Michael V. Boutsikas, Eutichia Vaggelatou

Source: Bernoulli, Volume 16, Number 2, 301--330.

Abstract:
Let X 1 , X 2 , …, X n be a sequence of independent or locally dependent random variables taking values in ℤ + . In this paper, we derive sharp bounds, via a new probabilistic method, for the total variation distance between the distribution of the sum ∑ i =1 n X i and an appropriate Poisson or compound Poisson distribution. These bounds include a factor which depends on the smoothness of the approximating Poisson or compound Poisson distribution. This “smoothness factor” is of order O( σ −2 ), according to a heuristic argument, where σ 2 denotes the variance of the approximating distribution. In this way, we offer sharp error estimates for a large range of values of the parameters. Finally, specific examples concerning appearances of rare runs in sequences of Bernoulli trials are presented by way of illustration.

Names, Personal -- England.

Thomson (Family)

Fuhlbohm (Family)

Braddock, William, 1798-1869 -- Correspondence.

St. Philip and St. James Church (Noarlunga, S.A.)

Moore, Amy, 1908-2005.

Hewish Henry -- Family.

Grant (Family)

Hicks (Family)

St. Philip and St. James Church (Noarlunga, S.A.)

South Australia -- Genealogy.

Penney, Anna -- Travels.

Family histories -- South Australia -- Bibliography.

Klemm (Family)

King's Orphan Schools (New Town, Tas.)

Dissenters, Religious -- Great Britain.

Names, Personal -- Welsh.

Names, Personal -- Scottish.

Genetic genealogy -- Handbooks, manuals, etc.

Kuerschner (Family)

Our Lady of Grace School (Glengowrie, S.A.)

Germans -- South Australia.

Gambling (Family)

Cheesman, John -- Family.

Daws, Revell.

South Australia -- History -- Sources.

Traeger, Ernst Wilhelm, 1805-1874.

Rungie (Family)

Fuhlbohm (Family)

Urlwin (Family).

Kraus, Peter -- Biography.

Huppatz (Family).

Sherwell (Family)

Nixon, Geoffrey Owen, 1921-2011.

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