Zero-Modified Power Series Models

• Grant number: 08/10613-1
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: August 01, 2009
• End date: January 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Francisco Louzada Neto
• Grantee: Katiane Silva Conceição
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

In this work, we present a family of distributions for count data, the so called Zero-Modified Power Series, which is an extension of the Power Series family of distributions whose support starts at zero. This extension consists in modifying the probability of observing zero of each Power Series distribution, allowing that the new zero-modified distribution being appropriately adjusted to datasets which have any amount of zero observations (for instance, zero-inflated or zero-deflated datasets). Modified distributions presented in the Zero-Modified Series Power family are: Zero-Modified Poisson, Zero-Modified Generalized Poisson, Zero-Modified Geometric, Zero-Modified Binomial, Zero-Modified Negative Binomial and Zero-Modified Generalized Negative Binomial. We present properties and particularities of the Zero-Modified Series Power distributions. In addition, we introduce the Zero-Modified Power Series regression models and propose a Bayesian approach, considering information matrix priori. Simulation studies are presented in order to illustrate the methodology developed in this work. Two real datasets, corresponding to leptospirosis notifications in cities of Bahia State at Brazil, are analyzed. The use of modified distribution belonging to the Zero-Modified Power Series family is very flexible to model count datasets without any previous assumptions about the frequency of zero in the dataset.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

CONCEICAO, KATIANE S.; PIRES, RUBIANE M.; LOUZADA, FRANCISCO; ANDRADE, MARINHO G.; DINIZ, CARLOS A. R.. A generalized species-area relationship: The Poisson distribution case. BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS, v. 28, n. 3, p. 446-460, AUG 2014. (08/10613-1)

CONCEICAO, KATIANE SILVA; ULRICH, WERNER; RIBEIRO DINIZ, CARLOS ALBERTO; RODRIGUES, FRANCISCO APARECIDO; DE ANDRADE, MARINHO GOMES. A Generalized Approach to the Modeling of the Species-Area Relationship. PLoS One, v. 9, n. 8, AUG 29 2014. (13/26416-9, 08/10613-1)