Bivariate Discrete Distributions

Kocherlakota, Subrahmaniam; Kocherlakota, Kathleen

doi:10.1002/0471667196.ess0605

Cited by 22 publications

(31 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The estimates of the regression parameters vectors 1 β and 2 β can be obtained iteratively by using Newton-Raphson method as follows ( ) ( )…”

Section: Zero Truncated Bivariate Poisson (Ztbvp) Modelmentioning

confidence: 99%

Zero Truncated Bivariate Poisson Model: Marginal-Conditional Modeling Approach with an Application to Traffic Accident Data

Chowdhury¹,

Islam²

2016

View full text Add to dashboard Cite

A new covariate dependent zero-truncated bivariate Poisson model is proposed in this paper employing generalized linear model. A marginal-conditional approach is used to show the bivariate model. The proposed model with estimation procedure and tests for goodness-of-fit and under (or over) dispersion are shown and applied to road safety data. Two correlated outcome variables considered in this study are number of cars involved in an accident and number of casualties for given number of cars.

show abstract

“…The estimates of the regression parameters vectors 1 β and 2 β can be obtained iteratively by using Newton-Raphson method as follows ( ) ( )…”

Section: Zero Truncated Bivariate Poisson (Ztbvp) Modelmentioning

confidence: 99%

Zero Truncated Bivariate Poisson Model: Marginal-Conditional Modeling Approach with an Application to Traffic Accident Data

Chowdhury¹,

Islam²

2016

View full text Add to dashboard Cite

show abstract

“…Thus, in opposite to most of the existing approaches for discrete distributions modelling (e.g. Kocherlakota & Kocherlakota (1992), Johnson et al (1997)), we neither restrict the domain of marginal densities to be nonnegative, nor we preclude negative contemporaneous dependence between them. In the following, we briefly describe the theoretical framework behind the standard MICH approach, where we first present the ICH model for the marginal densities.…”

Section: General Modelling Frameworkmentioning

confidence: 99%

“…Most of the existing approaches (e.g. Kocherlakota & Kocherlakota (1992), Johnson, Kotz & Balakrishnan (1997)) concentrate on the parametric modelling of multivariate discrete distributions with a nonnegative domain and a nonnegative contemporaneous dependency only. Alternatively, Cameron, Li, Trivedi & Zimmer (2004) exploit the concept of copula functions to derive a more flexible form of the bivariate distribution for non-negative count variables that allows for both a positive or a negative dependence between the discrete random variables.…”

Section: Introductionmentioning

confidence: 99%

An Inflated Multivariate Integer Count Hurdle Model: An Application to Bid and Ask Quote Dynamics

2009

View full text Add to dashboard Cite

In this paper we develop a model for the conditional inflated multivariate density of integer count variables with domain Z n . Our modelling framework is based on a copula approach and can be used for a broad set of applications where the primary characteristics of the data are: (i) discrete domain, (ii) the tendency to cluster at certain outcome values and (iii) contemporaneous dependence. These kind of properties can be found for high or ultra-high frequent data describing the trading process on financial markets. We present a straightforward method of sampling from such an inflated multivariate density through the application of an Independence Metropolis-Hastings sampling algorithm. We demonstrate the power of our approach by modelling the conditional bivariate density of bid and ask quote changes in a high frequency setup. We show how to derive the implied conditional discrete density of the bid-ask spread, taking quote clusterings (at multiples of 5 ticks) into account.

show abstract

“…The Holgate distribution appears in reliability theory, actuarial sciences and risk modeling, see for example Barlow and Prochan (1981), and Kocherlakota and Kocherlakota (1992). Let p(j; Â) denote the pdf of a Poisson distribution with mean Â.…”

Section: Holgate Distribution: Testing Independencementioning

confidence: 99%

Bayesian evidence test for precise hypotheses

Madruga

Pereira

Stern

2003

Journal of Statistical Planning and Inference

View full text Add to dashboard Cite

The full Bayesian signiÿcance test (FBST) for precise hypotheses is presented, with some illustrative applications. In the FBST we compute the evidence against the precise hypothesis. We discuss some of the theoretical properties of the FBST, and provide an invariant formulation for coordinate transformations, provided a reference density has been established. This evidence is the probability of the highest relative surprise set, "tangential" to the sub-manifold (of the parameter space) that deÿnes the null hypothesis.

show abstract

Bivariate Discrete Distributions

Cited by 22 publications

References 31 publications

Zero Truncated Bivariate Poisson Model: Marginal-Conditional Modeling Approach with an Application to Traffic Accident Data

Zero Truncated Bivariate Poisson Model: Marginal-Conditional Modeling Approach with an Application to Traffic Accident Data

An Inflated Multivariate Integer Count Hurdle Model: An Application to Bid and Ask Quote Dynamics

Bayesian evidence test for precise hypotheses

Contact Info

Product

Resources

About