On the uniform convergence of normalized Poisson mixtures to their mixing distribution

Adell, JoséA.; Cal, Jesús de la

doi:10.1016/0167-7152(93)90221-4

Cited by 13 publications

(15 citation statements)

References 7 publications

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“…For individual random variables, this method has been studied in Adell and de la Cal (1993), and further developed in Adell and de la Cal (1994) in connection with gamma distributions. In Section 2 we discuss general properties of this approximation method in the context of random sums.…”

Section: Consider the Random Summentioning

confidence: 98%

“…If we want to use this approximation procedure simultaneously for F * β and its successive convolutions, we need more detailed estimates. In particular we use the following result proven in Adell and Sangüesa (1999), in which the upper bounds are completely specified.…”

Section: Error Bounds In Approximation Of Gamma Distributionsmentioning

confidence: 99%

“…Secondly we deal with the problem of getting uniform error bounds for the distance between the distribution function of (1) and its discrete approximation. Following Adell and de la Cal (1993), this problem is related to an approximation problem by means of gamma-type positive linear operators (see Proposition 2.3). In the second part of the paper we particularize to the case where the common distribution of (X i ) i∈N * is a mixture of gamma distributions.…”

Section: Consider the Random Summentioning

confidence: 99%

“…In order to do so, we use the following approach which was first proposed in Adell and de la Cal (1993). Let X be a nonnegative random variable with distribution function F ∈ C[0, ∞).…”

Section: The Approximation Proceduresmentioning

confidence: 99%

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Error bounds in approximations of random sums using gamma-type operators

Sangüesa

2008

Insurance: Mathematics and Economics

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Section: Consider the Random Summentioning

confidence: 98%

Section: Error Bounds In Approximation Of Gamma Distributionsmentioning

confidence: 99%

Section: Consider the Random Summentioning

confidence: 99%

“…In order to do so, we use the following approach which was first proposed in Adell and de la Cal (1993). Let X be a nonnegative random variable with distribution function F ∈ C[0, ∞).…”

Section: The Approximation Proceduresmentioning

confidence: 99%

See 2 more Smart Citations

Error bounds in approximations of random sums using gamma-type operators

Sangüesa

2008

Insurance: Mathematics and Economics

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“…We shall firstly mention some examples in which both operators arise in a natural way (we refer to [ 1,2] for more details). …”

Section: Introductionmentioning

confidence: 99%

Direct and converse inequalities for positive linear operators on the positive semi-axis

Adell

Sangüesa

1999

J Aust Math Soc A

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We consider positive linear operators of probabilistic type L,f acting on real functions / defined on the positive semi-axis. We deal with the problem of uniform convergence of L,f to / , both in the usual sup-norm and in a uniform L p type of norm. In both cases, we obtain direct and converse inequalities in terms of a suitable weighted first modulus of smoothness of/. These results are applied to the Baskakov operator and to a gamma operator connected with real Laplace transforms, Poisson mixtures and Weyl fractional derivatives of Laplace transforms.1991 Mathematics subject classification (Amer. Math. Soc): primary 44A10,41A35, 60J30.

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Approximating gamma distributions by normalized negative binomial distributions

Adell

Cal

1994

J. Appl. Probab.

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Let F be the gamma distribution function with parameters a > 0 and α > 0 and let Gs be the negative binomial distribution function with parameters α and a/s, s > 0. By combining both probabilistic and approximation-theoretic methods, we obtain sharp upper and lower bounds for . In particular, we show that the exact order of uniform convergence is s–p , where p = min(1, α). Various kinds of applications concerning charged multiplicity distributions, the Yule birth process and Bernstein-type operators are also given.

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On the uniform convergence of normalized Poisson mixtures to their mixing distribution

Cited by 13 publications

References 7 publications

Error bounds in approximations of random sums using gamma-type operators

Error bounds in approximations of random sums using gamma-type operators

Direct and converse inequalities for positive linear operators on the positive semi-axis

Approximating gamma distributions by normalized negative binomial distributions

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