Geeta distribution and its properties

A new discrete distribution defined over all the positive integers and with the name of Geeta distribution is described. It is L-shaped like the logarithmic series distribution, Yule distribution and the discrete Pareto distribution but is far more versatile than them as it has two parameters. It belongs to the classes of location parameter distributions, modified power series distributions, Lagrange series distributions and exponential distributions. Its mean fi, variance a2 and two recurrence formulae for higher central moments are obtained. Convolution theorem and variations in the model with changes in the parameters have been considered. ML estimators, MVU estimators and estimators based of mean and variance and on mean and first frequency have been derived.     

Evaluation of an analysis approach used to account for extra-variation in clustered categorical responses

This article presents the results of a simulation study investigating the performance of an approach developed by Miller and Landis (1991) for the analysis of clustered categorical responses. Evaluation of this “two-step” approach, which utilizes the method of moments to estimate the extra-variation pardmeters and subsequently incorporates these parameters into estimating equations for modelling the marginal expectations, is carried out in an experimental setting involving a comparison between two groups of observations. We assume that data for both groups are collected from each cluster and responses are measured on a three-point ordinal scale. The performance of the estimators used in both “steps” of the analysisis investigated and comparisons are made to an alternative analysismethod that ignores the clustering. The results indicate that in the chosen setting the test for a difference between groups generally operatbs at the nominal α=0.05 for 10 or more clusters and hasincreasing power with both an increasing number of clusters and an inrreasing treatment effect. These results provide a striking contrasc to those obtained from an improper analysis that ignores clustering.     

On fractional moments of quadratic expressions in normal variables1

Fractional moments, product cumulants and product moments of general quadratic expressions in singular and nonsingular normal variables are explicitly evaluated. A general method of deriving such moments is also indicated. Particular cases art; shown to agree with known results.     

Identification of arma models with non-gaussian innovations

The problem of modelling time series driven by non-Gaussian innovation has been considered recently by Li and McLeod (1988). In this paper we have discussed the problem of identification of ARMA models with non-Gaussian innovations. Simulation experiments are used to study the applicability of theoretical results.     

Time series count data regression

The count data model studied in the paper extends the Poisson model by al-lowing for overdispersion and serial correlation. Alternative approaches to esti-mate nuisance parameters, required for the correction of the Poisson maximum likelihood covariance matrix estimator and for a quasi-likelihood estimator, are studied. The estimators are evaluated by finite sample Monte Carlo experi-mentation. It is found that the Poisson maximum likelihood estimator with corrected covariance matrix estimators provide reliable inferences for longer time series. Overdispersion test statistics are wellbehaved, while conventional portmanteau statistics for white noise have too large sizes. Two empirical illustrations are included.     

Generalized polya eggenberger family of distributions and its relation to lagrangian katz family

Janardan (1973) introduced the generalized Polya Eggenberger family of distributions (GPED) as a limiting distribution of the generalized Markov-Polya distribution (GMPD). Janardan and Rao (1982) gave a number of characterizing properties of the generalized Markov-Polya and generalized Polya Eggenberger distributions. Here, the GPED family characterized by four parameters, is formally defined and studied. The probability generating function, its moments, and certain recurrence relations with the moments are provided. The Lagrangian Katz family of distributions (Consul and Famoye (1996)) is shown to be a sub-class of the family of GPED (or GPED ₁ ) as it is called in this paper). A generalized Polya Eggenberger distribution of the second kind (GPED ₂ ) is also introduced and some of it's properties are given. Recurrence relations for the probabilities of GPED ₁ and GPED ₂ are given. A number of other structural and characteristic properties of the GPED ₁ are provided, from which the properties of Lagrangian Katz family follow. The parameters of GMPD ₁ are estimated by the method of moments and the maximum likelihood method. An application is provided.     

Tests for Cointegration Breakdown Over a Short Time Period

We derive a speculative trading model with endogenous informed trading that yields a conditionally heteroscedastic time series for trading volume and the squared price changes. We use half-hourly price-change and volume data for IBM during 1988 to test the model and estimate the structural parameters using the simulated method-of-moments estimation procedure. Although the model seems to do a reasonable job fitting the unconditional moments of the volume and the squared price change processes, it fares less well in fitting the relation between current trading volume and lags of trading volume and squared volume's (and its lag's) relation to squared price changes.     

Fast and Stable Algorithms for Computing and Sampling From the Noncentral Hypergeometric Distribution

Although the noncentral hypergeometric distribution underlies conditional inference for 2 × 2 tables, major statistical packages lack support for this distribution. This article introduces fast and stable algorithms for computing the noncentral hypergeometric distribution and for sampling from it. The algorithms avoid the expensive and explosive combinatorial numbers by using a recursive relation. The algorithms also take advantage of the sharp concentration of the distribution around its mode to save computing time. A modified inverse method substantially reduces the number of searches in generating a random deviate. The algorithms are implemented in a Java class, Hypergeometric, available on the World Wide Web.     

Geometric ergodicity of nonlinear autoregressive models with changing conditional variances

The authors give easy‐to‐check sufficient conditions for the geometric ergodicity and the finiteness of the moments of a random process x_t = ?(x_t‐1,…, x_t‐p) + ?_tσ(x_t‐1,…, x_t‐q) in which ?: R^p → R, σ R^q → R and (?_t) is a sequence of independent and identically distributed random variables. They deduce strong mixing properties for this class of nonlinear autoregressive models with changing conditional variances which includes, among others, the ARCH(p), the AR(p)‐ARCH(p), and the double‐threshold autoregressive models.     

Statistical Inference Based on Pooled Data: A Moment-Based Estimating Equation Approach

We consider statistical inference on parameters of a distribution when only pooled data are observed. A moment-based estimating equation approach is proposed to deal with situations where likelihood functions based on pooled data are difficult to work with. We outline the method to obtain estimates and test statistics of the parameters of interest in the general setting. We demonstrate the approach on the family of distributions generated by the Box-Cox transformation model, and, in the process, construct tests for goodness of fit based on the pooled data.