Goodness-Of-Fit Tests for Doubly Truncated Data

Abstract

Purpose – The paper regards the goodness-of-fit (GOF) tests for doubly truncated continuous data with known truncation points. The first goal of the paper is to derive computing formulas of several test statistics for doubly truncated data, when the number of truncated data is unknown. The second goal is to develop statistical inference procedure based on the derived formulas, which includes information regarding the number of truncated data, when it is available. Research method – The formulas and the inference procedure are developed with the use of the methods proposed by Chernobai, Rachev and Fabozzi [2015], who already developed GOF tests for the left truncated data, when the number of truncated data is unknown. Results – Several tests are developed in case of double truncation. Depending on the chosen truncation points, the tests for left, right or doubly truncated samples might be obtained. When no truncation occurs, the tests are reduced to the complete sample tests. The quality of the tests is assessed on the basis of the FTSE100 return distributions. Originality / value / implications / recommendations – To the best knowledge of the author, computing formulas of the GOF test statistics for doubly truncated distributions with known truncation points, when the number of truncated data is unknown, have not been presented in the literature yet.