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Characterizations of the Poisson process as a renewal process via two conditional moments (1994)

Li, Shun-Hwa ; Huang, Wen-Jang ; Huang, Mong-Na Lo

Springer

Annals of the Institute of Statistical Mathematics 46 (1994), S. 351-360

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ISSN: 1572-9052

Keywords: Characterization ; exponential distribution ; gamma distribution ; geometric distribution ; Poisson process ; renewal process

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract Given two independent positive random variables, under some minor conditions, it is known that fromE(Xr∥X+Y)=a(X+Y)r andE(Xs∥X+Y)=b(X+Y)s, for certain pairs ofr ands, wherea andb are two constants, we can characterizeX andY to have gamma distributions. Inspired by this, in this article we will characterize the Poisson process among the class of renewal processes via two conditional moments. More precisely, let {A(t), t≥0} be a renewal process, with {S k, k≥1} the sequence of arrival times, andF the common distribution function of the inter-arrival times. We prove that for some fixedn andk, k≤n, ifE(S k r ∥A(t)=n)=atr andE(S k s ∥A(t)=n)=bts, for certain pairs ofr ands, wherea andb are independent oft, then {A(t), t≥0} has to be a Poisson process. We also give some corresponding results about characterizingFto be geometric whenF is discrete.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01720591

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Demethylation in the 5′-flanking region of mouse cellular retinoic acid binding protein-I gene is associated with its high level of expression in mouse embryos and facilitates its induction by retinoic acid in P19 embryonal carcinoma cells (1994)

Wei, Li-Na ; Lee, Chih-Hao

New York, NY [u.a.] : Wiley-Blackwell

Developmental Dynamics 201 (1994), S. 1-10

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ISSN: 1058-8388

Keywords: CRABP-I ; P19 cells ; DNA methylation ; Gene expression ; Life and Medical Sciences ; Cell & Developmental Biology

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Medicine

Notes: The mouse cellular retinoic acid binding protein-I (CRABP-I) gene is specifically up-regulated by retinoic acid (RA) in P19 mouse embryonal carcinoma cells, and its expression in animals is spatially and temporally restricted to RA-sensitive tissues during embryonic development. This study demonstrates that, in adult mouse tissues and P19 cells where the expression of CRABP-I is detected at the basal level, the 5′- flanking region of the CRABP-I gene is hypermethylated at the C residues of all the Hpa II sites. Conversely, in mouse embryos during early stages of development when the expression of CRABP-I gene is detected at a much higher level, this region is demethylated at these Hpa II sites. In P19, enhancement on the RA-induced up-regulation of CRABP-I can be observed in cells treated with 5-azacytidine (5-AzaC) in conjunction with RA, where partial demethylation in the 5′-flanking region of CRABP-I gene is observed. Nuclear run-on experiments indicate that increased message levels of CRABP-I in P19 cells can be accounted for, at least partially, by increases in its transcription rates. The induction of retinoic acid receptor (RAR) β by RA can also be enhanced by 5-AzaC, but to a much lesser degree. In contrast, all the Hpa II sites in the structural gene portion, at least in the first two exons, are fully demethylated at the C residues. © 1994 Wiley-Liss, Inc.

Additional Material: 9 Ill.