We propose a method of spatial prediction using count data that can be reasonably modeled assuming the Conway-Maxwell Poisson distribution (COM-Poisson). The COM-Poisson model is a two parameter generalization of the Poisson distribution that allows for the flexibility needed to model count data that are either over or under-dispersed. The computationally limiting factor of the COM-Poisson distribution is that the likelihood function contains multiple intractable normalizing constants and is not always feasible when using Markov Chain Monte Carlo (MCMC) techniques. Thus, we develop a prior distribution of the parameters associated with the COM-Poisson that avoids the intractable normalizing constant. Also, allowing for spatial random effects induces additional variability that makes it unclear if a spatially correlated Conway-Maxwell Poisson random variable is over or under-dispersed. We propose a computationally efficient hierarchical Bayesian model that addresses these issues. In particular, in our model, the parameters associated with the COM-Poisson do not include spatial random effects (leading to additional variability that changes the dispersion properties of the data), and are then spatially smoothed in subsequent levels of the Bayesian hierarchical model. Furthermore, the spatially smoothed parameters have a simple regression interpretation that facilitates computation. We demonstrate the applicability of our approach using simulated examples, and a motivating application using 2016 US presidential election voting data in the state of Florida obtained from the Florida Division of Elections.
An extension of truncated Poisson distribution having two parameters for a group of two types of population is derived and named as Bounded Poisson (BP) distribution. To estimate the parameters, method of moment has been employed. To check the suitability and applicability of the model it has been applied on real data set on human fertility derived from the third round of National Family Health Survey conducted in 2005-06 in Uttar Pradesh, India. Proposed model provides a good fitting to the data under consideration.
A new class of distributions called the beta linear failure rate power series (BLFRPS) distributions is introduced and discussed. This class of distributions contains new and existing sub-classes of distributions including the beta exponential power series (BEPS) distribution, beta Rayleigh power series (BRPS) distribution, generalized linear failure rate power series (GLFRPS) distribution, generalized Rayleigh power series (GRPS) distribution, generalized exponential power series (GEPS) distribution, Rayleigh power series (RPS) distributions, exponential power series (EPS) distributions, and linear failure rate power series (LFRPS) distribution of Mahmoudi and Jafari (2014). The special cases of the BLFRPS distribution include the beta linear failure rate Poisson (BLFRP) distribution, beta linear failure rate geometric (BLFRG) distribution of Oluyede, Elbatal and Huang (2014), beta linear failure rate binomial (BLFRB) distribution, and beta linear failure rate logarithmic (BLFRL) distribution. The BLFRL distribution is also discussed in details as a special case of the BLFRPS class of distributions. Its structural properties including moments, conditional moments, deviations, Lorenz and Bonferroni curves and entropy are derived and presented. Maximum likelihood estimation method is used for parameters estimation. Maximum likelihood estimation technique is used for parameter estimation followed by a Monte Carlo simulation study. Application of the model to a real dataset is presented.
A new four-parameter lifetime distribution named as the power Lomax Poisson is introduced and studied. The subject distribution is obtained by combining the power Lomax and Poisson distributions. Structural properties of the power Lomax Poisson model are implemented. Estimation of the model parameters are performed using the maximum likelihood, least squares and weighted least squares techniques. An intensive simulation study is performed for evaluating the performance of different estimators based on their relative biases, standard errors and mean square errors. Eventually, the superiority of the new compounding distribution over some existing distribution is illustrated by means of two real data sets. The results showed the fact that, the suggested model can produce better fits than some well-known distributions.