A GENERALIZED VERSION OF FOSTER AND STUART'S d-STATISTIC


Tanıl H.

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, vol.68, no.1, pp.98-110, 2019 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 68 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.31801/cfsuasmas.443648
  • Title of Journal : COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
  • Page Numbers: pp.98-110
  • Keywords: Monotonic trend in location, kth-records, Top-k-lists, Bottom-k-lists, Distribution-free test, Empirical power comparison, TESTS, RECORDS, TREND, RANDOMNESS

Abstract

Assume that only the lists of upper k-records and lower k-records of a finite sequence are available and the existence of a monotonic trend in location is interested in. In this study, a distribution-free test based on the difference between the numbers of upper and lower k-records is proposed for this situation. The exact and asymptotic distributions of the proposed test statistic are obtained for a random continuous sequence which is independent and identically distributed (i.i.d.). Also, a comparison between the proposed test and some well-known distribution-free tests is made in terms of empirical powers.