Special Issue "Probability, Statistics and Their Applications"
Deadline for manuscript submissions: 31 July 2020.
“Costin C. Kiritescu” National Institute of Economic Research, Bucharest, Romania
Faculty of Mathematics and Computer Science, University of Bucharest, Romania
Interests: statistics; decision theory; operational research; variational inequalities; equilibrium theory; generalized convexity; information theory; biostatistics; actuarial statistics
Statistics and probability are important domains in the scientific world, having many applications in various fields, such as engineering, reliability, medicine, biology, economics, physics, and not only, probability laws providing an estimated image of the world we live in. This Special Volume deals targets some certain directions of the two domains as described below.
Some applications of statistics are clustering of random variables based on simulated and real data or scan statistics, the latter being introduced in 1963 by Joseph Naus. In reliability theory, some important statistical tools are hazard rate and survival functions, order statistics, and stochastic orders. In physics, the concept of entropy is at its core, while special statistics were introduced and developed, such as statistical mechanics and Tsallis statistics.
~In economics, statistics, mathematics, and economics formed a particular domain called econometrics. ARMA models, linear regressions, income analysis, and stochastic processes are discussed and analyzed in the context of real economic processes. Other important tools are Lorenz curves and broken stick models.
~Theoretical results such as modeling of discretization of random variables and estimation of parameters of new and old statistical models are welcome, some important probability laws being heavy-tailed distributions. In recent years, many distributions along with their properties have been introduced in order to better fit the growing data available.
The purpose of this Special Issue is to provide a collection of articles that reflect the importance of statistics and probability in applied scientific domains. Papers providing theoretical methodologies and applications in statistics are welcome.
Prof. Vasile Preda
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access monthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
- Applied and theoretical statistics
- New probability distributions and estimation methods
- Broken stick models
- Lorenz curve
- Scan statistics
- Discretization of random variables
- Clustering of random variables
The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.
Author: Gheorghiță Zbăganu
affiliation: Institute for Mathematical Statistics and Applied Mathematics
Abstract: We study the following problem: a stick of length 1 is broken at random into n smaller sticks using i.i.d. random variables (Xk)k=1,…,n-1 having a continuous probability distribution on [0,1] denoted by F. Normalize these small sticks in such a way that their average length is equal to 1. This is a broken stick model. Consider the empirical distribution of these n smaller sticks. What happens if n is great? Is there a limit distribution of these empirical distributions if n tends to infinity? It is known that if F is the uniform distribution then the limit distribution does exist and it is the exponential one. How much inequality among the small sticks does this procedure produce? Usually, when studying the inequality, one uses the Lorenz curve and the Gini coefficient. The more egalitarian a distribution, the closer is the Lorenz curve to the first diagonal of [0,1] 2. We conjecture that the limit does exist for any absolutely continuous distribution F and, moreover, that it produces more inequality that the uniform distribution. This seems to be an optimality property of the uniform distribution: it is the most equalitarian. We prove the conjecture when the density of F is a step function. In order to prepare the proof we study the empirical Lorenz and pre-Lorenz curves of a sequence of non-negative real numbers
2. Title: Discretization of Random Variables in Lp(Ω,F,P)
Author: George-Jason Siouris and Alex Karagrigoriou
Affiliation: Lab of Statistics and Data Analysis, Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Karlovasi, 83200 Samos, Greece
Abstract: This work deals with the modelling of the discrete nature of the returns by applying the discretization of the tail density function. Motivated by the discrete nature of returns and since it seems to be present in a number of scientific fields, we focus in this work on a general framework for the discretization of random variables in Lp(Ω,F,P). More specifically, we concentrate on finite moments after the discretization is applied and introduce two new families of random variables, namely the C(r) which contains all strictly continuous random variables with r finite moments and the D(r) that contains all discrete random variables with support of equidistant values. Hence, lp(Ω,F,P) is a subset of D(r). The extraordinary behavior the different discretizations exhibit, as well as the new possibilities they provide, are presented in this work.
3. Title: Estimation of Generalized Beta-Pareto distribution based on several optimization methods
Author: Badredine BOUMARAF, Nacira SEDDIK-AMEUR, Vlad Stefan BARBU
Abstract: In this paper, we are interested in the four-parameter generalized Beta-Pareto distribution introduced in Akinsete et al. (2008). Note that the family of the Pareto distribution and its generalizations has been found useful in the literature for providing appropriate models for many types of heavy-tailed data, like income series, city population sizes or the size of firms. This is one of the reasons for being successfully used in many applications in physics, biology, hydrology, finance, social sciences, engineering, etc. Since the maximum likelihood estimators of the parameters of the generalized Beta-Pareto distribution cannot be obtained explicitly, we use several nonlinear optimization methods for numerically obtaining these estimators: the Fletcher-Reeves’ method, the Polack-Ribière’s method and a variant of the Fletcher-Reeves’ method, called the Hesteness-Stiefel’s method. In order to evaluate an approximation of the Hessian matrix involved in the computation, several methods exist in the literature. Among these methods, three are retained in our work: the BFGS method (from Broyden - Fletcher - Goldfarb - Shanno), the DFP method (from Davidon - Fletcher - Powell) and the SR1 method (Symmetric Rank 1). We derive the corresponding algorithms for obtaining the estimators for the parameters of interest and investigate through simulations the accuracy of these methods.
4. Title: Simultaneous dimension reduction and multi-objective clustering
Author: Vincent Vandewalle
Abstract: In model based clustering of quantitative data it is often supposed that only one clustering latent variable explains the heterogeneity of all the others variables. However, when considering variables coming from different sources it is often unrealistic to suppose that the heterogeneity of the data can only be explained by one categorical variable. If such an assumption is made, this could lead to a high number of clusters which could be difficult to interpret. A model based multi-objective clustering is proposed, it assumes the existence of several latent clustering variables, each one explaining the heterogeneity of the
data on some clustering projection. In order to estimate the parameters of the model an EM algorithm is proposed, it relies on a probabilistic reinterpretation of the standard factorial discriminant analysis. The obtained results are projections of the data on some "principal clustering components" allowing some synthetic interpretation of the principal clusters raised by the data.
5. Title: Some dependent models for the one-dimensional discrete scan statistics
Author: Alexandru Amarioarei, Cristian Preda
Abstract: The distribution of the one-dimensional discrete scan statistics is approximated under k-dependence models obtained as block factors of i.i.d. sequences of real random variables. For binary trials, the distribution of the scan statistics associated to 1-dependent sequences is compared with those obtained under Markovian dependance model with the same bivariate distribution of two consecutive trials. In a more general framework (arbitrary distributions), the distribution of the scan statistics is related to the length of the longest increasing run...