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http://dx.doi.org/10.5351/CSAM.2014.21.5.461

Further Results on Characteristic Functions Without Contour Integration  

Song, Dae-Kun (Department of Statistics, Colorado State University)
Kang, Seul-Ki (Samsung Electronics)
Kim, Hyoung-Moon (Department of Applied Statistics, Konkuk University)
Publication Information
Communications for Statistical Applications and Methods / v.21, no.5, 2014 , pp. 461-469 More about this Journal
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;
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