Rates of convergence for the stability of large order statistics
Abstract Forr≥1 and eachn≥r, letM nr be therth largest ofX 1,X 2, ...,X n , where {X n ,n≥1} is an i.i.d. sequence. Necessary and sufficient conditions are presented for the convergence of $$\sum\nolimits_{n = r}^\infty {n^\alpha } P[\sup _{k \geqslant n} |M_{kr} /a_k - 1| > \varepsilon ]$$ for a...
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1996 |
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| Umfang: |
11 |
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| Reproduktion: |
Springer Online Journal Archives 1860-2002 |
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| Übergeordnetes Werk: |
in: Journal of theoretical probability - 1988, 9(1996) vom: Apr., Seite 841-851 |
| Übergeordnetes Werk: |
volume:9 ; year:1996 ; month:04 ; pages:841-851 ; extent:11 |
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NLEJ198005385 |
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| 520 | |a Abstract Forr≥1 and eachn≥r, letM nr be therth largest ofX 1,X 2, ...,X n , where {X n ,n≥1} is an i.i.d. sequence. Necessary and sufficient conditions are presented for the convergence of $$\sum\nolimits_{n = r}^\infty {n^\alpha } P[\sup _{k \geqslant n} |M_{kr} /a_k - 1| > \varepsilon ]$$ for all ∈>0 and some α≥−1, where {a n } is a real sequence. Furthermore, it is shown that this series converges for all α>−1, allr≥1 and all ∈>0 if it converges for some α>−1, somer≥1 and all ∈>0. | ||
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(DE-627)NLEJ198005385 DE-627 ger DE-627 rakwb eng Rates of convergence for the stability of large order statistics 1996 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract Forr≥1 and eachn≥r, letM nr be therth largest ofX 1,X 2, ...,X n , where {X n ,n≥1} is an i.i.d. sequence. Necessary and sufficient conditions are presented for the convergence of $$\sum\nolimits_{n = r}^\infty {n^\alpha } P[\sup _{k \geqslant n} |M_{kr} /a_k - 1| > \varepsilon ]$$ for all ∈>0 and some α≥−1, where {a n } is a real sequence. Furthermore, it is shown that this series converges for all α>−1, allr≥1 and all ∈>0 if it converges for some α>−1, somer≥1 and all ∈>0. Springer Online Journal Archives 1860-2002 Tomkins, R. J. oth in Journal of theoretical probability 1988 9(1996) vom: Apr., Seite 841-851 (DE-627)NLEJ18898562X (DE-600)2017303-9 1572-9230 nnns volume:9 year:1996 month:04 pages:841-851 extent:11 http://dx.doi.org/10.1007/BF02214253 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 9 1996 4 841-851 11 |
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(DE-627)NLEJ198005385 DE-627 ger DE-627 rakwb eng Rates of convergence for the stability of large order statistics 1996 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract Forr≥1 and eachn≥r, letM nr be therth largest ofX 1,X 2, ...,X n , where {X n ,n≥1} is an i.i.d. sequence. Necessary and sufficient conditions are presented for the convergence of $$\sum\nolimits_{n = r}^\infty {n^\alpha } P[\sup _{k \geqslant n} |M_{kr} /a_k - 1| > \varepsilon ]$$ for all ∈>0 and some α≥−1, where {a n } is a real sequence. Furthermore, it is shown that this series converges for all α>−1, allr≥1 and all ∈>0 if it converges for some α>−1, somer≥1 and all ∈>0. Springer Online Journal Archives 1860-2002 Tomkins, R. J. oth in Journal of theoretical probability 1988 9(1996) vom: Apr., Seite 841-851 (DE-627)NLEJ18898562X (DE-600)2017303-9 1572-9230 nnns volume:9 year:1996 month:04 pages:841-851 extent:11 http://dx.doi.org/10.1007/BF02214253 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 9 1996 4 841-851 11 |
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(DE-627)NLEJ198005385 DE-627 ger DE-627 rakwb eng Rates of convergence for the stability of large order statistics 1996 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract Forr≥1 and eachn≥r, letM nr be therth largest ofX 1,X 2, ...,X n , where {X n ,n≥1} is an i.i.d. sequence. Necessary and sufficient conditions are presented for the convergence of $$\sum\nolimits_{n = r}^\infty {n^\alpha } P[\sup _{k \geqslant n} |M_{kr} /a_k - 1| > \varepsilon ]$$ for all ∈>0 and some α≥−1, where {a n } is a real sequence. Furthermore, it is shown that this series converges for all α>−1, allr≥1 and all ∈>0 if it converges for some α>−1, somer≥1 and all ∈>0. Springer Online Journal Archives 1860-2002 Tomkins, R. J. oth in Journal of theoretical probability 1988 9(1996) vom: Apr., Seite 841-851 (DE-627)NLEJ18898562X (DE-600)2017303-9 1572-9230 nnns volume:9 year:1996 month:04 pages:841-851 extent:11 http://dx.doi.org/10.1007/BF02214253 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 9 1996 4 841-851 11 |
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(DE-627)NLEJ198005385 DE-627 ger DE-627 rakwb eng Rates of convergence for the stability of large order statistics 1996 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract Forr≥1 and eachn≥r, letM nr be therth largest ofX 1,X 2, ...,X n , where {X n ,n≥1} is an i.i.d. sequence. Necessary and sufficient conditions are presented for the convergence of $$\sum\nolimits_{n = r}^\infty {n^\alpha } P[\sup _{k \geqslant n} |M_{kr} /a_k - 1| > \varepsilon ]$$ for all ∈>0 and some α≥−1, where {a n } is a real sequence. Furthermore, it is shown that this series converges for all α>−1, allr≥1 and all ∈>0 if it converges for some α>−1, somer≥1 and all ∈>0. Springer Online Journal Archives 1860-2002 Tomkins, R. J. oth in Journal of theoretical probability 1988 9(1996) vom: Apr., Seite 841-851 (DE-627)NLEJ18898562X (DE-600)2017303-9 1572-9230 nnns volume:9 year:1996 month:04 pages:841-851 extent:11 http://dx.doi.org/10.1007/BF02214253 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 9 1996 4 841-851 11 |
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(DE-627)NLEJ198005385 DE-627 ger DE-627 rakwb eng Rates of convergence for the stability of large order statistics 1996 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract Forr≥1 and eachn≥r, letM nr be therth largest ofX 1,X 2, ...,X n , where {X n ,n≥1} is an i.i.d. sequence. Necessary and sufficient conditions are presented for the convergence of $$\sum\nolimits_{n = r}^\infty {n^\alpha } P[\sup _{k \geqslant n} |M_{kr} /a_k - 1| > \varepsilon ]$$ for all ∈>0 and some α≥−1, where {a n } is a real sequence. Furthermore, it is shown that this series converges for all α>−1, allr≥1 and all ∈>0 if it converges for some α>−1, somer≥1 and all ∈>0. Springer Online Journal Archives 1860-2002 Tomkins, R. J. oth in Journal of theoretical probability 1988 9(1996) vom: Apr., Seite 841-851 (DE-627)NLEJ18898562X (DE-600)2017303-9 1572-9230 nnns volume:9 year:1996 month:04 pages:841-851 extent:11 http://dx.doi.org/10.1007/BF02214253 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 9 1996 4 841-851 11 |
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rates of convergence for the stability of large order statistics |
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Rates of convergence for the stability of large order statistics |
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Abstract Forr≥1 and eachn≥r, letM nr be therth largest ofX 1,X 2, ...,X n , where {X n ,n≥1} is an i.i.d. sequence. Necessary and sufficient conditions are presented for the convergence of $$\sum\nolimits_{n = r}^\infty {n^\alpha } P[\sup _{k \geqslant n} |M_{kr} /a_k - 1| > \varepsilon ]$$ for all ∈>0 and some α≥−1, where {a n } is a real sequence. Furthermore, it is shown that this series converges for all α>−1, allr≥1 and all ∈>0 if it converges for some α>−1, somer≥1 and all ∈>0. |
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Abstract Forr≥1 and eachn≥r, letM nr be therth largest ofX 1,X 2, ...,X n , where {X n ,n≥1} is an i.i.d. sequence. Necessary and sufficient conditions are presented for the convergence of $$\sum\nolimits_{n = r}^\infty {n^\alpha } P[\sup _{k \geqslant n} |M_{kr} /a_k - 1| > \varepsilon ]$$ for all ∈>0 and some α≥−1, where {a n } is a real sequence. Furthermore, it is shown that this series converges for all α>−1, allr≥1 and all ∈>0 if it converges for some α>−1, somer≥1 and all ∈>0. |
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Abstract Forr≥1 and eachn≥r, letM nr be therth largest ofX 1,X 2, ...,X n , where {X n ,n≥1} is an i.i.d. sequence. Necessary and sufficient conditions are presented for the convergence of $$\sum\nolimits_{n = r}^\infty {n^\alpha } P[\sup _{k \geqslant n} |M_{kr} /a_k - 1| > \varepsilon ]$$ for all ∈>0 and some α≥−1, where {a n } is a real sequence. Furthermore, it is shown that this series converges for all α>−1, allr≥1 and all ∈>0 if it converges for some α>−1, somer≥1 and all ∈>0. |
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