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A class of continuous kernels and Cauchy type heavy tail distributions

Author

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  • Soltani, A.R.
  • Tafakori, L.

Abstract

We shed light on an interesting class of one sided continuous kernels on [0,∞). Then we present its properties, provide new integral formulas including an extension for the Kotz and Ostrovskii (1996) mixture representation, introduce a class of Cauchy type distributions, and finally enlarge the class of one sided stable densities. This study provides powerful tools in modeling erratic continuous data.

Suggested Citation

  • Soltani, A.R. & Tafakori, L., 2013. "A class of continuous kernels and Cauchy type heavy tail distributions," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1018-1027.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:4:p:1018-1027
    DOI: 10.1016/j.spl.2012.12.024
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    References listed on IDEAS

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    1. Tomasz Kozubowski, 2000. "Exponential Mixture Representation of Geometric Stable Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(2), pages 231-238, June.
    2. Soltani, A.R. & Shirvani, A. & Alqallaf, F., 2009. "A class of discrete distributions induced by stable laws," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1608-1614, July.
    3. Kotz, Samuel & Ostrovskii, I. V., 1996. "A mixture representation of the Linnik distribution," Statistics & Probability Letters, Elsevier, vol. 26(1), pages 61-64, January.
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