Models for Count Data in the Presence of Outliers and/or Excess Zero

Violations of Poisson assumptions usually result in overdispersion, where the variance of the model exceeds the value of the mean. Excess or (deficiency) of zero counts result in overdispersion. Violations of equidispersion indicate correlation in the data, which affect standard errors of the parameter estimates. Model fit is also affected. (Hilbe 2008). Therefore, this study examined the impact of outliers and excess zero on count data in causing overdispersion. The study focus on identifying model(s) which can handle the impact of outliers and excess zero in count data. Datasets based on Poisson model were simulated for sample sizes 20, 50 and 100 and incorporated with outliers and excess zero. Maximum likelihood estimation method was employed in estimating the parameters. Model selection is based on dispersion index, AIC, BIC and log likelihood statistics, putting into consideration Poisson, Negative Binomial, Zero Inflated Poisson and Zero Inflated Negative Binomial models and results obtained indicates that ZINB is the best models for analyzing count data in the presence of outliers and/or excess zero. Keywords: Count data, Overdispersion, Excess zero, outliers, Goodness of fit, Poisson, Negative Binomial and Zero inflated model

Modelling The Dynamic Relationship Between Rainfall and Temperature Time Series Data In Niger State, Nigeria.

Vector Autoregression (VAR) has some very attractive features and has provided a valuable tool for analysing dynamics among time series processes. This paper examined the dynamic relationship between rainfall and temperature time series data in Niger State, Nigeria, collected from the Meteorological station, NCRI, Badeggi, Niger State, Nigeria which spanned from January 1981 to December 2010. The VAR model favoured VAR at lag 8 which indicated bi-directional causation from rainfall to temperature and from temperature to rainfall. The Impulse Response Functions and the Forecast Error Variance Decomposition were further used to interpret the VAR model. We concluded that modelling rainfall and temperature together in Niger State will further improved the forecast of rainfall and temperature respectively. Keywords: Rainfall; Temperature; Modelling; Meteorological data; Time series; Vector Autoregression (VAR)

Development of a Test Statistic for Testing Equality of Two Means under Unequal Population Variances

In this paper, we propose a test statistic for testing equality of two independent sample means for unequal variances. When group variances differ, the pooled sample variance (  ) is inadequate as a single value for the variances. This problem is commonly known as the Behrens – Fisher problem. Instead, the sample harmonic mean of variances (  ) is proposed, examined and found to better represent the unequal variances. The distribution of  which is known to be generalized Beta is further approximated by the chi – square distribution with the degrees of freedom related to that of degrees of freedom of the chi – square distribution of   . Consequently, it is used to replace the pooled sample variance in the resulting proposed t – test. An example of application is provided. Keywords: Harmonic mean of variances, chi- square distribution, modified t – test statisti

On Hypothesis Testing Under Unequal Group Variances: The Use of the Harmonic Variance

The assumptions of equality of group variances required for ANOVA often fail for real life data. However, because the major aim is to test equality of group means, a single summary value for these group variances is a necessity. Previous works in literature have zeroed in on the choice of either the Harmonic or Geometric mean as a proper mean especially when extreme observation(s) are present which renders a simple mean inappropriate. In this work, the asymptotic sample distribution of harmonic mean of group variances is established to be a chi- square distribution though the degrees of freedom need not be an integer. Keywords:  Harmonic mean of group variances, three - parameter Beta distribution, chi – square distribution

Peddlers and Non-Drug Peddlers. The following

National Drug and Enforcement Agency has been using oral evidence in the past rather than a statistical tool to classify drug offenders into Drug Peddlers and Non-Drug Peddlers.The aim of this research is to construct a Discriminant Function that can be used to classify persons for drug related offences into two groups namely: Dru

Modeling fertility curves in Africa

The modeling of fertility patterns is an essential method researchers use to understand world-wide population patterns. Various types of fertility models have been reported in the literature to capture the patterns specific to developed countries. While much effort has been put into reducing fertility rates in Africa, models which describe the fertility patterns have not been adequately described. This article presents a flexible parametric model that can adequately capture the varying patterns of the age-specific fertility curves of African countries. The model has parameters that are interpretable in terms of demographic indices. The performance of this model was compared with other commonly used models and Akaike's Information Criterion was used for selecting the model with best fit. The presented model was able to reproduce the empirical fertility data of 11 out of 15 countries better than the other models considered