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Errors of misclassification and their probabilities are studied for classification problems associated with univariate Nelly distribution. The effect of applying the linear discriminant function (LDF) based on normality to Nelly populations are assessed by comparing probability (Optimum) based on the linear discriminant function (LDF) with those based on the likelihood ratio rule (LR) for the Nelly. Both theoretical and empirical results are presented

This work estimated the standard error of the maximum likelihood estimator (MLE) and the robust estimators of the exponential mixture parameter (θ) using the influence function and the bootstrap approaches. Mixture exponential random samples of sizes 10, 15, 20, 25, 50, and 100 were generated using 3 mixture exponential models at 2%, 5% and 10% contamination levels. The selected estimators namely: mean, median, alpha-trimmed mean, Huber M-estimate and their standard errors (Tn ) were estimated using the two approaches at the indicated sample sizes and contamination levels. The results were compared using the coefficient of variation, confidence interval and the asymptotic relative efficiency of Tn in order to find out which approach yields the more reliable, precise and efficient estimate of Tn. The results of the analysis show that the two approaches do not equally perform at all conditions. From the results, the bootstrap method was found to be more reliable and efficient method of estimating the standard error of the arithmetic mean at all sample sizes and contamination levels. In estimating the standard error of the median, the influence function method was found to be more effective especially when the sample size is small and yet contamination is high. The influence function based approach yielded more reliable, precise and efficient estimates of the standard errors of the alpha-trimmed mean and the Huber M-estimate for all sample sizes and levels of contamination although the reliability of the bootstrap method improved better as sample size increased to 50 and above. All simulations and analysis were carried out in R programming language.

The generalization of probability distributions in view of improving their flexibility in capturing the shape and tail behavior of disparate data sets has become one of the most active aspects of statistical research. We developed a new Pareto distribution by using Kumaraswamy method which gave rise to a new distribution called Kumaraswamy Pareto distribution. This method is called transmutation. The mathematical properties of the new generalized distribution was presented using quartiles, moments, entropy, order statistics mean deviation and maximum likelihood method of parameter estimation. The new generalized distribution was applied to a real life data on the exceedances of flood peaks (in m3/s) where it was observed to be superior to its sub models in terms of some goodness-of-fit test such as log likelihood criterion, Akaike Information Criterion (AIC) and Kolmogorov-Smirnov (K-S) measures.

This paper focuses on the robust classification procedures in two group discriminant analysis with multivariate binary variables. A normal distribution based data set is generated using the R-software statistical analysis system 2.15.3 using Barlett’s approximation to chi-square, the data set was found to be homogenous and was subjected to five linear classifiers namely: maximum likelihood discriminant function, fisher’s linear discriminant function, likelihood ratio function, full multinomial function and nearest neighbour function rule. To judge the performance of these procedures, the apparent error rates for each procedure are obtained for different sample sizes. The results obtained ranked the procedures as follows: fisher’s linear discriminant function, maximum likelihood, full multinomial, likelihood function and nearest neigbour function.