Statistics and Its Interface

Volume 13 (2020)

Number 3

Estimation of a distribution function using Lagrange polynomials with Tchebychev-Gauss points

Pages: 399 – 410



Salima Helali (Laboratoire de Probabilité et Statistiques, Université de Sfax, Tunisia)

Yousri Slaoui (Laboratoire de Mathématiques et Applications, Université de Poitiers, France)


The estimation of the distribution function of a real random variable is an intrinsic topic in non parametric estimation. To this end, a distribution estimator based on Lagrange polynomials and Tchebychev–Gauss points, is introduced. Some asymptotic properties of the proposed estimator are investigated, such as its asymptotic bias, variance, mean squared error and Chung–Smirnov propriety. The asymptotic normality and the uniform convergence of the estimator are also established. Lastly, the performance of the proposed estimator is explored through a certain simulation examples.


Distribution estimator, Lagrange polynomials, Tchebychev-Gauss points, Asymptotic properties.

2010 Mathematics Subject Classification

Primary 62E20, 97N50. Secondary 41A50.

This work benefited from the financial support of the GDR 3477 GeoSto.

Received 7 November 2019

Accepted 21 March 2020

Published 22 April 2020