| 1. |
- Bondesson, Lennart, 1944-, et al.
(författare)
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A class of infinitely divisible distributions connected to branching processes and random walks
- 2004
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier. - 0022-247X. ; 295:1, s. 134-143
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Tidskriftsartikel (refereegranskat)abstract
- A class of infinitely divisible distributions on {0,1,2,…} is defined by requiring the (discrete) Lévy function to be equal to the probability function except for a very simple factor. These distributions turn out to be special cases of the total offspring distributions in (sub)critical branching processes and can also be interpreted as first passage times in certain random walks. There are connections with Lambert's W function and generalized negative binomial convolutions.
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| 2. |
- Bondesson, Lennart, 1944-
(författare)
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A class of probability distributions that is closed with respect to addition as well as multiplication of independent random variables
- 2015
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Ingår i: Journal of theoretical probability. - : Springer. - 0894-9840 .- 1572-9230. ; 28:3, s. 1063-1081
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Tidskriftsartikel (refereegranskat)abstract
- Thorin’s class of generalized gamma convolutions (GGCs) is closed with respect to change in scale, weak limits, and addition of independent random variables. Here, it is shown that the GGC class also has the remarkable property of being closed with respect to multiplication of independent random variables. This novel result, which has a simple extension to symmetric distributions on R, has many consequences and applications. In particular, it follows that X∼ GGC implies that exp(X)∼ GGC. The latter result is used to find a large class of explicit probability functions on {0,1,2,…} which are generalized negative binomial convolutions (GNBCs). The paper ends with several open problems.
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| 3. |
- Bondesson, Lennart, 1944-, et al.
(författare)
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A non-symmetric matrix with integer eigenvalues
- 2007
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Ingår i: Linear and Multilinear Algebra. - : Taylor & Francis Group. - 0308-1087 .- 1563-5139. ; 55:3, s. 239-247
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Tidskriftsartikel (refereegranskat)abstract
- A nonsymmetric N × N matrix with elements as certain simple functions of N distinct real or complex numbers r 1, r 2, …, rN is presented. The matrix is special due to its eigenvalues − the consecutive integers 0,1,2, …, N−1. Theorems are given establishing explicit expressions of the right and left eigenvectors and formulas for recursive calculation of the right eigenvectors. A special case of the matrix has appeared in sampling theory where its right eigenvectors, if properly normalized, give the inclusion probabilities of the conditional Poisson sampling design.
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| 4. |
- Bondesson, Lennart, 1944-, et al.
(författare)
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An extension of Sampford's method for unequal probability sampling
- 2011
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Ingår i: Scandinavian Journal of Statistics. - : John Wiley & Sons. - 0303-6898 .- 1467-9469. ; 38:2, s. 377-392
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Sampford's (1967) unequal probability sampling method is extended to the case that the inclusion probabilities do not sum to an integer. In this case the sampling outcome is left open for exactly one randomly chosen unit and that unit gets a new inclusion probability. Three applications are presented. Two of them challenge traditional sampling routines. The simple Pareto sampling design, which was introduced by Rosén (1997a,b), is also extended. The extended Pareto design is shown to be close to the extended Sampford design.
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| 5. |
- Bondesson, Lennart, 1944-
(författare)
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Conditional and restricted Pareto sampling : two new methods for unequal probability sampling
- 2010
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Ingår i: Scandinavian Journal of Statistics. - : Wiley-Blackwell. - 0303-6898 .- 1467-9469. ; 37:3, s. 514-530
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Tidskriftsartikel (refereegranskat)abstract
- Two new unequal probability sampling methods are introduced: conditional and restricted Pareto sampling. The advantage of conditional Pareto sampling compared with standard Pareto sampling, introduced by Rosén (J. Statist. Plann. Inference, 62, 1997, 135, 159), is that the factual inclusion probabilities better agree with the desired ones. Restricted Pareto sampling, preferably conditioned or adjusted, is able to handle cases where there are several restrictions on the sample and is an alternative to the recent cube method for balanced sampling introduced by Deville and Tillé (Biometrika, 91, 2004, 893). The new sampling designs have high entropy and the involved random numbers can be seen as permanent random numbers.
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| 6. |
- Bondesson, Lennart, 1944-
(författare)
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Dear reader
- 2001
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Ingår i: Scandinavian Journal of Statistics. - : John Wiley & Sons. - 0303-6898 .- 1467-9469. ; 28:1, s. 1-1
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
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| 7. |
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| 8. |
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| 9. |
- Bondesson, Lennart, 1944-
(författare)
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On a minimum correlation problem
- 2003
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Ingår i: Statistics and Probability Letters. - Amsterdam : Elsevier. - 0167-7152 .- 1879-2103. ; 62:4, s. 361-370
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Tidskriftsartikel (refereegranskat)abstract
- A stationary sequence of Bernoulli(p) distributed variables is considered. For a general class of 1-dependent sequences the minimum and the maximum of the lag 1 autocorrelation is found. The correlation is never below −1/3 and attains this value only for certain values of p.
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| 10. |
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