Posts about Mathematics

2023

  1. Central limit theorem and log-normal distribution (September 19)
  2. Hodges-Lehmann Gaussian efficiency: location shift vs. shift of locations (September 12)
  3. Thoughts on automatic statistical methods and broken assumptions (September 5)
  4. Ratio estimator based on the Hodges-Lehmann approach (August 29)
  5. Weighted Mann-Whitney U test, Part 2 (August 22)
  6. Exploring the power curve of the Cucconi test (August 15)
  7. Parametric, Nonparametric, Robust, and Defensive statistics (August 8)
  8. Insidious implicit statistical assumptions (August 1)
  9. Four main books on robust statistics (July 25)
  10. Multimodal distributions and effect size (July 18)
  11. Unobvious limitations of R *signrank Wilcoxon Signed Rank functions (July 11)
  12. Weighted Mann-Whitney U test, Part 1 (July 4)
  13. Joining modes of multimodal distributions (June 27)
  14. Understanding the pitfalls of preferring the median over the mean (June 20)
  15. Introducing the defensive statistics (June 13)
  16. Edgeworth expansion for the Mann-Whitney U test, Part 2: increased accuracy (June 6)
  17. Edgeworth expansion for the Mann-Whitney U test (May 30)
  18. Confusing tie correction in the classic Mann-Whitney U test implementation (May 23)
  19. Efficiency of the central tendency measures under the uniform distribution (May 16)
  20. Unobvious problems of using the R's implementation of the Hodges-Lehmann estimator (May 9)
  21. When Python's Mann-Whitney U test returns extremely distorted p-values (May 2)
  22. When R's Mann-Whitney U test returns extremely distorted p-values (April 25)
  23. Preprint announcement: 'Weighted quantile estimators' (April 18)
  24. Rethinking Type I/II error rates with power curves (April 11)
  25. Adaptation of continuous scale measures to discrete distributions (April 4)
  26. Weighted modification of the Hodges-Lehmann location estimator (March 28)
  27. p-value distribution of the Brunner–Munzel test in the finite case (March 14)
  28. Comparing statistical power of the Mann-Whitney U test and the Brunner-Munzel test (March 7)
  29. p-value distribution of the Mann–Whitney U test in the finite case (February 28)
  30. Corner case of the Brunner–Munzel test (February 21)
  31. Examples of the Mann–Whitney U test misuse cases (February 14)
  32. Types of finite-sample consistency with the standard deviation (February 7)
  33. Thoughts about outlier removal and ozone holes (January 31)
  34. Nonparametric effect size: Cohen's d vs. Glass's delta (January 24)
  35. Trinal statistical thresholds (January 17)
  36. Trimmed Hodges-Lehmann location estimator, Part 2: Gaussian efficiency (January 10)
  37. Trimmed Hodges-Lehmann location estimator, Part 1: breakdown point (January 3)

2022

  1. Median of the shifts vs. shift of the medians, Part 2: Gaussian efficiency (December 27)
  2. Median of the shifts vs. shift of the medians, Part 1 (December 20)
  3. Resistance to the low-density regions: the Hodges-Lehmann location estimator (December 13)
  4. Kernel density estimation boundary correction: reflection (ggplot2 v3.4.0) (December 6)
  5. Sheather & Jones vs. unbiased cross-validation (November 29)
  6. Resistance to the low-density regions: the Harrell-Davis median (November 22)
  7. Resistance to the low-density regions: the mean and the median (November 15)
  8. Finite-sample Gaussian efficiency of the trimmed Harrell-Davis median estimator (November 8)
  9. Finite-sample Gaussian efficiency of the Harrell-Davis median estimator (November 1)
  10. Weighted quantile estimation for a weighted mixture distribution (October 25)
  11. Preprint announcement: 'Finite-sample Rousseeuw-Croux scale estimators' (October 18)
  12. Sensitivity curve of the Harrell-Davis quantile estimator, Part 3 (October 11)
  13. Sensitivity curve of the Harrell-Davis quantile estimator, Part 2 (October 4)
  14. Sensitivity curve of the Harrell-Davis quantile estimator, Part 1 (September 27)
  15. Weighted quantile estimators for exponential smoothing and mixture distributions (September 20)
  16. The Huggins-Roy family of effective sample sizes (September 13)
  17. Finite-sample bias correction factors for Rousseeuw-Croux scale estimators (September 6)
  18. Preprint announcement: 'Quantile absolute deviation' (September 1)
  19. Standard trimmed Harrell-Davis median estimator (August 31)
  20. Optimal quantile absolute deviation (August 30)
  21. Quantile absolute deviation of the Pareto distribution (August 29)
  22. Quantile absolute deviation of the Exponential distribution (August 26)
  23. Quantile absolute deviation of the Uniform distribution (August 25)
  24. Quantile absolute deviation of the Normal distribution (August 24)
  25. Standard quantile absolute deviation (August 23)
  26. Asymptotic Gaussian efficiency of the quantile absolute deviation (August 16)
  27. Finite-sample efficiency of the Rousseeuw-Croux estimators (August 9)
  28. Caveats of using the median absolute deviation (August 2)
  29. Preprint announcement: 'Finite-sample bias-correction factors for the median absolute deviation based on the Harrell-Davis quantile estimator and its trimmed modification' (July 26)
  30. Challenges of change point detection in CI performance data (July 19)
  31. Dynamical System Case Study 2 (Piecewise linear LLL-system) (July 17)
  32. Degenerate point of dispersion estimators (July 12)
  33. Untied quantile absolute deviation (July 5)
  34. Middle non-zero quantile absolute deviation, Part 2 (June 28)
  35. The expected number of takes from a discrete distribution before observing the given element (June 21)
  36. Folded medians (June 14)
  37. Gastwirth's location estimator (June 7)
  38. Dynamical System Case Study 1 (symmetric 3d system) (June 5)
  39. Beeping Busy Beavers and twin prime conjecture (June 1)
  40. Hodges-Lehmann-Sen shift and shift confidence interval estimators (May 31)
  41. Statistical efficiency of the Hodges-Lehmann median estimator, Part 2 (May 24)
  42. Statistical efficiency of the Hodges-Lehmann median estimator, Part 1 (May 17)
  43. Expected value of the maximum of two standard half-normal distributions (May 10)
  44. Expected value of the minimum of two standard half-normal distributions (May 3)
  45. Unbiased median absolute deviation for n=2 (April 26)
  46. Weighted trimmed Harrell-Davis quantile estimator (April 19)
  47. Minimum meaningful statistical level for the Mann–Whitney U test (April 12)
  48. Fence-based outlier detectors, Part 2 (April 5)
  49. Fence-based outlier detectors, Part 1 (March 29)
  50. Publication announcement: 'Trimmed Harrell-Davis quantile estimator based on the highest density interval of the given width' (March 22)
  51. Asymmetric decile-based outlier detector, Part 2 (March 15)
  52. Asymmetric decile-based outlier detector, Part 1 (March 8)
  53. Probability of observing outliers using Tukey's fences (March 1)
  54. Gamma effect size powered by the middle non-zero quantile absolute deviation (February 22)
  55. Middle non-zero quantile absolute deviation (February 15)
  56. Unbiased median absolute deviation based on the trimmed Harrell-Davis quantile estimator (February 8)
  57. Median absolute deviation vs. Shamos estimator (February 1)
  58. Moving extended P² quantile estimator (January 25)
  59. Extended P² quantile estimator (January 18)
  60. P² quantile estimator marker adjusting order (January 11)
  61. P² quantile estimator initialization strategy (January 4)

2021

  1. Misleading geometric mean (December 28)
  2. Matching quantile sets using likelihood based on the binomial coefficients (December 21)
  3. Ratio function vs. ratio distribution (December 14)
  4. Shift function vs. shift distribution (December 7)
  5. Preprint announcement: 'Trimmed Harrell-Davis quantile estimator based on the highest density interval of the given width' (November 30)
  6. Non-normal median sampling distribution (November 23)
  7. Misleading kurtosis (November 16)
  8. Misleading skewness (November 9)
  9. Greenwald-Khanna quantile estimator (November 2)
  10. P² quantile estimator rounding issue (October 26)
  11. Trimmed Harrell-Davis quantile estimator based on the highest density interval of the given width (October 19)
  12. Optimal window of the trimmed Harrell-Davis quantile estimator, Part 2: Trying Planck-taper window (October 12)
  13. Optimal window of the trimmed Harrell-Davis quantile estimator, Part 1: Problems with the rectangular window (October 5)
  14. Beta distribution highest density interval of the given width (September 28)
  15. Quantile estimators based on k order statistics, Part 8: Winsorized Harrell-Davis quantile estimator (September 21)
  16. Quantile estimators based on k order statistics, Part 7: Optimal threshold for the trimmed Harrell-Davis quantile estimator (September 14)
  17. Quantile estimators based on k order statistics, Part 6: Continuous trimmed Harrell-Davis quantile estimator (September 7)
  18. Quantile estimators based on k order statistics, Part 5: Improving trimmed Harrell-Davis quantile estimator (August 31)
  19. Quantile estimators based on k order statistics, Part 4: Adopting trimmed Harrell-Davis quantile estimator (August 24)
  20. Quantile estimators based on k order statistics, Part 3: Playing with the Beta function (August 17)
  21. Quantile estimators based on k order statistics, Part 2: Extending Hyndman-Fan equations (August 10)
  22. Quantile estimators based on k order statistics, Part 1: Motivation (August 3)
  23. Avoiding over-trimming with the trimmed Harrell-Davis quantile estimator (July 27)
  24. Optimal threshold of the trimmed Harrell-Davis quantile estimator (July 20)
  25. Estimating quantile confidence intervals: Maritz-Jarrett vs. jackknife (July 13)
  26. Using Kish's effective sample size with weighted quantiles (July 6)
  27. Partial binning compression of performance series (June 29)
  28. Calculating gamma effect size for samples with zero median absolute deviation (June 22)
  29. Discrete performance distributions (June 15)
  30. Customization of the nonparametric Cohen's d-consistent effect size (June 8)
  31. Robust alternative to statistical efficiency (June 1)
  32. Improving the efficiency of the Harrell-Davis quantile estimator for special cases using custom winsorizing and trimming strategies (May 25)
  33. Comparing the efficiency of the Harrell-Davis, Sfakianakis-Verginis, and Navruz-Özdemir quantile estimators (May 18)
  34. Dispersion exponential smoothing (May 11)
  35. Quantile exponential smoothing (May 4)
  36. Improving quantile-respectful density estimation for discrete distributions using jittering (April 27)
  37. How to build a smooth density estimation for a discrete sample using jittering (April 20)
  38. Kernel density estimation and discrete values (April 13)
  39. Efficiency of the winsorized and trimmed Harrell-Davis quantile estimators (April 6)
  40. Trimmed modification of the Harrell-Davis quantile estimator (March 30)
  41. Efficiency of the Harrell-Davis quantile estimator (March 23)
  42. Navruz-Özdemir quantile estimator (March 16)
  43. Sfakianakis-Verginis quantile estimator (March 9)
  44. Winsorized modification of the Harrell-Davis quantile estimator (March 2)
  45. Misleading standard deviation (February 23)
  46. Unbiased median absolute deviation based on the Harrell-Davis quantile estimator (February 16)
  47. Unbiased median absolute deviation (February 9)
  48. Comparing distribution quantiles using gamma effect size (February 2)
  49. A single outlier could completely distort your Cohen's d value (January 26)
  50. Better moving quantile estimations using the partitioning heaps (January 19)
  51. MP² quantile estimator: estimating the moving median without storing values (January 12)
  52. Case study: Accuracy of the MAD estimation using the Harrell-Davis quantile estimator (Gumbel distribution) (January 5)

2020

  1. Fast implementation of the moving quantile based on the partitioning heaps (December 29)
  2. Coverage of quantile confidence intervals (December 22)
  3. Statistical approaches for performance analysis (December 15)
  4. Quantile confidence intervals for weighted samples (December 8)
  5. Quantile absolute deviation: estimating statistical dispersion around quantiles (December 1)
  6. P² quantile estimator: estimating the median without storing values (November 24)
  7. Plain-text summary notation for multimodal distributions (November 17)
  8. Intermodal outliers (November 10)
  9. Lowland multimodality detection (November 3)
  10. Quantile-respectful density estimation based on the Harrell-Davis quantile estimator (October 27)
  11. Misleading histograms (October 20)
  12. The importance of kernel density estimation bandwidth (October 13)
  13. The median absolute deviation value of the Gumbel distribution (October 6)
  14. Weighted quantile estimators (September 29)
  15. Nonparametric Cohen's d-consistent effect size (June 25)
  16. DoubleMAD outlier detector based on the Harrell-Davis quantile estimator (June 22)

2019

  1. Distribution comparison via the shift and ratio functions (October 11)
  2. Normality is a myth (October 9)
  3. Implementation of efficient algorithm for changepoint detection: ED-PELT (October 7)

2017

  1. Reflecting on performance testing (August 1)