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Limit theorems of general functions of independent and identically distributed random variables

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  • Nidhin, K.
  • Chandran, C.

Abstract

In this paper we derive limit theorems of some general functions of independent and identically distributed random variables. A stability property is used to derive the limit theory for general functions. A procedure followed in de Haan (1976) and Leadbetter et al. (1983) is used to prove the main result. The limit theorems for the maximum, minimum and sum of fixed sample sizes and random sample sizes are derived as special cases of the main result.

Suggested Citation

  • Nidhin, K. & Chandran, C., 2009. "Limit theorems of general functions of independent and identically distributed random variables," Statistics & Probability Letters, Elsevier, vol. 79(23), pages 2397-2404, December.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:23:p:2397-2404
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    References listed on IDEAS

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    1. Laurens de Haan, 1976. "Sample extremes: an elementary introduction," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 30(4), pages 161-172, December.
    2. Sreehari, M., 1995. "Maximum stability and a generalization," Statistics & Probability Letters, Elsevier, vol. 23(4), pages 339-342, June.
    3. de Haan, Laurens, 1976. "Sample Extremes: An Elementary Introduction," Econometric Institute Archives 272130, Erasmus University Rotterdam.
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