Modeling spatial overdispersion via the generalized Waring point process

Modeling spatial overdispersion requires point process models with finite‐dimensional distributions that are overdisperse relative to the Poisson distribution. Fitting such models usually heavily relies on the properties of stationarity, ergodicity, and orderliness. In addition, although processes based on negative binomial finite‐dimensional distributions have been widely considered, they typically fail to simultaneously satisfy the three required properties for fitting. Indeed, it has been conjectured by Diggle and Milne that no negative binomial model can satisfy all three properties. In light of this, we change perspective and construct a new process based on a different overdisperse count model, namely, the generalized Waring (GW) distribution. While comparably tractable and flexible to negative binomial processes, the GW process is shown to possess all required properties and additionally span the negative binomial and Poisson processes as limiting cases. In this sense, the GW process provides an approximate resolution to the conundrum highlighted by Diggle and Milne.     

Hazard functions and life distributions in discrete time

The problem of studying lifelength distributions in discrete time is considered for certain forms of hazard functions. A class of life distributions that consists of the geometric, the Waring and the negative hypergeometric distributions is shown to result when the hazard function is inversely proportional to some linear function of time.     

Factorial moment estimation for the bivariate generalized Waring distribution

In the context of accident theory, the bivariate generalized Waring distribution (Xekalaki, 1984) is known to offer the possibility of obtaining distinguishable estimates of the “contribution” of chance, risk exposure and proneness to an accident situation. In this paper an estimation procedure based on the first and second order factorial moments is discussed for fitting the distribution to data. Expressions for the asymptotic standard errors of the estimators of the distribution parameters as well as of the resulting estimators of the variance components that represent the roles of the above mentioned factors are given.     

The multivariate generalized waring distribution

The robust procedure given by Balakrishnan, Tiku and Shaarawi (1985) for classifying an observation in one of the two univariate populations _πand _πare generalized to situations where the two populations differ not only in their means but their variances also.     

The bivariate yule distribution and some of its properties

In this paper, a bivariate extension of the YULE distribution is defined and some of its structural properties are examined. It is shown in particular, that it can be obtained in the context of a bivariate STER model and as the only distribution with tail probabilities satisfying certain conditions     

Identifiability of income distributions in the context of damage and generating models

In the context of additive or multiplicative damage models, and under mild conditions, it is shown that the functional forms of suitably chosen regressions on a random variable X or/and its recorded part Y are characteristic of the distribution of X. The paper treats the cases where the recorded value is either an understatement or an overstatement of the true observation.     

Improving the EM algorithm for mixtures

One of the estimating equations of the Maximum Likelihood Estimation method, for finite mixtures of the one parameter exponential family, is the first moment equation. This can help considerably in reducing the labor and the cost of calculating the Maximum Likelihood estimates. In this paper it is shown that the EM algorithm can be substantially improved by using this result when applied for mixture models. A short discussion about other methods proposed for the calculation of the Maximum Likelihood estimates are also reported showing that the above findings can help in this direction too.     

A property of the yule distribution and its applications

The relationship Y = RX between two random variables X and Y, where R is distributed independently of X in (0, l), is known to have important consequences in different fields such as income distribution analysis, Inventory decision models, etc.

In this paper it is shown that when X and Y are discrete random variables, relationships of similar nature lead to Yule-type distributions. The implications of the results are studied in connection with problems of income underreporting and inventory decision making.     

On some distributions arising in inverse cluster sampling

In this paper, distributions of items sampled inversely in clusters are derived. In particular, negative binomial type of distributions are obtained and their properties are studied. A logarithmic series type of distribution is also defined as a limiting form of the obtained generalized negative binomial distribution.     

On some distributions arising from certain generalized sampling schemes

With the notion of success in a series of trials extended tD refer to a run of like outcomes, several new distributions are obtained as the result of sampling from an urn without replacement. or with additional replacements., In this context, the hy-pergeometric, negative hypergeometric, logarithmic series, generalized Waring, Polya and inverse Polya distributions are extended and their properties are studied