Existence of moments and an asymptotic result based on a mixture of exponential distributions

Shaul K. Bar-Lev; Peter Enis

doi:10.1016/0167-7152(87)90104-0

Existence of moments and an asymptotic result based on a mixture of exponential distributions

Research output: Contribution to journal › Article › peer-review

Abstract

Let {F_t: 0 <st < t₀ </ ∞} be a family of distribution associated with positive random variables {Y_t}. The limiting distribution of Y_t^t, as t → 0+, and the finiteness and form of E(Y_t^k), for any real k < 1, are obtained. The technique used to obtain these results is based on a mixture of exponential distributions, with F_t being the mixing distribution. Several illustrative examples are provided with an emphasis on distributions related to symmetric random walks and compound Poisson and extreme stable distributions.

Original language	English
Pages (from-to)	273-277
Number of pages	5
Journal	Statistics and Probability Letters
Volume	5
Issue number	4
DOIs	https://doi.org/10.1016/0167-7152(87)90104-0
State	Published - Jun 1987
Externally published	Yes

Keywords

fractional moments
limiting distributions
mixture of exponential distributions

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.1016/0167-7152(87)90104-0

Cite this

@article{1a101927d48843158088e80e6caa78c8,

title = "Existence of moments and an asymptotic result based on a mixture of exponential distributions",

abstract = "Let {Ft: 0 0 </ ∞} be a family of distribution associated with positive random variables {Yt}. The limiting distribution of Ytt, as t → 0+, and the finiteness and form of E(Ytk), for any real k < 1, are obtained. The technique used to obtain these results is based on a mixture of exponential distributions, with Ft being the mixing distribution. Several illustrative examples are provided with an emphasis on distributions related to symmetric random walks and compound Poisson and extreme stable distributions.",

keywords = "fractional moments, limiting distributions, mixture of exponential distributions",

author = "Bar-Lev, {Shaul K.} and Peter Enis",

year = "1987",

month = jun,

doi = "10.1016/0167-7152(87)90104-0",

language = "English",

volume = "5",

pages = "273--277",

journal = "Statistics and Probability Letters",

issn = "0167-7152",

publisher = "Elsevier",

number = "4",

}

TY - JOUR

T1 - Existence of moments and an asymptotic result based on a mixture of exponential distributions

AU - Bar-Lev, Shaul K.

AU - Enis, Peter

PY - 1987/6

Y1 - 1987/6

N2 - Let {Ft: 0 0 </ ∞} be a family of distribution associated with positive random variables {Yt}. The limiting distribution of Ytt, as t → 0+, and the finiteness and form of E(Ytk), for any real k < 1, are obtained. The technique used to obtain these results is based on a mixture of exponential distributions, with Ft being the mixing distribution. Several illustrative examples are provided with an emphasis on distributions related to symmetric random walks and compound Poisson and extreme stable distributions.

AB - Let {Ft: 0 0 </ ∞} be a family of distribution associated with positive random variables {Yt}. The limiting distribution of Ytt, as t → 0+, and the finiteness and form of E(Ytk), for any real k < 1, are obtained. The technique used to obtain these results is based on a mixture of exponential distributions, with Ft being the mixing distribution. Several illustrative examples are provided with an emphasis on distributions related to symmetric random walks and compound Poisson and extreme stable distributions.

KW - fractional moments

KW - limiting distributions

KW - mixture of exponential distributions

UR - http://www.scopus.com/inward/record.url?scp=45949122973&partnerID=8YFLogxK

U2 - 10.1016/0167-7152(87)90104-0

DO - 10.1016/0167-7152(87)90104-0

M3 - Article

AN - SCOPUS:45949122973

SN - 0167-7152

VL - 5

SP - 273

EP - 277

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 4

ER -

Existence of moments and an asymptotic result based on a mixture of exponential distributions

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this