A Binomial Distribution With Dependent Trials And Its Use in Stochastic Model Evaluation

A model of Markov dependent trials is considered that leads to a generalization of the binomial distribution in the context of evaluating models of a time series by exploiting the sequential nature of model-based predictions. Adopting an evaluation method similar in nature to that suggested by Xekalaki & Katti (1984), the behaviour of the model is assigned a score that reflects the concordance or discordance of predicted and observed values for each of a sequence of points in time. The resulting series of scores leads to a final rating which is considered as a measure of the predictive ability of the model. The Markov dependent distribution is used to develop exact theory for the construction of confidence intervals and for testing hypotheses pertaining to the forecasting protential of a model. Some asymptotic theory is also developed.Model evaluation, Model validation, Dependent Bernouli trials, Forecasting models

A Predictive Model Evaluation and Selection Approach - The Correlated Gamma Ratio Distribution

In this paper, an evaluation method is suggested for selecting one of two competing models based on certain predictive ability ratings. The main focus is on the case of linear models that are not necessarily nested. In the context of such models, the test procedure is based on a sample statistic whose distribution is shown to arise as the distribution of the ratio of two correlated gamma variables termed as the Correlated Gamma Ration Distribution. Percentage points of this distribution are obtained. The procedure is illustrated on real data.Model selection, Bivariate gamma distribution, F distribution, Correlated gamma-ratio distribution, Predictive ability

On a Distribution Arising in the Context of Comparative Model Performance Evaluation Problems

The paper deals with a distribution that arises as the distribution of a sample statistic used to compare the predictive ability of two competing linear models. It is defined as the distribution of the ratio of two correlated gamma variables and its probabilities are tabulated in order that they become readily available for practical useModel selection, Bivariate gamma distribution, F distribution

Identifiability of Compound Poisson Distributions

Compound Poisson distributions (CPD's) are frequently used as alternatives in studying situations where a simple Poisson model is found inadequate to describe. In this paper an attempt is made to identify compound Poisson distributions when it is known that the conditional distribution of two random variables (r.v.'s) is compound binomial. Some interesting special cases and their application to accident theory are discussed

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 limiting form of the obtained generalized negative binomial distributionCluster negative binomial distribution, Generalized Poisson distribution, Sluttering generalized Waring distribution, Cluster logarithmic series distribution

The Stuttering Generalized Waring Distribution

The stuttering generalized Waring distribution is introduced and shown to arise through two urn genesis schemes. Its probability generating function and moments are derived and some potential applications are discussedgeneralized Waring distribution, compound Poisson distribution, urn model

Identifiability of Compound Poisson Distributions

Compound Poisson distributions (CPD's) are frequently used as alternatives in studying situations where a simple Poisson model is found inadequate to describe. In this paper an attempt is made to identify compound Poisson distributions when it is known that the conditional distribution of two random variables (r.v.'s) is compound binomial. Some interesting special cases and their application to accident theory are discussed.

Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review

Autoregressive Conditional Heteroscedasticity (ARCH) models have successfully been employed in order to predict asset return volatility. Predicting volatility is of great importance in pricing financial derivatives, selecting portfolios, measuring and managing investment risk more accurately. In this paper, a number of univariate and multivariate ARCH models, their estimating methods and the characteristics of financial time series, which are captured by volatility models, are presented. The number of possible conditional volatility formulations is vast. Therefore, a systematic presentation of the models that have been considered in the ARCH literature can be useful in guiding one’s choice of a model for exploiting future volatility, with applications in financial markets