Abstract
There exist distributions for which standard estimation techniques based on the probability density function are not applicable. As an alternative, the characteristic function is used. Certain distributions whose characteristic functions can be expressed in terms of |t|α are such examples. Tailweight properties are first examined; it is shown that these laws are Paretian, their tail index a being one of the parameters defining these laws. Estimators similar to those proposed by Press (1972) for stable laws are then used for the estimation of the parameters of such laws and asymptotic properties are proved. As an illustration, the Linnik distribution is examined.
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Rémillard, B., Theodorescu, R. (2001). Estimation Based on the Empirical Characteristic Function. In: Balakrishnan, N., Ibragimov, I.A., Nevzorov, V.B. (eds) Asymptotic Methods in Probability and Statistics with Applications. Statistics for Industry and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0209-7_31
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DOI: https://doi.org/10.1007/978-1-4612-0209-7_31
Publisher Name: Birkhäuser, Boston, MA
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