, December 2021, MDPI AG

    Professor Wolf-Dieter Richter

  14. Three-Complex Numbers and Related Algebraic Structures

    Article • Symmetry, February 2021, MDPI AG

    Professor Wolf-Dieter Richter

  15. Chi-Square and Student Bridge Distributions and the Behrens–Fisher Statistic

    Article • Stats, August 2020, MDPI AG

    Professor Wolf-Dieter Richter

  16. On lp-Complex Numbers

    Article • Symmetry, May 2020, MDPI AG

    Professor Wolf-Dieter Richter

  17. Mysterious Circle Numbers.Does πp,q Approach πp When q Is Tending to p ?

    Article • Mathematics, September 2019, MDPI AG

    Professor Wolf-Dieter Richter

  18. On Ball Numbers

    Article • Mathematics, August 2019, MDPI AG

    Professor Wolf-Dieter Richter

  19. On (p1,…,pk)-spherical distributions

    Article • Journal of Statistical Distributions and Applications, June 2019, Springer Science + Business Media

    Professor Wolf-Dieter Richter

  20. High-dimensional star-shaped distributions

    Article • Journal of Statistical Distributions and Applications, June 2019, Springer Science + Business Media

    Professor Wolf-Dieter Richter

  21. On p-generalized elliptical random processes

    Article • Journal of Statistical Distributions and Applications, March 2019, Springer Science + Business Media

    Professor Wolf-Dieter Richter

  22. Statistical reasoning in dependent p-generalized elliptically contoured distributions and beyond

    Article • Journal of Statistical Distributions and Applications, September 2017, Springer Science + Business Media

    Professor Wolf-Dieter Richter

  23. The Class of (p,q)-spherical Distributions with an Extension of the Sector and Circle Number Functions

    Article • Risks, July 2017, MDPI AG

    Professor Wolf-Dieter Richter

  24. The Class of (p,q)-spherical Distributions

    Article • July 2017, MDPI AG

    Professor Wolf-Dieter Richter

  25. Simulation of polyhedral convex contoured distributions

    Article • Journal of Statistical Distributions and Applications, March 2017, Springer Science + Business Media

    Professor Wolf-Dieter Richter

  26. Polyhedral Star-Shaped Distributions

    Article • Journal of Probability and Statistics, January 2017, Hindawi Publishing Corporation

    Professor Wolf-Dieter Richter

  27. Estimation of Star-Shaped Distributions

    Article • Risks, November 2016, MDPI AG

    Professor Wolf-Dieter Richter

  28. Skewness-Kurtosis Controlled Higher Order Equivalent Decisions

    Article • The Open Statistics & Probability Journal, April 2016, Bentham Science Publishers

    Professor Wolf-Dieter Richter

  29. Ball numbers of platonic bodies

    Article • Journal of Mathematical Analysis and Applications, August 2014, Elsevier

    Professor Wolf-Dieter Richter

  30. Kullback–Leibler life time testing

    Article • Applied Mathematics and Computation, August 2014, Elsevier

    Professor Wolf-Dieter Richter

  31. Exact extreme value, product, and ratio distributions under non-standard assumptions

    Article • AStA Advances in Statistical Analysis, March 2014, Springer Science + Business Media

    Professor Wolf-Dieter Richter

  32. Maximum distributions for

    Article • Statistics & Probability Letters, October 2013, Elsevier

    Professor Wolf-Dieter Richter

  33. Simulation of thep-generalized Gaussian distribution

    Article • Journal of Statistical Computation and Simulation, April 2013, Taylor & Francis

    Professor Wolf-Dieter Richter

  34. Geometric and Stochastic Representations for Elliptically Contoured Distributions

    Article • Communication in Statistics- Theory and Methods, February 2013, Taylor & Francis

    Professor Wolf-Dieter Richter

  35. Linear Combinations, Products and Ratios of Simplicial or Spherical Variates

    Article • Communication in Statistics- Theory and Methods, February 2013, Taylor & Francis

    Professor Wolf-Dieter Richter

  36. Geometric approach to the skewed normal distribution

    Article • Journal of Statistical Planning and Inference, December 2012, Elsevier

    Professor Wolf-Dieter Richter

  37. Reverse triangle inequality. Antinorms and semi-antinorms

    Article • Studia Scientiarum Mathematicarum Hungarica, March 2012, Akademiai Kiado

    Professor Wolf-Dieter Richter

  38. Exact distributions under non-standard model assumptions

    Article • January 2012, American Institute of Physics

    Professor Wolf-Dieter Richter

  39. On the ball number function

    Article • Lithuanian Mathematical Journal, July 2011, Springer Science + Business Media

    Professor Wolf-Dieter Richter

  40. Ellipses numbers and geometric measure representations

    Article • Journal of Applied Analysis, January 2011, De Gruyter

    Professor Wolf-Dieter Richter

  41. Continuous l n,p -symmetric distributions

    Article • Lithuanian Mathematical Journal, January 2009, Springer Science + Business Media

    Professor Wolf-Dieter Richter

  42. On the π-function for nonconvex l 2,p -circle discs

    Article • Lithuanian Mathematical Journal, July 2008, Springer Science + Business Media

    Professor Wolf-Dieter Richter

  43. On l 2,p -circle numbers

    Article • Lithuanian Mathematical Journal, April 2008, Springer Science + Business Media

    Professor Wolf-Dieter Richter

  44. Generalized spherical and simplicial coordinates

    Article • Journal of Mathematical Analysis and Applications, December 2007, Elsevier

    Professor Wolf-Dieter Richter

  45. Exact tests and confidence regions in nonlinear regression

    Article • Statistics, February 2005, Taylor & Francis

    Professor Wolf-Dieter Richter

  46. Exact probabilities of correct classifications for uncorrelated repeated measurements from elliptically contoured distributions

    Article • Journal of Multivariate Analysis, April 2004, Elsevier

    Professor Wolf-Dieter Richter

  47. Geometric Generalization of the Exponential Law

    Article • Journal of Multivariate Analysis, May 2002, Elsevier

    Professor Wolf-Dieter Richter

  48. Asymptotic Expansions for Large Deviation Probabilities of Noncentral Generalized Chi-Square Distributions

    Article • Journal of Multivariate Analysis, November 2000, Elsevier

    Professor Wolf-Dieter Richter

  49. A Geometric Approach to an Asymptotic Expansion for Large Deviation Probabilities of Gaussian Random Vectors

    Article • Journal of Multivariate Analysis, July 1996, Elsevier

    Professor Wolf-Dieter Richter

  50. A geometric approach to finite sample and large deviation properties in two-way ANOVA with spherically distributed error vectors

    Article • Metrika, December 1994, Springer Science + Business Media

    Dr Josef G. Steinebach, Professor Wolf-Dieter Richter

  51. The laplace integral and probabilities of moderate deviations in Rk

    Article • Journal of Soviet Mathematics, September 1987, Springer Science + Business Media

    Professor Wolf-Dieter Richter

  52. Moderate deviations for densities in Rk

    Article • Journal of Soviet Mathematics, December 1984, Springer Science + Business Media

    Professor Wolf-Dieter Richter

  53. Probabilities of large deviations of sums of independent identically distributed random vectors

    Article • Lithuanian Mathematical Journal, January 1980, Springer Science + Business Media

    Professor Wolf-Dieter Richter