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.     

Estimation of long-run inefficiency levels: a dynamic frontier approach

Cornwell, Schmidt, and Sickles (1990) and Kumbhakar (1990), among others, developed stochasticfrontier production models which allow firm specific inefficiency levels to change over time. These studies assumed arbitrary restrictions on the short-run dynamics of efficiency levels which have little theoretical justification. Further, the models are inappropriate for estimation of long-run efficiencies. We consider estimation of an alternative frontier model in which firmspecific technical inefficiency levels are autoregressive. This model is particularly useful to examine a potential dynamic link between technical innovations and production inefficiency levels. We apply our methodology to a panel of US airlines.     

Testing Target-Zone Models Using Efficient Method of Moments

The objectives of this article are threefold—(1) to test target-zone models using more efficient and direct econometric methodology than previous research, (2) to identify an implicit band, if it exists, from observed data and to test target-zone models based on the estimated implicit band rather than the stated official band, and (3) to examine whether the exchange rate can be modeled as a managed float system with a central parity that lacks a band. We find strong evidence that a model with intramarginal intervention and a narrower implicit (unofficial) band can describe the dynamics of the French franc/Deutsche mark exchange rate from January 1, 1987–July 30, 1993.     

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 the moment generating functions for integer valued random variables

Abstract

In this note, we give explicit expressions of moment generating functions for integer valued random variables in both univariate and multivariate cases, which extend the results obtained by Nadarajah and Mitov [Communications in Statistics–Theory and Methods, 32, 2003, 47–60] and more recently by Chakraborti, Jardim and Epprecht [The American Statistician, 2017], Kwong and Nadarajah [Communications in Statistics–Theory and Methods, 2017]. Some examples are also discussed.     

On a Class of Nonlinear AR(P) Models with Nonlinear ARCH Errors

This paper studies general sufficient conditions for the geometric ergodicity and the existence of moments for a class of nonlinear autoregressive models with nonlinear ARCH errors. Applications of these conditions to various well-known nonlinear time series models yield specific sufficient conditions, many of which are new or generalizations of existing conditions.     

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.     

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.     

Cutting Experimental Designs into Blocks

Most experimental material in agriculture and industry is heterogeneous in nature and therefore its statistical analysis benefits from blocking. Many experiments are restricted in time or space, and again blocking is useful. This paper adopts the idea of orthogonal blocking of Box & Hunter (1957) and applies it to optimal blocking designs. This approach is then compared with the determinant-based approach described in the literature for constructing block designs.     

On the power of durbin-watson statistic against fractionally integrated processes

This paper provides the theoretical explanation and Monte Carlo experiments of using a modified version of Durbin-Watson ( D W ) statistic to test an 1 ( 1 ) process against I ( d ) alternatives, that is, integrated process of order d, where d is a fractional number. We provide the exact order of magnitude of the modified D W test when the data generating process is an I ( d ) process with d E (0. 1.5). Moreover, the consistency of the modified DW statistic as a unit root test against I ( d ) alternatives with d E ( 0 , l ) U ( 1 , 1.5) is proved in this paper. In addition to the theoretical analysis, Monte Carlo experiments show that the performance of the modified D W statistic reveals that it can be used as a unit root test against I ( d ) alternatives.