Lower bounds on the expectations of upper record values

Goroncy, Agnieszka

doi:10.1016/j.jspi.2011.02.023

Cited by 7 publications

(6 citation statements)

References 28 publications

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“…These distributions have analogous form to Raqab and Rychlik (2002) for the upper bounds and Goroncy and Rychlik (2011) for the lower ones and therefore their specification is omitted.…”

Section: Theorem 4 For Any Continuous Cdf F With Finite Mean μ and Vamentioning

confidence: 99%

“…In Tables 1, 2 Nagaraja (1978) for k = 1 (Table 1), Raqab (1997) for k ≥ 2 (Tables 2 and 3) and Goroncy and Rychlik (2011) (Table 4).…”

Section: We Close This Section With Numerical Values Of the Bounds B (K)mentioning

confidence: 99%

“…it may suffice to apply upper bounds on EY (k) n of Raqab (1997) or Raqab and Rychlik (2002), and lower bounds on EY (k) r of Goroncy and Rychlik (2011). But the bounds obtained this way are not optimal since the equality in the above inequality holds iff Y (k) r = Y (k) n which holds with probability 0.…”

Section: Introductionmentioning

confidence: 99%

“…The bounds valid in the general class of distributions are obtained by Moriguti's approach of the greatest convex minorants and the bounds in restricted classes-by making use of slight generalization of the results of Danielak (2003). For exhaustive review on results concerning bounds on expectations of kth record values and their functions valid in general and restricted families of distributions we refer to Section 1 of Goroncy and Rychlik (2011).…”

Section: Introductionmentioning

confidence: 99%

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Optimal evaluations for the bias of trimmed means of $$k$$ k th record values

Bieniek

2014

Metrika

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We provide sharp upper and lower mean-variance bounds on the expectations of trimmed means of kth record values from general family of distributions. Also we improve these bounds in the case of non-trimmed means for parent distributions with decreasing density or decreasing failure rate. They can be viewed as bounds on the bias of approximation of expectation of the parent population by mean or trimmed mean of record values. The results are illustrated with numerical examples.

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“…These distributions have analogous form to Raqab and Rychlik (2002) for the upper bounds and Goroncy and Rychlik (2011) for the lower ones and therefore their specification is omitted.…”

Section: Theorem 4 For Any Continuous Cdf F With Finite Mean μ and Vamentioning

confidence: 99%

“…In Tables 1, 2 Nagaraja (1978) for k = 1 (Table 1), Raqab (1997) for k ≥ 2 (Tables 2 and 3) and Goroncy and Rychlik (2011) (Table 4).…”

Section: We Close This Section With Numerical Values Of the Bounds B (K)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal evaluations for the bias of trimmed means of $$k$$ k th record values

Bieniek

2014

Metrika

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show abstract

“…However, there are some results concerning kth records which do not follow from the corresponding ones for records. An example of such non-trivial results are various bounds on moments of kth records, see for example Raqab and Rychlik (2002, Rychlik (2004, 2005), Charalambides and Rychlik (2008), Goroncy andRychlik (2011), Jasiński (2016), Kozyra and Rychlik (2017).…”

Section: Introductionmentioning

confidence: 99%