On the Discrete Quasi Xgamma Distribution

• Published in: Methodology and computing in applied probability Vol. 22; no. 2; pp. 747 - 775
• Main Authors: Mazucheli, Josmar, Bertoli, Wesley, Oliveira, Ricardo P., Menezes, André F. B.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2020; Springer Nature B.V
• Subjects: Analogs; Business and Management; Computer simulation; Datasets; Discretization; Economics; Electrical Engineering; Infinite series; Life Sciences; Mathematics and Statistics; Maximum likelihood estimators; Statistical analysis; Statistics; Maximum likelihood estimation; Simulation study; Discretization methods; Quasi xgamma distribution; Count data; Data dispersion; 62F10; 62Q05; 62E15
• ISSN: 1387-5841; 1573-7713
• DOI: 10.1007/s11009-019-09731-7

Methods to obtain discrete analogs of continuous distributions have been widely applied in recent years. In general, the discretization process provides probability mass functions that can be competitive with traditional models used in the analysis of count data. The discretization procedure also avoids the use of continuous distribution to model strictly discrete data. In this paper, we propose two discrete analogs for the quasi xgamma distribution as alternatives to model under- and overdispersed datasets. The methods of infinite series and survival function have been considered to derive the models and, despite the difference between the methods, the resulting distributions are interchangeable. Several statistical properties of the proposed models have been derived. The maximum likelihood theory has been considered for estimation and asymptotic inference concerns. An intensive simulation study has been carried out in order to evaluate the main properties of the maximum likelihood estimators. The usefulness of the proposed models has been assessed by using two real datasets provided by literature. A general comparison of the proposed models with some well-known discrete distributions has been provided.