TITLE

# Distributions of Random Partitions and Their Applications

AUTHOR(S)
Charalambides, Charalambos A.
PUB. DATE
June 2007
SOURCE
Methodology & Computing in Applied Probability;Jun2007, Vol. 9 Issue 2, p163
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
Assume that a random sample of size m is selected from a population containing a countable number of classes (subpopulations) of elements (individuals). A partition of the set of sample elements into (unordered) subsets, with each subset containing the elements that belong to same class, induces a random partition of the sample size m, with part sizes { Z 1, Z 2,..., Z N } being positive integer-valued random variables. Alternatively, if N j is the number of different classes that are represented in the sample by j elements, for j=1,2,..., m, then ( N 1, N 2,..., N m ) represents the same random partition. The joint and the marginal distributions of ( N 1, N 2,..., N m ), as well as the distribution of $N=\sum^m_{j=1}N_{\!j}$ are of particular interest in statistical inference. From the inference point of view, it is desirable that all the information about the population is contained in ( N 1, N 2,..., N m ). This requires that no physical, genetical or other kind of significance is attached to the actual labels of the population classes. In the present paper, combinatorial, probabilistic and compound sampling models are reviewed. Also, sampling models with population classes of random weights (proportions), and in particular the Ewens and Pitman sampling models, on which many publications are devoted, are extensively presented.
ACCESSION #
24942845

## Related Articles

• Asymptotic Results for the Sum of Dependent Non-identically Distributed Random Variables. Kortschak, Dominik; Albrecher, Hansjörg // Methodology & Computing in Applied Probability;Sep2009, Vol. 11 Issue 3, p279

In this paper we extend some results about the probability that the sum of n dependent subexponential random variables exceeds a given threshold u. In particular, the case of non-identically distributed and not necessarily positive random variables is investigated. Furthermore we establish...

• A Simple Normal Approximation for Weibull Distribution with Application to Estimation of Upper Prediction Limit. Kulkarni, H. V.; Powar, S. K. // Journal of Probability & Statistics;2011, p1

We propose a simple close-to-normal approximation to a Weibull random variable (r.v.) and consider the problem of estimation of upper prediction limit (UPL) that includes at least l out of m future observations from a Weibull distribution at each of r locations, based on the proposed...

• Distribution-Free Approximations for Chance Constraints. Allen, F. M.; Braswell, R. N.; Rao, P. V. // Operations Research;May/Jun74, Vol. 22 Issue 3, p610

This paper concerns developing methods for approximating a chance-constrained set when any information concerning the random variables must be derived from actual samples. Such a situation has not been presented in the literature. When existing chance-constrained programming techniques are used,...

• Stability of the Ramachandran-Rao characterization of the Cauchy distribution. Yanushkevichius, R. // Journal of Mathematical Sciences;Oct2007, Vol. 146 Issue 4, p6066

The article examines stability regarding the characterization of the cauchy distribution. The independent identically distributed (i.i.d.) random variables of the Cauchy distribution were taken into account, as well as the distribution of monomial X1. Key information about the theorems and its...

• Extreme observations and risk assessment in the equity markets of MENA region: Tail measures and Value-at-Risk. Assaf, A. // International Review of Financial Analysis;Jun2009, Vol. 18 Issue 3, p109

Abstract: The standard ï¿½delta-normalï¿½ Value-at-Risk methodology requires that the underlying returns generating distribution for the security in question is normally distributed, with moments which can be estimated using historical data and are time-invariant. However, the stylized...

• Small deviation probabilities for sums of independent positive random variables. Rozovsky, L. // Journal of Mathematical Sciences;Dec2007, Vol. 147 Issue 4, p6935

In this note, we give estimates of small deviation probabilities of the sum âˆ‘jâ‰¥1 Î»j Xj, where {Î»j} are nonnegative numbers and {Xj} are i.i.d. positive random variables that satisfy mild assumptions at zero and infinity. Bibliography: 10 titles.

• ASYMPTOTIC BASELINE OF THE HAZARD RATE FUNCTION OF MIXTURES. Yulin Li // Journal of Applied Probability;Sep2005, Vol. 42 Issue 3, p892

In this article, we consider the limit behavior of the hazard rate function of mixture distributions, assuming knowledge of the behavior of each individual distribution. We show that the asymptotic baseline function of the hazard rate function is preserved under mixture.

• A COVERAGE FUNCTION FOR INTERVAL ESTIMATORS OF SIMULATION RESPONSE. Schruben, Lee W. // Management Science;Jan1980, Vol. 26 Issue 1, p18

The coverage function presented here measures confidence interval robustness. It is suggested that this function be used in the analysis of empirical interval estimator studies. Some approaches for determining appropriate sample sizes in such experiments are also discussed. A short study of two...

• Applying the bootstrap to the multivariate case: Bootstrap component/factor analysis. Zientek, Linda Reichwein; Thompson, Bruce // Behavior Research Methods;May2007, Vol. 39 Issue 2, p318

The bootstrap method, which empirically estimates the sampling distribution for either inferential or descriptive statistical purposes, can be applied to the multivariate case. When conducting bootstrap component, or factor, analysis, resampling results must be located in a common factor space...

Share