Characterizations of distributions via linearity of regression of generalized order statistics

Bieniek, Mariusz; Szynal, Dominik

doi:10.1007/s001840300263

Cited by 29 publications

(19 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Various recent extensions and complements of this result can be found e.g. in , , Beg et al (2013), Bieniek and Szynal (2003), Cramer et al (2004), Ferguson (2002) or Gupta and Ahsanullah (2004).…”

mentioning

confidence: 59%

Linearity of regression for overlapping order statistics

Dołęgowski

Wesołowski

2014

Metrika

View full text Add to dashboard Cite

We consider a problem of characterization of continuous distributions for which linearity of regression of overlapping order statistics, E(X i:m |X j:n ) = a X j:n + b, m ≤ n, holds. Due to a new representation of conditional expectation E(X i:m |X j:n ) in terms of conditional expectations E(X l:n |X j:n ), l = i, . . . , n − m + i, we are able to use the already known approach based on the Rao-Shanbhag version of the Cauchy integrated functional equation. However this is possible only if j ≤ i or j ≥ n −m +i. In the remaining cases the problem essentially is still open.

show abstract

mentioning

confidence: 59%

Linearity of regression for overlapping order statistics

Dołęgowski

Wesołowski

2014

Metrika

View full text Add to dashboard Cite

show abstract

“…As mentioned in [B] such relations are used to establish characterizations of distributions. For characterization results based on moments and conditional expectations we refer to Keseling and Kamps (2003), Bieniek and Szynal (2003), and .…”

Section: Moments Bounds and Relationsmentioning

confidence: 99%

Comments on: Progressive censoring methodology: an appraisal

Kamps

Cramer

2007

TEST

View full text Add to dashboard Cite

Since the mid-90s, when Dr. Balakrishnan together with coauthors Sandhu 1995, 1996; Viveros and Balakrishnan 1994) revisited progressive censoring, a huge number of papers were published dealing with both theoretical and practical aspects. It is one of Dr. Balakrishnan's major scientific merits to reconsider the model of progressive censoring, to see the potential in it, and to advance the methods and properties. His contributions illustrate that progressively Type II censored order statistics are a very useful and powerful model. They lead to a toolbox of properties and statistical procedures, which make the model really applicable. His monograph (Balakrishnan and Aggarwala 2000) on this topic jointly written with R. Aggarwala clearly remains a basic reference work. Now Dr. Balakrishnan provides us with an excellent up-to-date survey on progressive censoring. It impressively illustrates, what has been established in the last decade. We are very pleased to comment on selected topics and to supplement this work, which, of course, can not be exhaustive in some 40 pages. We refer to Dr. Balakrishnan's paper by [B], throughout. Model and distribution theoryThe author points out that progressively Type II censored order statistics are a particular case of generalized order statistics (see Kamps 1995) choosing γ r = k + m − r + m−1 j =r R j , 1 ≤ r ≤ m and k = R m + 1. Hence, the distribution of any choice of progressively Type II censored order statistics can be viewed as a marginal distribution of respective generalized order statistics (see, e.g., (2) in [B]). Thus, the results This comment refers to the invited paper available at: http://dx.

show abstract

“…Several authors utilized the concept of gos in their studies. References may be made to Kamps and Gather [2], Keseling [3], Cramer and Kamps [4], Ahsanullah [5], Habibullah and Ahsanullah [6], Raqab [7], Kamps and Cramer [8], Ahmad and Fawzy [9], Beiniek and Syznal [10], Al-Hussaini and Ahmad [11] , Cramer et al [12], Khan and Alzaid [13], Jaheen [14], Khan et al ([15], [16]), Khan and Zia [17] among others.…”

Section: Introductionmentioning

confidence: 99%

Moment Properties of Generalized Order Statistics from Exponential-Weibull Lifetime Distribution

Khan¹,

Khan²

2016

JAS

View full text Add to dashboard Cite

Abstract. In this paper, simple explicit expressions and some recurrence relations satisfied by single and product moments of generalized order statistics from exponential-Weibull lifetime distribution have been obtained. These relations are deduced for moments of order statistics and upper record values. Further, conditional moments and a recurrence relation for single moments of the generalized order statistics are used to characterize this distribution and some computational works are also carried out.

show abstract

Characterizations of distributions via linearity of regression of generalized order statistics

Abstract: no keyword,

Cited by 29 publications

References 9 publications

Linearity of regression for overlapping order statistics

Linearity of regression for overlapping order statistics

Comments on: Progressive censoring methodology: an appraisal

Moment Properties of Generalized Order Statistics from Exponential-Weibull Lifetime Distribution

Contact Info

Product

Resources

About