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蒋岳祥 《浙江大学学报(A卷英文版)》2004,5(3):335-342
Suppose {Xi,i≥1} and {Yi, i≥1} are two independent sequences with distribution functions and , respectively. Zi,n is the combination of Xi and Yi with a probability for each I with 1≤ i≤n. The extreme value distribution GZ(x) of this particular triangular array of the i.i.d. Random variables Z1,n,… Z2,n, Zn,n is discussed. We found a new form of the extreme value distributions i)ΦAα1(x)Φα2 and ii) ψAα(x)ψα2(x)α1<α2), which are not max-stable. It occurs if FX and FY belong to the same MDA(Φ) or MDA(Ψ). 相似文献
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蒋岳祥 《浙江大学学报(A卷英文版)》2004,5(5)
Suppose {Xi, i≥1} and {Yi, i≥1} are two independent sequences with distribution functions FX(x) and FY(x), respectively. Zi,n is the combination of Xi and Yi with a probability pn for each i with 1≤i≤n. The extreme value distribution GZ(x) of this particular triangular array of the i.i.d. random variables Z1,n , Z2,n ,…, Zn,n is discussed. We found a new form of the extreme value distribution (A(ρx)(ρx)(0<ρ<1), which is not max-stable. It occurs if FX(x) and FY(x) belong to the same MDA(ρ). GZ(x) does not exist as mixture forms of the different types of extreme value distributions. 相似文献
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蒋岳祥 《浙江大学学报(A卷英文版)》2005,6(4):315-321
The sequences {Zi,n, l≤i≤n}, n≥l have multi-nomial distribution among i.i.d. random variables {X1,i, i≥1}, {X2,i,u≥l }, …, {Xm,i, i≥1 }. The extreme value distribution Gz(x) of this particular triangular array of i.i.d, random variables Z1,n, Z2Zn,n is discussed in this paper. We found a new type of not max-stable extreme value distributions, i) Gz(x) = r-1∏i=1ФAiαi(x) × Фαr (x);ii) Gz (x) = r-1∏i=1ψAiαi (x) × ψαr (x); iii) Gz (x) = r-1∏i=1 ∧Ai (λix) × A(x), r≥2, 0＜α1≤α2≤…≤αr and λi∈ (0,1] for i, l≤i≤r-1 which occur if Fj, …, Fm belong to the same MDA. 相似文献
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INTRODUCTION Let {Xi, i ≥1} and {Yi, i ≥1} be two independ-ent sequences of independent and identicallydistributed random variables with distribution func-tions FX(x)∈MDA(GX) and FY(x)∈MDA(GY), res-pectively. We deal with the case when {Zi , 1≤i≤n},nis a mixture of two independent sequences {Xi, i≥1}and {Yi, i≥1}, for pn∈[0, 1) which is defined by: Zi,n = ???Yi Xi with probability pn with probability 1? pn.We consider the extreme value distribution GZ(x) of{Zi , 1≤i≤n}… 相似文献
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蒋岳祥 《浙江大学学报(A卷英文版)》2005,6(7):769-774
The sequences {Zi,n, 1≤i≤n}, n≥1 are multi-nomial distribution among i.i.d. random variables {X1,i, i≥1}, {X2,i, i≥1},..., {Xm,i, i≥1}. The extreme value distribution Gz(x) of this particular triangular array of i.i.d. random variables Z1,n, Z2,n,..., Zn,n is discussed. A new type of not max-stable extreme value distributions which are Frechet mixture, Gumbel mixture and Weibull mixture has been found if Fj,...,Fm belong to the same MDA. Whether mixtures of different types of extreme value distributions exist or not and the more general case are discussed in this paper. We found that GZ(X) does not exist as mixture forms of the different types of extreme value distributions after we investigated all cases. 相似文献
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INTRODUCTIONSuppose{Xn,n1}isasequenceofinde-pendentandidenticallydistributedrandomvari-ableswithcommoncontinuousdistributionfunc-tionFX(x).DefineMn(X)=max(X1,X2,,Xn).WeconsiderthenondegeneratedlimitdistributionofPr{Mn(X)anx bn}whereanandbnaresomenormalizingconstants{}()limPr()XnnnnGxMXxab=?.Fori.i.d.randomvariablesX,FisherandTippettfoundin1928thatlimitdistributionsexistandthatthereareonlythreetypesofdistributions,theso-calledExtremeValueDistributionsandthatGX(x)iseitherofthefol… 相似文献
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