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Title: Bias, precision and accuracy of skewness and kurtosis estimators for frequently used continuous distributions
Author: Bono Cabré, Roser
Arnau Gras, Jaume
Alarcón Postigo, Rafael
Blanca Mena, M. José
Keywords: Probabilitats
Distribució (Teoria de la probabilitat)
Distribution (Probability theory)
Issue Date: 2020
Publisher: MDPI
Abstract: Several measures of skewness and kurtosis were proposed by Hogg (1974) in order to reduce the bias of conventional estimators when the distribution is non-normal. Here we conducted a Monte Carlo simulation study to compare the performance of conventional and Hogg's estimators, considering the most frequent continuous distributions used in health, education, and social sciences (gamma, lognormal and exponential distributions). In order to determine the bias, precision and accuracy of the skewness and kurtosis estimators for each distribution we calculated the relative bias, the coefficient of variation, and the scaled root mean square error. The effect of sample size on the estimators is also analyzed. In addition, a SAS program for calculating both conventional and Hogg's estimators is presented. The results indicated that for the non-normal distributions investigated, the estimators of skewness and kurtosis which best reflect the shape of the distribution are Hogg's estimators. It should also be noted that Hogg's estimators are not as affected by sample size as are conventional estimators.
Note: Reproducció del document publicat a:
It is part of: Symmetry, 2020, vol. 12, num. 1, p. 19
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ISSN: 2073-8994
Appears in Collections:Articles publicats en revistes (Psicologia Social i Psicologia Quantitativa)

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