Draft:Modeest

modeest
modeest
Developer	Paul Poncet
Stable release	2.4.0 / November 18, 2019
Written in	R
Operating system	Cross-platform
License	GPL (>= 2)
Website	cran.r-project.org/package=modeest

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Declined by I2Overcome 16 days ago. Last edited by I2Overcome 16 days ago. Reviewer: Inform author.

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Comment: Evidence of LLM use including non-existent categories and multiple bolded lists. References are listed in multiple sections; most seem irrelevant to the topic of the article. No evidence of coverage in reliable secondary sources. I₂Overcome ^talk 01:14, 8 December 2025 (UTC)

Comment: In accordance with Wikipedia's Conflict of interest policy, I disclose that I have a conflict of interest regarding the subject of this article. Ο ηλίθιος (talk) 23:26, 13 November 2025 (UTC)

modeest is an R package designed for estimating the mode of univariate data or distributions. Authored by Paul Poncet, it provides a collection of estimators suitable for unimodal and occasionally multimodal datasets. The package is available on the Comprehensive R Archive Network (CRAN) and is licensed under the GNU General Public License version 2 or later.

Overview

The modeest package focuses on robust methods for mode estimation in statistical analysis. It includes functions to compute modes using various techniques, such as kernel-based estimators, iterative procedures, and distribution-specific calculations. The package is particularly useful in fields requiring precise identification of central tendencies beyond mean or median, including data analysis in economics, biology, and engineering.

First released in its current form as version 2.4.0 on November 18, 2019, modeest depends on R version 3.2 or higher. It has been referenced in statistical software literature for its contributions to mode assessment tools.

Citations and Usage

The package has been cited in several academic and practical contexts:

Poncet, P. (2019). modeest: Mode Estimation. R package version 2.4.0. https://CRAN.R-project.org/package=modeest. This serves as the primary citation for works employing its functions.^[1]
Ameijeiras-Alonso, J., Crujeiras, R. M., & Rodríguez-Casal, A. (2021). multimode: An R Package for Mode Assessment. Journal of Statistical Software, 97(9), 1–32. References modeest as a complementary tool for mode estimation when the underlying distribution is unimodal.^[2]
Delignette-Muller, M. L., & Dutang, C. (2015). fitdistrplus: An R Package for Fitting Distributions. Journal of Statistical Software, 64(4), 1–34. Acknowledges modeest among packages providing mode estimation capabilities in the context of distribution fitting.^[3]
Practical applications are evident in educational resources, such as tutorials on calculating modes in R, where functions like mfv from modeest are demonstrated.^[4] Similarly, Stack Overflow discussions employ modeest for handling unimodal or multimodal datasets.^[5]
The package is also mentioned in broader guides on R packages for probability distributions, emphasizing its role in mode estimation within research workflows.^[6]

Functions

The package includes the following functions, each with specific parameters, descriptions, and underlying methodological references where applicable.

asselin

Parameters: x (numeric vector of observations), bw (numeric in (0, 1]), ... (arguments passed to quantile).
Description: Computes the mode estimator based on Asselin de Beauville's method. Returns a numeric mode estimate. Invoked via mlv(x, method = "asselin", ...).

References:

Asselin de Beauville, J.-P. (1978). Estimation non parametrique de la densite et du mode, exemple de la distribution Gamma. Revue de Statistique Appliquée, 26(3), 47–70.

distrMode

Parameters: x (character name of distribution), ... (additional parameters). Variants include betaMode(shape1, shape2, ncp = 0).
Description: Calculates the mode of standard probability distributions in R, such as normal or Cauchy. Returns a numeric value representing the true mode.

References: No specific journal articles, as it computes theoretical modes for standard distributions.

grenander

Parameters: x (numeric vector), bw (numeric in (0, 1]), k (numeric), p (numeric; Inf uses venter), ... (arguments for venter).
Description: Implements the Grenander mode estimator. Returns a numeric mode estimate. If p = Inf, it uses the venter estimator. Accessible via mlv(x, method = "grenander", bw, k, p, ...).

References:

Grenander, U. (1965). Some direct estimates of the mode. The Annals of Mathematical Statistics, 36, 131–138.
Dalenius, T. (1965). The Mode - A Neglected Statistical Parameter. Journal of the Royal Statistical Society. Series A (General), 128(1), 110–117.
Adriano, K. N., Gentle, J. E., & Sposito, V. A. (1977). On the asymptotic bias of Grenander’s mode estimator. Communications in Statistics - Theory and Methods, 6(8), 773–776.
Hall, P. (1982). Asymptotic Theory of Grenander’s Mode Estimator. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 60(3), 315–334.

hrm

Parameters: x (numeric vector), bw (numeric in (0, 1]), ... (additional arguments).
Description: Computes Bickel's half-range mode estimator. Currently defunct due to dependency on the Bioconductor package 'genefilter'. Returns a numeric mode estimate. Called via mlv(x, method = "hrm", bw, ...).

References:

Bickel, D. R. (2002). Robust estimators of the mode and skewness of continuous data. Computational Statistics & Data Analysis, 39(2), 153–163.
Hedges, S. B., & Shah, P. (2003). Comparison of mode estimation methods and application in molecular clock analysis. BMC Bioinformatics, 4, 31.
Bickel, D. R., & Fruehwirth, R. (2006). On a Fast, Robust Estimator of the Mode: Comparisons to Other Robust Estimators with Applications. Computational Statistics & Data Analysis, 50(12), 3500–3530.

hsm

Parameters: x (numeric vector), bw (numeric or function in (0, 1]), k (numeric), tie.action (character), tie.limit (numeric), ... (additional arguments).
Description: Implements the Robertson-Cryer mode estimator, known as half-sample mode (if bw = 1/2) or fraction-sample mode. Returns a numeric mode estimate and handles ties. Invoked via mlv(x, method = "hsm", ...).

References:

Robertson, T., & Cryer, J. D. (1974). An iterative procedure for estimating the mode. Journal of the American Statistical Association, 69(348), 1012–1016.
Bickel, D. R., & Fruehwirth, R. (2006). On a Fast, Robust Estimator of the Mode: Comparisons to Other Robust Estimators with Applications. Computational Statistics & Data Analysis, 50(12), 3500–3530.

lientz

Parameters: x (numeric vector or "lientz" object), bw (numeric in (0, 1)).
Description: Determines the Lientz mode estimator by minimizing the empirical Lientz function. Returns an object of class c("lientz", "function"). Callable via mlv(x, method = "lientz", ...).

References:

Lientz, B. P. (1969). On estimating points of local maxima and minima of density functions. In M. L. Puri (Ed.), Nonparametric Techniques in Statistical Inference (pp. 275–282). Cambridge University Press.
Lientz, B. P. (1970). Results on nonparametric modal intervals. SIAM Journal on Applied Mathematics, 19(2), 356–366.
Lientz, B. P. (1972). Properties of modal intervals. SIAM Journal on Applied Mathematics, 23(1), 1–5.

meanshift

Parameters: x (numeric vector), bw (numeric), kernel (character, e.g., "biweight"), par (numeric initial value), iter (numeric iterations), tolerance (numeric stopping criteria).
Description: Applies the mean-shift mode estimator. Returns a numeric mode estimate with an "iterations" attribute. Called via mlv(x, method = "meanshift", ...).

References:

Fukunaga, K., & Hostetler, L. (1975). The estimation of the gradient of a density function, with applications in pattern recognition. IEEE Transactions on Information Theory, 21(1), 32–40.

mlv

Parameters: x (numeric vector, factor, integer, or character distribution name), bw (numeric), method (character, e.g., "lientz"), na.rm (logical), ... (arguments for computation).
Description: Generic function for mode estimation in univariate distributions. Returns a vector matching x's type. Supports distribution modes if x is a character (e.g., "beta").

References: No specific journal articles, as it is a wrapper for various methods.

naive

Parameters: x (numeric vector), bw (numeric in (0, 1)).
Description: Computes the Chernoff or 'naive' mode estimator as the center of the interval with the most observations. Returns a numeric mode estimate. Invoked via mlv(x, method = "naive", bw).

References:

Chernoff, H. (1964). Estimation of the mode. Annals of the Institute of Statistical Mathematics, 16(1), 31–41.
Leclerc, J. (1997). Comportement limite fort de deux estimateurs du mode : le shorth et l’estimateur naif. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 325(11), 1207–1210.

parzen

Parameters: x (numeric vector), bw (numeric), kernel (character), abc (logical), tolerance (numeric), ... (arguments for optim).
Description: Implements Parzen's kernel mode estimator by maximizing the kernel density estimate. Returns a numeric mode estimate. If kernel = "uniform", it reverts to the naive estimator. Called via mlv(x, method = "parzen", ...).

References:

Parzen, E. (1962). On estimation of a probability density function and mode. The Annals of Mathematical Statistics, 33(3), 1065–1076.
Konakov, V. D. (1973). On the asymptotic normality of the mode of multidimensional distributions. Theory of Probability & Its Applications, 18(4), 794–803.
Eddy, W. F. (1980). Optimum kernel estimators of the mode. The Annals of Statistics, 8(4), 870–882.
Eddy, W. F. (1982). The Asymptotic Distributions of Kernel Estimators of the Mode. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 59(3), 279–290.
Romano, J. P. (1988). On weak convergence and optimality of kernel density estimates of the mode. The Annals of Statistics, 16(2), 629–647.
Abraham, C., Biau, G., & Cadre, B. (2003). Simple Estimation of the Mode of a Multivariate Density. Canadian Journal of Statistics, 31(1), 23–34.
Abraham, C., Biau, G., & Cadre, B. (2004). On the Asymptotic Properties of a Simple Estimate of the Mode. ESAIM: Probability and Statistics, 8, 1–11.

skewness

Parameters: x (numeric vector), na.rm (logical), method (character: "moment", "fisher", "bickel"), M (numeric mode estimate, default shorth(x)), ... (additional arguments).
Description: Calculates skewness using various methods. Returns a numeric value with a method attribute.

References:

Bickel, D. R. (2002). Robust estimators of the mode and skewness of continuous data. Computational Statistics & Data Analysis, 39(2), 153–163. (For the "bickel" method.)

tsybakov

Parameters: x (numeric vector), bw (numeric vector), a (numeric vector), alpha (numeric, default 0.9), kernel (character), dmp (logical), par (numeric initial, default shorth(x)).
Description: Applies the Tsybakov mode estimator via a gradient-like recursive algorithm. Returns a numeric mode estimate. Invoked via mlv(x, method = "tsybakov", ...).

References:

Mizoguchi, R., & Shimura, M. (1976). Nonparametric Learning Without a Teacher Based on Mode Estimation. IEEE Transactions on Computers, C-25(11), 1109–1117.
Tsybakov, A. (1990). Recursive estimation of the mode of a multivariate distribution. Problems of Information Transmission, 26(1), 31–37.
Djeddour, K., Mokkadem, A., & Pelletier, M. (2003). Sur l’estimation recursive du mode et de la valeur modale d’une densite de probabilite. Technical report 105.
Djeddour, K., Mokkadem, A., & Pelletier, M. (2003). Application du principe de moyennisation a l’estimation recursive du mode et de la valeur modale d’une densite de probabilite. Technical report 106.

venter

Parameters: x (numeric vector), bw (numeric in (0, 1]), k (numeric), iter (numeric), type (numeric/character, e.g., "shorth"), tie.action (character), tie.limit (numeric), warn (logical), ... (additional arguments).
Description: Computes the Venter mode estimator (also known as Dalenius or LMS). Returns a numeric mode estimate and handles ties. Called via mlv(x, method = "venter", ...).

References:

Dalenius, T. (1965). The Mode - A Neglected Statistical Parameter. Journal of the Royal Statistical Society. Series A (General), 128(1), 110–117.
Venter, J. H. (1967). On estimation of the mode. The Annals of Mathematical Statistics, 38(5), 1446–1455.
Ekblom, H. (1972). A Monte Carlo investigation of mode estimators in small samples. Journal of the Royal Statistical Society. Series C (Applied Statistics), 21(2), 177–184.
Leclerc, J. (1997). Comportement limite fort de deux estimateurs du mode : le shorth et l’estimateur naif. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 325(11), 1207–1210.

vieu

Parameters: x (numeric vector), bw (numeric), kernel (character), abc (logical), ... (arguments for uniroot).
Description: Implements Vieu's mode estimator where the kernel density derivative estimate is zero. Returns a numeric mode estimate. Invoked via mlv(x, method = "vieu", ...).

References:

Vieu, P. (1996). A note on density mode estimation. Statistics & Probability Letters, 26(4), 297–307.

References

Comprehensive R Archive Network (CRAN). (n.d.). modeest: Mode Estimation. Retrieved from https://cran.r-project.org/package=modeest
Additional references are listed under individual functions.

External links

^ Poncet, Paul (18 November 2019). "modeest: Mode Estimation". CRAN. The Comprehensive R Archive Network. Retrieved November 13, 2025.
^ Ameijeiras-Alonso, Jose; Crujeiras, Rosa M.; Rodríguez-Casal, Alberto (2021). "multimode: An R Package for Mode Assessment". Journal of Statistical Software. 97 (9): 1–32. doi:10.18637/jss.v097.i09.
^ Delignette-Muller, Marie Laure; Dutang, Christophe (2015). "fitdistrplus: An R Package for Fitting Distributions". Journal of Statistical Software. 64 (4): 1–34. doi:10.18637/jss.v064.i04.
^ "Module 2.1". GitHub Pages. Retrieved November 13, 2025.
^ "R modeest package: Which method of mode estimation?". Stack Overflow. Retrieved November 13, 2025.
^ "CRAN Task View: Probability Distributions". CRAN. The Comprehensive R Archive Network. Retrieved November 13, 2025.

[1] Poncet, Paul (18 November 2019). "modeest: Mode Estimation". CRAN. The Comprehensive R Archive Network. Retrieved November 13, 2025.

[2] Ameijeiras-Alonso, Jose; Crujeiras, Rosa M.; Rodríguez-Casal, Alberto (2021). "multimode: An R Package for Mode Assessment". Journal of Statistical Software. 97 (9): 1–32. doi:10.18637/jss.v097.i09.

[3] Delignette-Muller, Marie Laure; Dutang, Christophe (2015). "fitdistrplus: An R Package for Fitting Distributions". Journal of Statistical Software. 64 (4): 1–34. doi:10.18637/jss.v064.i04.

[4] "Module 2.1". GitHub Pages. Retrieved November 13, 2025.

[5] "R modeest package: Which method of mode estimation?". Stack Overflow. Retrieved November 13, 2025.

[6] "CRAN Task View: Probability Distributions". CRAN. The Comprehensive R Archive Network. Retrieved November 13, 2025.

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