On the Hyper-Poisson Distribution and its Generalization with Applications
Journal Title: Journal of Advances in Mathematics and Computer Science - Year 2017, Vol 21, Issue 3
Abstract
In this paper, we fit the hyper-Poisson, and the Mittag-Leffer function (MLFD) distributions to data exhibiting over and under dispersion. Three frequency data sets were employed with one exhibiting under-dispersion. We also extend these distributions to GLM situations where we have a set of covariates defined in the form x ' β. In all, we compared the negative-binomial (NB), the generalized Poisson (GP), the Conway-Maxwell Poisson (COMP), the Hyper-Poisson (HP) and the MLFD models to the selected data sets. The generalized linear model (GLM) data employed in this study is the German national health registry data which has 3874 observations with 41.56% being zeros-thus the data is zero-inflated. Our results contrast the results from these various distributions. Further, theoretical means and variances of each model are computed together with their corresponding empirical means and variances. It was obvious that the two do not match for each of our data sets. The reason being that the models all have infinite range of values than the random variable Y can take, but the data has a finite range of values. It is therefore not unusual for the sum of estimated probabilities being less than 1.00 and consequently, the sum of the expected values are usually less that the sample size n. However, if the range of values of Y are extended beyond the given data value,
Authors and Affiliations
Bayo H. Lawal
Keywords
Related Articles
- EP ID EP322038
- DOI 10.9734/BJMCS/2017/32184
- Views 77
- Downloads 0
Simple Mathematical Model for Malaria Transmission
Our model is made up of two sections: In the first section, we study a simple SEIR model, estimated the reproduction number, discussed the disease-free and endemic equilibria using the Routh-Hurwitz criterion and second...
Fixed Point of Presic Type Mapping in G-Metric Spaces
In this paper, we give a xed point theorem for Presic type contractive mapping in G-metric space. We also present an example to validate our result.
Time Series Analysis for Modeling and Forecasting International Tourist Arrivals in Sri Lanka
Tourism is one of the income generating industries in a developing country which directly contribute to the economy. Therefore, forecasting tourist arrivals is important for making policy decisions to improve facilities...
Some Commutativity Theorems in Prime Rings with Involution and Derivations
Let R be a ring with involution ′∗′ . An additive map x 7→ x ∗ of R into itself is called an involution if (i) (xy) ∗ = y ∗ x ∗ and (ii) (x∗)∗ = x holds for all x; y ∈ R. An additive mapping δ : R → R is called a derivat...
Computation of k-out-of-n System Reliability via Reduced Ordered Binary Decision Diagrams
A prominent reliability model is that of the partially-redundant (k-out-of-n) system. We use algebraic as well as signal-flow-graph methods to explore and expose the AR algorithm for computing k-out-of-n reliability. We...