A COMPARISON BETWEEN MAXIMUM LIKELIHOOD RULE AND LOGISTIC DISCRIMINANT ANALYSIS IN THE CLASSIFICATION OF MIXTURE OF DISCRETE AND CONTINOUS VARIABLES

An optimal measure of performance is the one that lead to maximization of average error rate or probability of misclassification. This paper aimed to compare between the maximum likelihood rule and logistic discriminant analysis in the classification of mixture of discrete and continuous variables. The efficiency of the methods was tested using simulated and real dataset. The result obtained showed that the maximum likelihood rule performed better than the logistic discriminant analyses, in maximizing the average error rate in both experiment conducted. Keyword: Maximum likelihood rule, Logistic discriminants, error rate, Likelihood ratio, Discriminant analysis

A Review of the Limitations of Some Discriminant Analysis Procedures in Multi-Group Classification.

A review is given on existing work and result of the performance of some discriminant analysis procedures under varying conditions. Few of the developed methods (Fisher’s Linear Discriminant Function, Logistic Regression and Quadratic discriminant function) were reviewed. Some new results are presented for the case involving allocation with more than two groups. Shortfalls in the reviewed procedures necessitated the need for an improved procedure that can classify observations into multiple groups with high efficiency (minimal error rate). Keywords: Multivariate, Discrimnant function, Classification, Multi-groups, Optimal

EVALUATION OF THREE CLASSIFICATION RULES FOR MIXTURE OF DISCRETE AND CONTINOUS VARIABLES

The best classification rule is the one that leads to the smallest probability of misclassification which is called the error rate. This work focused on three classification rules for mixture of discrete and continuous variables with the aim to evaluate the performance of these rules to in classification of individuals into several categories. Applications were done using simulated data and real life data. The result obtained revealed that the location model achieved better result than the other two rules in minimizing the average error rate in both datasets. Keyword: Location Model, Linear Discriminant Models, Quadratic, Discriminant Model, Error Rate

On single server batch arrival queueing system with balking, three types of heterogeneous service and Bernoulli schedule server vacation

This paper investigates a batch arrival queueing system in which customers arrives at the system in a Poisson stream following a compound Poisson process and the system has a single server providing three types of general heterogeneous services. At the beginning of each service, a customer is allowed to choose any one of the three services and as soon as a service of any type gets completed, the server may take a vacation or may continue staying in the system. The vacation time is assumed to follow a general (arbitrary) distribution and the server vacation is based on Bernoulli schedule under a single vacation policy. During the server vacation period, impatient customers are assumed to balk. This paper described the model as a bivariate Markov chain and employed the supplementary variable technique to find closed-form solutions of the steady state probability generating function of number of customers, the steady state probabilities of various states of the system, the average queue size, the average system size, and the average waiting time in the queue as well as the average waiting time in the system. Further, some interesting special cases of the model are also derived. Keywords Batch Arrivals. Queueing System. Balking. Heterogeneous types of Service. Bernoulli schedule server vacation. Bivariate Markov Processes. MSC2020-Mathematics Subject Classification 34B07, 60G05, 62E1

A Generalized Multi-Group Discriminant Function Procedure for Classification: an Application To Ten Groups Of Yam Species

Multivariate Analysis (MVA) is based on the Statistical principle of Multivariate Statistics which involves observation and analysis of more than one Statistical outcome variables at a time. Classification in Multivariate analysis deals with developing a statistical rule for allocating observation to one or more groups. A closely associated multivariate technique is discriminant analysis which predicts group membership for an observation. Fishers (1936) developed a technique (Fishers Linear Discriminant Function) that optimally discriminate only two groups. The challenges of developing a mathematical based procedure with some underlying distribution for multiple groups have remained a task to be accomplished as it only exist in theory but not in practice. Owing to these challenges, this work introduces and suggests a mathematical procedure that is based on combinatorial analysis which gave rise to All Possible Pair of functions and allocation rules for a multiple group case. The developed procedure was generalized and applied to both real and simulated data. The developed procedure gave a higher accuracy rate for the real and simulated data under various sample sizes when compared with other conventional methods. It is therefore recommended that the All Possible Pair procedure could be a better approach in situations of any multivariate data structure. Key Words: Discriminant, Function, Classification, combination, Accuracy Rate.

Multivariate Rank Discriminant Classifier of Small Sample

This article studied discriminant analysis procedure that is based on multivariate ranking with emphasis on Spatial or L1 depth classifier using Eviews and SPSS computer packages. The performance of the classifier is assessed using both simulated and real life data. The result of the study revealed that the classifier is optimal in classifying observations into one of the two pre-defined groups

Exponentiated Inverse Power Pranav distribution: Properties and Application

In this article, we proposed a new distribution known as the Exponentiated Inverse Power Pranav distribution for modeling lifetime data sets with monotone and non-monotone shapes in their hazard rates. Along with some of the basic properties, we however, studied the maximum likelihood estimation of the parameters of the proposed distribution. The model was subjected to life application with a dataset and compared to other sub-models. The new distribution was found to have a best fit more than the competing sub-models. Keywords: Pranav distribution, Inverse Power Pranav distribution, Exponentiated distributions, Maximum Likelihood estimation, Exponentiated Inverse Power Pranav distributio

Method of Principal Component Factors Estimation of Optimal Number of Factors: An Information Criteria Approach

Abstract This paper try to x-ray the number of factors (k) to be retained in a factor analysis for different sample sizes using the method of Principal Component Factor estimation when the number of variables are ten (10). Stimulated data were used for ample sizes of 30,50 and 70 and the Akaike Information Criterion (AIC), the Schwarz Information Criterion (SIC) and the Hannan Quinne Information Criterion (HQIC) values were obtained when the number of factors(k) are two, three, and five (2,3 and 5). It was discovered that the optimal number of factors to retain using the method of Principal Component Factors method of estimation is two (2) from all the sample sizes and also for all the methods considered except for the AIC in which the best is when k=3 follows by k=2 and k=5 respectively of sample thirty (30). Hence, conclusion is drawn that for the three sample sizes considered, the optimal number of factors to retain is 2