# Posts about Mathematics

## 2022

- 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)* - Dynamical System Case Study 2 (Piecewise linear LLL-system)
*(July 17)* - 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)* - Dynamical System Case Study 1 (symmetric 3d system)
*(June 5)* - Beeping Busy Beavers and twin prime conjecture
*(June 1)* - 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)*