ON THE STABILITY INDEX ESTIMATORS OF THE -STABLE DISTRIBUTIONS AND DISTRIBUTIONS ATTRACTED IN THEIR DOMAIN

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NEMATOLLAHI A.R.; Tafakori L.

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Seminar Paper

Paper Information

Seminar: IRANIAN STATISTICAL CONFERENCE
Year:2014 | Issue:12

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Title

ON THE STABILITY INDEX ESTIMATORS OF THE -STABLE DISTRIBUTIONS AND DISTRIBUTIONS ATTRACTED IN THEIR DOMAIN

Author(s)

NEMATOLLAHI A.R. | Tafakori L. | Issue Writer Certificate

Keywords

STABLE DISTRIBUTIONS

DOMAIN OF ATTRACTION

ORDER STATISTICS

Abstract

THE MOST IMPORTANT OF TAIL ESTIMATORS FOR THE STABLE INDEX OF A HEAVY TAILED DISTRIBUTIONS IS THE HILL'S ESTIMATOR WHICH IS OFTEN APPLIED TO STABLE DISTRIBUTIONS WITH INDEX< 2, AND DISTRIBUTIONS IN THEIR DOMAIN OF ATTRACTION. HOWEVER, FOR STABLE DISTRIBUTIONS WITH INDEX CLOSE TO 2, THE BEHAVIOR IS NOT SATISFACTORY.UNDER THE SAME ASSUMPTION ON THE DISTRIBUTIONS, PRESS (1972) AND ZOLOTAREV (1986) CONSTRUCTED DI ERENT ESTIMATORS FOR STABLE INDEX BASED ON CHARACTERISTIC FUNCTION OF STABLE RANDOM VARIABLES, SEPARATELY. DE HAAN AND PEREIRA (1999) DEVELOPED A FURTHER ESTIMATOR BASED ON THE ORDER STATISTICS AND DESCRIBED SOME OF THE DISADVANTAGES OF HILL'S ESTIMATOR. FAN (2004) ESTABLISH A NEW ESTIMATOR WITH U-STATISTICS STRUCTURE FOR THE TAIL INDEX OF HEAVY-TAILED DISTRIBUTIONS. IN THIS PAPER, WE STUDY THESE FIVE ESTIMATORS, AND THEN COMPARE ALL OF THEM IN THE SENSE OF THE MEAN SQUARE ERROR CRITERIA. THE SIMULATION STUDY CONDUCTED TO EVALUATE THE PERFORMANCES OF THESE ESTIMATORS IN THE SENSE THAT, WHETHER THE DISTRIBUTION OF THE PARENT POPULATION IS -STABLE, PRESS'S ESTIMATOR PERFORMS BETTER THAN ZOLOTAREV'S ESTIMATOR, ZOLOTAREV'S ESTIMATOR PERFORMS BETTER THAN FAN'S ESTIMATOR, FAN'S ESTIMATOR PERFORMS BETTER THAN HILL'S ESTIMATOR AND FINALLY, HILL'S ESTIMATOR PERFORMS BETTER THAN DE HAAN AND PEREIRA ESTIMATOR. ON THE OTHER HAND, WHETHER THE PARENT DISTRIBUTION IS ATTRACTED TO SOME -STABLE LAW, WE WILL SHOW THAT THE PRESS'S ESTIMATOR WILL BE MOST ACCURATE IN CONTRAST WITH HILL'S ESTIMATOR.

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APA: Copy

NEMATOLLAHI, A.R., & Tafakori, L.. (2014). ON THE STABILITY INDEX ESTIMATORS OF THE -STABLE DISTRIBUTIONS AND DISTRIBUTIONS ATTRACTED IN THEIR DOMAIN. IRANIAN STATISTICAL CONFERENCE. SID. https://sid.ir/paper/920268/en

Vancouver: Copy

NEMATOLLAHI A.R., Tafakori L.. ON THE STABILITY INDEX ESTIMATORS OF THE -STABLE DISTRIBUTIONS AND DISTRIBUTIONS ATTRACTED IN THEIR DOMAIN. 2014. Available from: https://sid.ir/paper/920268/en

IEEE: Copy

A.R. NEMATOLLAHI, and L. Tafakori, “ON THE STABILITY INDEX ESTIMATORS OF THE -STABLE DISTRIBUTIONS AND DISTRIBUTIONS ATTRACTED IN THEIR DOMAIN,” presented at the IRANIAN STATISTICAL CONFERENCE. 2014, [Online]. Available: https://sid.ir/paper/920268/en

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