Mbanefo Madukaife

• Ph.D Statistics
• Professor (Associate) at University of Nigeria

The adequacy of an experimental design can be determined from the information matrix. The D-optimality criterion is based on the determinant of the information matrix M(ξ) (ξ is any design measure) of a design, that is it maximizes the determinant of the information matrix M(ξ) or, equivalently, minimizes the determinant of inverse of the informati...

In this paper, a probability plots class of tests for multivariate normality is introduced. Based on independent standardized principal components of a d-variate normal data set, we obtained the sum of squared differences between corresponding observations of an ordered set of each principal component observations and the set of the population pth...

The behaviour of empirical critical values in asymptotic tests for exponentiality with respect to their protection against errors of type – I and type – II when approximated by exact theoretical values is discussed. Three tests for exponentiality whose statistics are normally distributed are arbitrarily selected for the study. Each of the tests is...

A new technique for assessing multivariate normality (MVN) is proposed in this work based on a beta transform of the multivariate normal data set. The statistic is the sum of interpoint squared distances between an ordered set of the transformed observations and the set of the beta population pth quantiles. We showed that the statistic is affine in...

In this research work, a total of 45 different estimators of the Shannon differential entropy were reviewed. The estimators were mainly based on three classes, namely: window size spacings, kernel density estimation (KDE) and k-nearest neighbour (kNN) estimation. A total of 16, 5 and 6 estimators were selected from each of the classes, respectively...

Current procedures for estimating the parameters of [Formula: see text]th order vector autoregressive (VAR [Formula: see text]) model are usually based on assuming that the ensuing error distribution is multivariate normal. But there exists large body of evidence that several data encountered in real life are skewed; thereby making estimators deriv...

A monte Carlo comparison of normality tests based on entropy estimators Mbanefo S Madukaife Abstract In this paper, seven tests for normality of datasets that are based on entropy estimators are presented. The type-I-error rates and the powers of the statistics are compared through extensive simulation studies at a sample size of n = 10. The altern...

In this paper, a new Jarque-Bera type statistic for assessing the multivariate normality of a multivariate datasets is obtained. The affine-invariant and consistent statistic is shown to follow, asymptotically, a chi-square distribution with 2 degrees of freedom. The critical values of the test were evaluated empirically through extensive simulatio...

In this paper, a new estimator of the Shannon entropy of a random variable X having a probability density function \(\mathit{f}\)(\(\mathit{x}\)) is obtained based on window size spacings. Under the standard normal, standard exponential and uniform distributions, the estimator is shown to have relative low bias and low RMSE through extensive simula...

In this paper, extended Markov manpower models are formulated by incorporating a new class of members of a departmentalized manpower system in a homogeneous Markov manpower model. The new class, called limbo class, admits members of the system who exit to a limbo state for possible re-engagement in the active class. This results to two channels of...

In this paper, a more robust estimator of the Shannon entropy is applied in place of an earlier estimator, to obtain an improved goodness-of-fit test to normality which is based on the Balakrishnan-Sanghvi measure of divergence. The statistic is affine invariant and consistent against fixed alternatives. The critical values of the new statistic and...

This paper aims at obtaining the optimum number of states for a hidden Markov manpower model, which, hitherto, has been chosen arbitrarily. A search procedure that attains this optimum number after a few steps across a series of N hidden Markov manpower models is proposed. The likelihood ratio statistic is employed to conduct pairwise model compari...

In recent works in manpower planning interest has been awakened in modelling manpower systems in departmentalized framework. This, as a form of disaggregation, may solve the problem of observable heterogeneity but not latent heterogeneity; it rather opens up other aspects of latent heterogeneity hitherto unaccounted for in classical (non-department...

In this research work we introduce a new sampling design, namely a two-stage cluster sampling, where probability proportional to size with replacement is used in the first stage unit and ranked set sampling in the second in order to address the issue of marked variability in the sizes of population units concerned with first stage sampling. We obta...

Type III beta phosphatidylinositol 4-kinase (PI4KIIIβ) is the only clinically validated drug target in Plasmodium kinases and therefore a critical target in developing novel drugs for malaria. Current PI4KIIIβ inhibitors have solubility and off-target problems. Here we set out to identify new Plasmodium PI4K ligands that could serve as leads for th...

This paper proposes a new goodness-of-fit for the two-parameter distribution. It is based on a function of squared distances between empirical and theoretical quantiles of a set of observations being hypothesized to have come from the gamma distribution. The critical values of the proposed statistic are evaluated through extensive simulations of th...

Different estimators of the Shannon's measure of entropy of absolutely continuous distributions based on spacings have been proposed in the literature. It has also been noted that the performance of these estimators is dependent on the window size (: / 2, where is the sample size) m m n n ≤. In this paper, three different estimators are studied. A...

This paper compares the empirical power performances of eight tests for multivariate normality classified under Baringhaus-Henze-Epps-Pulley (BHEP) class of tests. The tests are compared under eight different alternative distributions. The result shows that the eight statistics have good control over type-I-error. Also, some tests are more sensitiv...

Plasmodium species that cause malaria, a disease responsible for about half a million deaths per annum despite concerted efforts to combat it. The causative agent depends on type III beta phosphatidylinositol 4-kinase (PPI4K) during the development of merozoite. PPI4K is the only clinically validated Plasmodium kinase so far and its inhibitors are...

In this paper, 91 different tests for exponentiality are reviewed. Some of the tests are universally consistent while others are against some special classes of life distributions. Power performances of 40 of these different tests for exponentiality of datasets are compared through extensive Monte Carlo simulations. The comparisons are conducted fo...

A new technique for testing whether or not a set of data is drawn from an exponential distribution is proposed in this paper. It is based on the equivalence property between kth order statistic and the pth quantile of a distribution. The critical values of the test were evaluated for different sample sizes through extensive simulations. The empiric...

In this paper, the equivalence of the sample pth quantile of a distribution and the kth order statistic of a random sample obtained from the distribution is reviewed. Based on the review, a new corollary on the almost sure convergence of the kth order statistic to the pth quantile was obtained without proof. Through an extensive Monte Carlo simulat...

Based on a chi square transform of the multivariate normal data set, we proposed a technique for testing multinormality which is the sum of interpoint squared distances between an ordered set of the transformed observations and the set of the population pth quantiles of the chi squared distribution. The critical values of the test were evaluated fo...

The book, principles of applied statistics, revised edition, covers almost every aspect of fundamentals of statistical theory. It begins with various methods of data description and presentation such as tabular and graphical presentations of data as well as various measures of location and variation. It continues with various aspects of elementary...

ABSTRACT In the search for a D-optimal exact design using the combinatorial iterative technique introduced by Onukogu and Iwundu, 2008, all the support points that make up the experimental region are grouped into H concentric balls according to their distances from the centre. Any selection of N support points from the balls defines a class of desi...