Hassan S. Bakouch

A bivariate INAR(1) time series model with geometric marginals

Abstract In this paper we introduce a simple bivariate integer-valued time series model with positively correlated geometric marginals based on the negative binomial thinning mechanism. Some properties of the model are considered. The unknown parameters of the model are estimated using the modified conditional least squares method.

A new lifetime model with decreasing failure rate

In this paper, we introduce a new lifetime distribution by compounding exponential and Poisson–Lindley distributions, named the exponential Poisson–Lindley (EPL) distribution. A practical situation where the EPL distribution is most appropriate for modelling lifetime data than exponential–geometric, exponential–Poisson and exponential–logarithmic distributions is presented. We obtain the density and failure rate of the EPL distribution and properties such as mean lifetime, moments, order statistics and Rényi entropy. Furthermore, estimation by maximum likelihood and inference for large samples are discussed. The paper is motivated by two applications to real data sets and we hope that this model will be able to attract wider applicability in survival and reliability.

A new discrete distribution

A new one-parameter discrete distribution is introduced. Its mathematical properties and estimation procedures are derived. Four real data sets are used to show that the new model performs at least as well as the traditional one-parameter discrete models and other newly proposed two-parameter discrete models.

Pareto Poisson–Lindley distribution with applications

A new lifetime distribution is introduced based on compounding Pareto and Poisson–Lindley distributions. Several statistical properties of the distribution are established, including behavior of the probability density function and the failure rate function, heavy- and long-right tailedness, moments, the Laplace transform, quantiles, order statistics, moments of residual lifetime, conditional moments, conditional moment generating function, stress–strength parameter, Rényi entropy and Songs measure. We get maximum-likelihood estimators of the distribution parameters and investigate the asymptotic distribution of the estimators via Fishers information matrix. Applications of the distribution using three real data sets are presented and it is shown that the distribution fits better than other related distributions in practical uses.

A First-Order Spatial Integer-Valued Autoregressive SINAR(1, 1) Model

Binomial thinning operator has a major role in modeling one-dimensional integer-valued autoregressive time series models. The purpose of this article is to extend the use of such operator to define a new stationary first-order spatial non negative, integer-valued autoregressive SINAR(1, 1) model. We study some properties of this model like the mean, variance and autocorrelation function. Yule-Walker estimator of the model parameters is also obtained. Some numerical results of the model are presented and, moreover, this model is applied to a real data set.

Lindley first-order autoregressive model with applications

ABSTRACT A new stationary first-order autoregressive process with Lindley marginal distribution, denoted as LAR(1) is introduced. We derive the probability function for the innovation process. We consider many properties of this process, involving spectral density, some multi-step ahead conditional measures, run probabilities, stationary solution, uniqueness and ergodicity. We estimate the unknown parameters of the process using three methods of estimation and investigate properties of the estimators with some numerical results to illustrate them. Some applications of the process are discussed to two real data sets and it is shown that the LAR(1) model fits better than other known non Gaussian AR(1) models.

Time series: Modeling, Computation, and Inference

The book, with its 10 chapters, represents a good introduction to Bayesian analysis of time series; the exposition includes theory, methods and applications. The book analyses time series in both time domain and frequency domain, and proposes various models for them. Also, it investigates properties of these models considering certain continuous marginals for modelling. Moreover, it concentrates on Bayesian analysis of the proposed models using different techniques, like Markov chain Monte Carlo and sequential Monte Carlo. The material is valuable and has a good representation of the subject. It represents a good course to graduate level and also provides good material to all who are interested in Bayesian time series analysis. Despite this, the book is not perfect. It proposes many Bayesian ideas without going deeply into Bayesian estimation and inference for model parameters.Also, it does not cover recent models such as integer-valued time series or categorical time series (see, for example 1).