scholarly journals On lower bounds for Poisson approximation to 2-runs statistic

2010 ◽  
Vol 51 ◽  
Author(s):  
Jūratė Petrauskienė ◽  
Vydas Čekanavičius
Keyword(s):  
Lower Bounds ◽  
Asymptotic Expansions ◽  
Poisson Approximation ◽  
Second Order ◽  
Compound Poisson ◽  
Poisson Distributions

Two-runs statistic is approximated by various compound Poisson distributions and second order asymptotic expansions. Estimates of lower bounds are obtained for the uniform Kolmogorov and local metrics.

Compound poisson approximations for the numbers of extreme spacings

1993 ◽  
Vol 25 (04) ◽  
pp. 847-874 ◽  
Author(s):  
Małgorzata Roos
Keyword(s):  
Poisson Approximation ◽  
Expected Number ◽  
Compound Poisson ◽  
Poisson Distributions ◽  
Poisson Approximations ◽  
Better Than

The accuracy of the Poisson approximation to the distribution of the numbers of large and small m-spacings, when n points are placed at random on the circle, was analysed using the Stein–Chen method in Barbour et al. (1992b). The Poisson approximation for m≧2 was found not to be as good as for 1-spacings. In this paper, rates of approximation of these distributions to suitable compound Poisson distributions are worked out, using the CP–Stein–Chen method and an appropriate coupling argument. The rates are better than for Poisson approximation for m≧2, and are of order O((log n)2/n) for large m-spacings and of order O(1/n) for small m-spacings, for any fixed m≧2, if the expected number of spacings is held constant as n → ∞.

Compound poisson approximations for the numbers of extreme spacings

1993 ◽  
Vol 25 (4) ◽  
pp. 847-874 ◽  
Author(s):  
Małgorzata Roos
Keyword(s):  
Poisson Approximation ◽  
Expected Number ◽  
Compound Poisson ◽  
Poisson Distributions ◽  
Poisson Approximations ◽  
Better Than

The accuracy of the Poisson approximation to the distribution of the numbers of large and small m-spacings, when n points are placed at random on the circle, was analysed using the Stein–Chen method in Barbour et al. (1992b). The Poisson approximation for m≧2 was found not to be as good as for 1-spacings. In this paper, rates of approximation of these distributions to suitable compound Poisson distributions are worked out, using the CP–Stein–Chen method and an appropriate coupling argument. The rates are better than for Poisson approximation for m≧2, and are of order O((log n)2/n) for large m-spacings and of order O(1/n) for small m-spacings, for any fixed m≧2, if the expected number of spacings is held constant as n → ∞.

Infinitely divisible approximations for discrete nonlattice variables

2003 ◽  
Vol 35 (04) ◽  
pp. 982-1006
Author(s):  
V. Čekanavičius
Keyword(s):  
Asymptotic Expansions ◽  
Random Variables ◽  
Second Order ◽  
Independent Random Variables ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible ◽  
Compound Poisson ◽  
Set Of Points ◽  
Poisson Measures

Sums of independent random variables concentrated on discrete, not necessarily lattice, set of points are approximated by infinitely divisible distributions and signed compound Poisson measures. A version of Kolmogorov's first uniform theorem is proved. Second-order asymptotic expansions are constructed for distributions with pseudo-lattice supports.

Infinitely divisible approximations for discrete nonlattice variables

2003 ◽  
Vol 35 (4) ◽  
pp. 982-1006 ◽  
Author(s):  
V. Čekanavičius
Keyword(s):  
Asymptotic Expansions ◽  
Random Variables ◽  
Second Order ◽  
Independent Random Variables ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible ◽  
Compound Poisson ◽  
Set Of Points ◽  
Poisson Measures

Sums of independent random variables concentrated on discrete, not necessarily lattice, set of points are approximated by infinitely divisible distributions and signed compound Poisson measures. A version of Kolmogorov's first uniform theorem is proved. Second-order asymptotic expansions are constructed for distributions with pseudo-lattice supports.

Compound Poisson approximations for sums of discrete nonlattice variables

2003 ◽  
Vol 35 (1) ◽  
pp. 228-250 ◽  
Author(s):  
V. Čekanavičius ◽  
Y. H. Wang
Keyword(s):  
Normal Distribution ◽  
Asymptotic Expansions ◽  
Random Variables ◽  
Independent Random Variables ◽  
Compound Poisson ◽  
Poisson Distributions ◽  
Set Of Points ◽  
Poisson Measures ◽  
Poisson Approximations

Sums of independent random variables concentrated on the same finite discrete, not necessarily lattice, set of points are approximated by compound Poisson distributions and signed compound Poisson measures. Such approximations can be more accurate than the normal distribution. Short asymptotic expansions are constructed.

Compound Poisson approximations for sums of discrete nonlattice variables

2003 ◽  
Vol 35 (01) ◽  
pp. 228-250 ◽  
Author(s):  
V. Čekanavičius ◽  
Y. H. Wang
Keyword(s):  
Normal Distribution ◽  
Asymptotic Expansions ◽  
Random Variables ◽  
Independent Random Variables ◽  
Compound Poisson ◽  
Poisson Distributions ◽  
Set Of Points ◽  
Poisson Measures ◽  
Poisson Approximations

Sums of independent random variables concentrated on the same finite discrete, not necessarily lattice, set of points are approximated by compound Poisson distributions and signed compound Poisson measures. Such approximations can be more accurate than the normal distribution. Short asymptotic expansions are constructed.

Asymptotic Expansions in the Exponent: a Compound Poisson Approach

1997 ◽  
Vol 29 (02) ◽  
pp. 374-387 ◽  
Author(s):  
V. Čekanavičius
Keyword(s):  
Asymptotic Expansion ◽  
Large Deviations ◽  
Poisson Distribution ◽  
Asymptotic Expansions ◽  
Compound Poisson ◽  
Poisson Measures ◽  
Poisson Approximations

The accuracy of the Normal or Poisson approximations can be significantly improved by adding part of an asymptotic expansion in the exponent. The signed-compound-Poisson measures obtained in this manner can be of the same structure as the Poisson distribution. For large deviations we prove that signed-compound-Poisson measures enlarge the zone of equivalence for tails.

Approximation of sums by compound Poisson distributions with respect to stop-loss distances

1990 ◽  
Vol 22 (2) ◽  
pp. 350-374 ◽  
Author(s):  
S. T. Rachev ◽  
L. Rüschendorf
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Compound Poisson ◽  
Poisson Distributions ◽  
Stop Loss ◽  
Scale Transformations

The approximation of sums of independent random variables by compound Poisson distributions with respect to stop-loss distances is investigated. These distances are motivated by risk-theoretic considerations. In contrast to the usual construction of approximating compound Poisson distributions, the method suggested in this paper is to fit several moments. For two moments, this can be achieved by scale transformations. It is shown that the new approximations are more stable and improve the usual approximations by accompanying laws in examples where the probability 1 – pi that the ith summand is zero is not too large.

Sign in / Sign up

Export Citation Format

Share Document