arXiv subjects

Niloufar Dousti Mousavi

Publications and source records attributed to Niloufar Dousti Mousavi.

3 recordsLinked to original sources

arXiv2026

From Poisson Observations to Fitted Negative Binomial Distribution

The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a negative binomial distribution with extreme parameter values, and existing maximum likelihood estimation procedures for the negative binomial distribution may fail or produce unstable estimates. To address this issue, we develop a new algorithm for computing the maximum likelihood estimate of negative binomial parameters, which is more efficient and more accurate than existing methods. We further extend negative binomial distributions with a new parameterization to cover Poisson distributions as a special class. We provide theoretical justifications showing that, when applied to a Poisson data, the estimated parameters of the extended negative binomial distribution can consistently recover the true Poisson distribution.

math.ST↗

arXiv2024

A Trigamma-free Approach for Computing Information Matrices Related to Trigamma Function

Negative binomial related distributions have been widely used in practice. The calculation of the corresponding Fisher information matrices involves the expectation of trigamma function values which can only be calculated numerically and approximately. In this paper, we propose a trigamma-free approach to approximate the expectations involving the trigamma function, along with theoretical upper bounds for approximation errors. We show by numerical studies that our approach is highly efficient and much more accurate than previous methods. We also apply our approach to compute the Fisher information matrices of zero-inflated negative binomial (ZINB) and beta negative binomial (ZIBNB) probabilistic models, as well as ZIBNB regression models.

stat.CO↗

arXiv2023

An R Package AZIAD for Analyzing Zero-Inflated and Zero-Altered Data

We introduce a newly developed R package AZIAD for analyzing zero-inflated or zero-altered data. Compared with existing R packages, AZIAD covers a much larger class of zero-inflated and hurdle models, including both discrete and continuous cases. It provides more accurate parameter estimates, along with the corresponding Fisher information matrix and confidence intervals. It achieves significantly larger power for model identification and selection. To facilitate the potential users, in this paper we provide detailed formulae and theoretical justifications for AZIAD, as well as new theoretical results on zero-inflated and zero-altered models. We use simulation studies to show the advantages of AZIAD functions over existing R packages and provide real data examples and executable R code to illustrate how to use our package for sparse data analysis and model selection.

stat.CO↗