Nonparametric Estimation for Quantile and Sparsity Functions via Trimmed L-moments | ||||
| The Egyptian Statistical Journal | ||||
| Article 3, Volume 54, Issue 1, June 2010, Page 33-46 | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/esju.2010.314302 | ||||
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| Abstract | ||||
| Trimmed Linear moments (TL-moments) are natural generalization of L-moments that do not require the mean of the underlying distribution to exist. Therefore, they are defined for heavy tailed distributions where they do not involve some values at the extreme ends of the distribution. We introduce and study properties of a new class of approximations to population quantile and sparsity functions based on TL-moments by minimizing the weighted mean square error between the population quantile function and its TL-moments representation. Also, we study properties of the corresponding sample estimator of population quantile in terms of sample L-moments and Jacobi polynomial from some known distributions. Our estimators have a good approximation to population quantile for a broad class of probability distribution functions. An example is given that illustrates the benefits of the proposed method. | ||||
| Keywords | ||||
| Estimation; Moments - Jacobi Polynomial - Order Statistics - Quantile Function | ||||
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