7 Recurrence relations and identities for moments of order statistics

Balakrishnan, N.; Sultan, K.S.

doi:10.1016/s0169-7161(98)16009-1

Cited by 23 publications

(12 citation statements)

References 99 publications

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“…The idea of obtaining moments of usual order statistics in a recursive manner has been discussed by many authors for a wide array of distributions; for example, see Arnold and Balakrishnan (1989) and Balakrishnan and Sultan (1998). In this section, we establish recurrence relations satisfied by the single moments of progressively Type-II right censored order statistics from the logistic distribution.…”

Section: Single Moments Of Progressively Type-ii Censored Order Statimentioning

confidence: 99%

Recurrence relations for moments of progressively censored order statistics from logistic distribution with applications to inference

AL-Hussaini

Saleh

2011

Journal of Statistical Planning and Inference

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Section: Single Moments Of Progressively Type-ii Censored Order Statimentioning

confidence: 99%

Recurrence relations for moments of progressively censored order statistics from logistic distribution with applications to inference

AL-Hussaini

Saleh

2011

Journal of Statistical Planning and Inference

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“…Let

v_{(i : m)}

and

v_{(i : m - 1)}

be the i th‐order statistics in random samples of size m and

(m - 1)

, respectively. We have a useful recurrence relation

i E [v_{(i + 1 : m)} - v_{(i : m)}] + m E [v_{(i : m)} - v_{(i : m - 1)}] = 0, 1 \leq i \leq m - 1,

which follows directly from a lemma of Balakrishnan and Sultan () in Appendix D. Denote

s_{v_{(i + 1 : m)}} = v_{(i + 1 : m)} - v_{(i : m)}

for

1 \leq i \leq m - 1

.…”

Section: The Gmm Approachmentioning

confidence: 99%

A social interaction model with an extreme order statistic

Tao

Lee

2014

The Econometrics Journal

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Summary In this paper, we introduce a social interaction econometric model with an extreme order statistic to model peer effects. We show that the model is a well‐defined system of equations and that it is a static game with complete information. The social interaction model can include exogenous regressors and group effects. Instrumental variables estimators are proposed for the general model that includes exogenous regressors. We also consider distribution‐free methods that use recurrence relations to generate moment conditions for estimation. For a model without exogenous regressors, the maximum likelihood approach is computationally feasible.

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“…Several recurrence relations are known for densities and joint densities of the usual order statistics; see Arnold and Balakrishnan (1989) and Balakrishnan and Sultan (1998). For example,…”

Section: Relationsmentioning

confidence: 99%

“…; see, for example, Arnold and Balakrishnan (1989), Arnold et al (1992, Chap. 4), and Balakrishnan and Sultan (1998). Some of these results have been generalized to the case of progressive Type-II right censoring, but the proofs are somewhat involved and are of different type compared to those for the corresponding results for the usual order statistics.…”

Section: Recurrence Relations For Specific Distributionsmentioning

confidence: 99%