Further Results on Characteristic Functions Without Contour Integration

- Journal title : Communications for Statistical Applications and Methods
- Volume 21, Issue 5, 2014, pp.461-469
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CSAM.2014.21.5.461

Title & Authors

Further Results on Characteristic Functions Without Contour Integration

Song, Dae-Kun; Kang, Seul-Ki; Kim, Hyoung-Moon;

Song, Dae-Kun; Kang, Seul-Ki; Kim, Hyoung-Moon;

Abstract

Characteristic functions play an important role in probability and statistics; however, a rigorous derivation of these functions requires contour integration, which is unfamiliar to most statistics students. Without resorting to contour integration, Datta and Ghosh (2007) derived the characteristic functions of normal, Cauchy, and double exponential distributions. Here, we derive the characteristic functions of t, truncated normal, skew-normal, and skew-t distributions. The characteristic functions of normal, cauchy distributions are obtained as a byproduct. The derivations are straightforward and can be presented in statistics masters theory classes.

Keywords

t distribution;truncated normal;skew-normal;skew-t;stochastic representation;

Language

English

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