Posts about Statistics
2023
- Central limit theorem and log-normal distribution (September 19)
- Hodges-Lehmann Gaussian efficiency: location shift vs. shift of locations (September 12)
- Thoughts on automatic statistical methods and broken assumptions (September 5)
- Ratio estimator based on the Hodges-Lehmann approach (August 29)
- Weighted Mann-Whitney U test, Part 2 (August 22)
- Exploring the power curve of the Cucconi test (August 15)
- Parametric, Nonparametric, Robust, and Defensive statistics (August 8)
- Insidious implicit statistical assumptions (August 1)
- Four main books on robust statistics (July 25)
- Multimodal distributions and effect size (July 18)
- Unobvious limitations of R *signrank Wilcoxon Signed Rank functions (July 11)
- Weighted Mann-Whitney U test, Part 1 (July 4)
- Joining modes of multimodal distributions (June 27)
- Understanding the pitfalls of preferring the median over the mean (June 20)
- Introducing the defensive statistics (June 13)
- Edgeworth expansion for the Mann-Whitney U test, Part 2: increased accuracy (June 6)
- Edgeworth expansion for the Mann-Whitney U test (May 30)
- Confusing tie correction in the classic Mann-Whitney U test implementation (May 23)
- Efficiency of the central tendency measures under the uniform distribution (May 16)
- Unobvious problems of using the R's implementation of the Hodges-Lehmann estimator (May 9)
- When Python's Mann-Whitney U test returns extremely distorted p-values (May 2)
- When R's Mann-Whitney U test returns extremely distorted p-values (April 25)
- Preprint announcement: 'Weighted quantile estimators' (April 18)
- Rethinking Type I/II error rates with power curves (April 11)
- Adaptation of continuous scale measures to discrete distributions (April 4)
- Weighted modification of the Hodges-Lehmann location estimator (March 28)
- Performance stability of GitHub Actions (March 21)
- p-value distribution of the Brunner–Munzel test in the finite case (March 14)
- Comparing statistical power of the Mann-Whitney U test and the Brunner-Munzel test (March 7)
- p-value distribution of the Mann–Whitney U test in the finite case (February 28)
- Corner case of the Brunner–Munzel test (February 21)
- Examples of the Mann–Whitney U test misuse cases (February 14)
- Types of finite-sample consistency with the standard deviation (February 7)
- Thoughts about outlier removal and ozone holes (January 31)
- Nonparametric effect size: Cohen's d vs. Glass's delta (January 24)
- Trinal statistical thresholds (January 17)
- Trimmed Hodges-Lehmann location estimator, Part 2: Gaussian efficiency (January 10)
- Trimmed Hodges-Lehmann location estimator, Part 1: breakdown point (January 3)
2022
- Median of the shifts vs. shift of the medians, Part 2: Gaussian efficiency (December 27)
- Median of the shifts vs. shift of the medians, Part 1 (December 20)
- Resistance to the low-density regions: the Hodges-Lehmann location estimator (December 13)
- Kernel density estimation boundary correction: reflection (ggplot2 v3.4.0) (December 6)
- Sheather & Jones vs. unbiased cross-validation (November 29)
- Resistance to the low-density regions: the Harrell-Davis median (November 22)
- Resistance to the low-density regions: the mean and the median (November 15)
- Finite-sample Gaussian efficiency of the trimmed Harrell-Davis median estimator (November 8)
- Finite-sample Gaussian efficiency of the Harrell-Davis median estimator (November 1)
- Weighted quantile estimation for a weighted mixture distribution (October 25)
- Preprint announcement: 'Finite-sample Rousseeuw-Croux scale estimators' (October 18)
- Sensitivity curve of the Harrell-Davis quantile estimator, Part 3 (October 11)
- Sensitivity curve of the Harrell-Davis quantile estimator, Part 2 (October 4)
- Sensitivity curve of the Harrell-Davis quantile estimator, Part 1 (September 27)
- Weighted quantile estimators for exponential smoothing and mixture distributions (September 20)
- The Huggins-Roy family of effective sample sizes (September 13)
- Finite-sample bias correction factors for Rousseeuw-Croux scale estimators (September 6)
- Preprint announcement: 'Quantile absolute deviation' (September 1)
- Standard trimmed Harrell-Davis median estimator (August 31)
- Optimal quantile absolute deviation (August 30)
- Quantile absolute deviation of the Pareto distribution (August 29)
- Quantile absolute deviation of the Exponential distribution (August 26)
- Quantile absolute deviation of the Uniform distribution (August 25)
- Quantile absolute deviation of the Normal distribution (August 24)
- Standard quantile absolute deviation (August 23)
- Asymptotic Gaussian efficiency of the quantile absolute deviation (August 16)
- Finite-sample efficiency of the Rousseeuw-Croux estimators (August 9)
- Caveats of using the median absolute deviation (August 2)
- 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)
- Challenges of change point detection in CI performance data (July 19)
- Degenerate point of dispersion estimators (July 12)
- Untied quantile absolute deviation (July 5)
- Middle non-zero quantile absolute deviation, Part 2 (June 28)
- The expected number of takes from a discrete distribution before observing the given element (June 21)
- Folded medians (June 14)
- Gastwirth's location estimator (June 7)
- Hodges-Lehmann-Sen shift and shift confidence interval estimators (May 31)
- Statistical efficiency of the Hodges-Lehmann median estimator, Part 2 (May 24)
- Statistical efficiency of the Hodges-Lehmann median estimator, Part 1 (May 17)
- Expected value of the maximum of two standard half-normal distributions (May 10)
- Expected value of the minimum of two standard half-normal distributions (May 3)
- Unbiased median absolute deviation for n=2 (April 26)
- Weighted trimmed Harrell-Davis quantile estimator (April 19)
- Minimum meaningful statistical level for the Mann–Whitney U test (April 12)
- Fence-based outlier detectors, Part 2 (April 5)
- Fence-based outlier detectors, Part 1 (March 29)
- Publication announcement: 'Trimmed Harrell-Davis quantile estimator based on the highest density interval of the given width' (March 22)
- Asymmetric decile-based outlier detector, Part 2 (March 15)
- Asymmetric decile-based outlier detector, Part 1 (March 8)
- Probability of observing outliers using Tukey's fences (March 1)
- Gamma effect size powered by the middle non-zero quantile absolute deviation (February 22)
- Middle non-zero quantile absolute deviation (February 15)
- Unbiased median absolute deviation based on the trimmed Harrell-Davis quantile estimator (February 8)
- Median absolute deviation vs. Shamos estimator (February 1)
- Moving extended P² quantile estimator (January 25)
- Extended P² quantile estimator (January 18)
- P² quantile estimator marker adjusting order (January 11)
- P² quantile estimator initialization strategy (January 4)
2021
- Misleading geometric mean (December 28)
- Matching quantile sets using likelihood based on the binomial coefficients (December 21)
- Ratio function vs. ratio distribution (December 14)
- Shift function vs. shift distribution (December 7)
- Preprint announcement: 'Trimmed Harrell-Davis quantile estimator based on the highest density interval of the given width' (November 30)
- Non-normal median sampling distribution (November 23)
- Misleading kurtosis (November 16)
- Misleading skewness (November 9)
- Greenwald-Khanna quantile estimator (November 2)
- P² quantile estimator rounding issue (October 26)
- Trimmed Harrell-Davis quantile estimator based on the highest density interval of the given width (October 19)
- Optimal window of the trimmed Harrell-Davis quantile estimator, Part 2: Trying Planck-taper window (October 12)
- Optimal window of the trimmed Harrell-Davis quantile estimator, Part 1: Problems with the rectangular window (October 5)
- Beta distribution highest density interval of the given width (September 28)
- Quantile estimators based on k order statistics, Part 8: Winsorized Harrell-Davis quantile estimator (September 21)
- Quantile estimators based on k order statistics, Part 7: Optimal threshold for the trimmed Harrell-Davis quantile estimator (September 14)
- Quantile estimators based on k order statistics, Part 6: Continuous trimmed Harrell-Davis quantile estimator (September 7)
- Quantile estimators based on k order statistics, Part 5: Improving trimmed Harrell-Davis quantile estimator (August 31)
- Quantile estimators based on k order statistics, Part 4: Adopting trimmed Harrell-Davis quantile estimator (August 24)
- Quantile estimators based on k order statistics, Part 3: Playing with the Beta function (August 17)
- Quantile estimators based on k order statistics, Part 2: Extending Hyndman-Fan equations (August 10)
- Quantile estimators based on k order statistics, Part 1: Motivation (August 3)
- Avoiding over-trimming with the trimmed Harrell-Davis quantile estimator (July 27)
- Optimal threshold of the trimmed Harrell-Davis quantile estimator (July 20)
- Estimating quantile confidence intervals: Maritz-Jarrett vs. jackknife (July 13)
- Using Kish's effective sample size with weighted quantiles (July 6)
- Partial binning compression of performance series (June 29)
- Calculating gamma effect size for samples with zero median absolute deviation (June 22)
- Discrete performance distributions (June 15)
- Customization of the nonparametric Cohen's d-consistent effect size (June 8)
- Robust alternative to statistical efficiency (June 1)
- Improving the efficiency of the Harrell-Davis quantile estimator for special cases using custom winsorizing and trimming strategies (May 25)
- Comparing the efficiency of the Harrell-Davis, Sfakianakis-Verginis, and Navruz-Özdemir quantile estimators (May 18)
- Dispersion exponential smoothing (May 11)
- Quantile exponential smoothing (May 4)
- Improving quantile-respectful density estimation for discrete distributions using jittering (April 27)
- How to build a smooth density estimation for a discrete sample using jittering (April 20)
- Kernel density estimation and discrete values (April 13)
- Efficiency of the winsorized and trimmed Harrell-Davis quantile estimators (April 6)
- Trimmed modification of the Harrell-Davis quantile estimator (March 30)
- Efficiency of the Harrell-Davis quantile estimator (March 23)
- Navruz-Özdemir quantile estimator (March 16)
- Sfakianakis-Verginis quantile estimator (March 9)
- Winsorized modification of the Harrell-Davis quantile estimator (March 2)
- Misleading standard deviation (February 23)
- Unbiased median absolute deviation based on the Harrell-Davis quantile estimator (February 16)
- Unbiased median absolute deviation (February 9)
- Comparing distribution quantiles using gamma effect size (February 2)
- A single outlier could completely distort your Cohen's d value (January 26)
- Better moving quantile estimations using the partitioning heaps (January 19)
- MP² quantile estimator: estimating the moving median without storing values (January 12)
- Case study: Accuracy of the MAD estimation using the Harrell-Davis quantile estimator (Gumbel distribution) (January 5)
2020
- Fast implementation of the moving quantile based on the partitioning heaps (December 29)
- Coverage of quantile confidence intervals (December 22)
- Statistical approaches for performance analysis (December 15)
- Quantile confidence intervals for weighted samples (December 8)
- Quantile absolute deviation: estimating statistical dispersion around quantiles (December 1)
- P² quantile estimator: estimating the median without storing values (November 24)
- Plain-text summary notation for multimodal distributions (November 17)
- Intermodal outliers (November 10)
- Lowland multimodality detection (November 3)
- Quantile-respectful density estimation based on the Harrell-Davis quantile estimator (October 27)
- Misleading histograms (October 20)
- The importance of kernel density estimation bandwidth (October 13)
- The median absolute deviation value of the Gumbel distribution (October 6)
- Weighted quantile estimators (September 29)
- Nonparametric Cohen's d-consistent effect size (June 25)
- DoubleMAD outlier detector based on the Harrell-Davis quantile estimator (June 22)
2019
- Distribution comparison via the shift and ratio functions (October 11)
- Normality is a myth (October 9)
- Implementation of efficient algorithm for changepoint detection: ED-PELT (October 7)
2017
- Reflecting on performance testing (August 1)