Journal of Advances in Mathematics and Computer Science
In this paper, a new Jarque-Bera type statistic for assessing the multivariate normality of a mul... more 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 simulation studies for different sample sizes and different random vector dimensions. Also, the empirical type-I-error rates and empirical powers of the proposed test were compared with some other well-known competing statistics in the literature. The results obtained showed that the proposed omnibus statistic is a powerful tool for assessing multivariate normality (MVN) of multivariate datasets.
In this paper, a new estimator of the Shannon entropy of a random variable X having a probability... more 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 simulation study at sample sizes 10, 20, and 30. Based on the results, it is recommended as a good estimator of the entropy. Also, the new estimator is applied in goodness-of-fit test to normality. The statistic is affine invariant and consistent and the results show that it is a good statistic for assessing univariate normality of datasets.
This paper aims at obtaining the optimum number of states for a hidden Markov manpower model, whi... more 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 comparison tests on the N hidden Markov manpower models ordered according to their level of parsimony. The illustration shows the usefulness of the procedure in choosing the right number of states for a hidden Markov manpower model to avoid wrong specification of such models. The proposed procedure can be useful in other areas of research, such as in biological, medical and social sciences, where application of hidden Markov model may require the determination of number of hidden states based on unobserved data with latent heterogeneity. The procedure has a straightforward formulation and its application in other areas requires mainly the adaptat...
In this research work we introduce a new sampling design, namely a two-stage cluster sampling, wh... more 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 obtained an unbiased estimator of the population mean and total, as well as the variance of the mean estimator. We calculated the relative efficiency of the new sampling design to the two-stage cluster sampling with simple random sampling in the first stage and ranked set sampling in the second stage. The results demonstrated that the new sampling design is more efficient than the competing design when a significant variation is observed in the first stage units.
Journal of Advances in Mathematics and Computer Science
In this paper, a more robust estimator of the Shannon entropy is applied in place of an earlier e... more 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 those of a competing statistic as well as their power comparisons are obtained through extensive simulation study. The result of the power comparison showed that the statistic can be recommended as a good test for normality especially at small samples and against symmetric alternative distributions.
In recent works in manpower planning interest has been awakened in modelling manpower systems in ... more 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-departmentalized) manpower models. In this paper a multinomial Markov-switching model is formulated for investigating latent heterogeneity in intra-departmental and interdepartmental transitions in departmentalized manpower systems. The model incorporates the mover-mediocre-stayer principle. The use of EM algorithm for estimation of the model parameters and a validity test for assessing the model performance in comparison to the classical Markov manpower model are presented.
Type III beta phosphatidylinositol 4-kinase (PI4KIIIβ) is the only clinically validated drug targ... more 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 the development of new antimalarial drugs by building a PPI4K homology model since there was no available three-dimensional structure of PfPI4K and virtually screened a small library of ~ 22 000 fragments against it. Sixteen compounds from the fragment-based virtual screening (FBVS) were selected based on ≤ − 9.0 kcal/mol binding free energy cut-off value. These were subjected to similarity and sub-structure searching after they had passed PAINS screening and the obtained derivatives showed improved binding affinity for PfPI4K (− 10.00 to − 13.80 kcal/mol). Moreover, binding hypothesis of the top-scoring compound (31) was confirmed in a 100 ...
This paper compares the empirical power performances of eight tests for multivariate normality cl... more 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 sensitive to distributional differences with respect to their power performances than others. Also, some tests are generally more powerful than others. The generally most powerful ones are therefore recommended.
This paper presents an adaptive technique for assessing multivariate normality (MVN). It is shown... more This paper presents an adaptive technique for assessing multivariate normality (MVN). It is shown that the squared L2¬ norm otherwise known as the squared Euclidean distance of a standard d-variate normal distribution is chi-squared distributed with d degrees of freedom. Based on this, an adaptive test for MVN was proposed as the sum of squared differences between the ordered set of the squared normalized L2 norms of the observation vectors and the set of the population pth quantiles from the chi-squared distribution with d degrees of freedom. The critical values of the test were evaluated for different sample sizes and different number of random variables contained in the multivariate data through extensive simulations. For some selected sample sizes and number of random variables, the empirical power of the proposed test was compared with those of some other widely used techniques for assessing multivariate normality. The results showed that the test can be recommended as a good t...
International journal of statistics and applications, 2019
A new technique for testing whether or not a set of data is drawn from an exponential distributio... more 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 empirical type-I-error rates and powers of the proposed test were compared with those of some other well known tests for exponentiality and the result showed that the proposed technique can be recommended as a good test for exponentiality.
In this paper, the equivalence of the sample p th quantile of a distribution and the k th order s... more In this paper, the equivalence of the sample p th quantile of a distribution and the k th 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 k th order statistic to the p th quantile was obtained without proof. Through an extensive Monte Carlo simulation, the extreme as well as the central k th order statistics of five different continuous distributions were obtained at different sample sizes and the asymptotic normality of the order statistics were investigated with the use of the Anderson – Darling (AD) statistic for normality test. The result showed among other things that asymptotic normality holds only for the central order statistics.
A new technique for assessing multivariate normality (MVN) is proposed in this work based on a be... more 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 invariant. The critical values of the test were evaluated for different sample sizes and different random vector dimensions through extensive simulations. For some selected sample sizes and random vector dimensions, the empirical type-I-error rates and powers of the proposed test were compared with those of other already in use tests for MVN. The results showed that the test is a good and competitive tool for testing MVN.
In this paper, 91 different tests for exponentiality are reviewed. Some of the tests are universa... more 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 performanc...
Plasmodium species that cause malaria, a disease responsible for about half a million deaths per ... more 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 effective both in vitro and in vivo. In this work, a small library of ~22 000 fragments was virtually screened using PPI4K homology model to discover potential ligands of the enzyme. 16 virtual hits were selected based on ≤ -9.0 kcal/mol binding energy cut off and were subjected to similarity and substructure searching after they had passed PAINS screening. The derivatives obtained showed improved binding energies, which ranged from -10.00 to -13.80 kcal/mol. Moreover, the topmost ranking compound 31, with interesting drug-like quality was stable within the protein’s binding cavity during the 10 ns molecular dynamics simulation period. In ...
This paper proposes a new goodness-of-fit for the two-parameter distribution. It is based on a fu... more 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 the unit-scaled gamma distributions and computations. The empirical powers of the statistic are obtained and compared with some well-known tests for the gamma distribution, and the results show that the proposed statistic can be recommended as a test for the gamma distribution.
Journal of Advances in Mathematics and Computer Science
In this paper, a new Jarque-Bera type statistic for assessing the multivariate normality of a mul... more 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 simulation studies for different sample sizes and different random vector dimensions. Also, the empirical type-I-error rates and empirical powers of the proposed test were compared with some other well-known competing statistics in the literature. The results obtained showed that the proposed omnibus statistic is a powerful tool for assessing multivariate normality (MVN) of multivariate datasets.
In this paper, a new estimator of the Shannon entropy of a random variable X having a probability... more 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 simulation study at sample sizes 10, 20, and 30. Based on the results, it is recommended as a good estimator of the entropy. Also, the new estimator is applied in goodness-of-fit test to normality. The statistic is affine invariant and consistent and the results show that it is a good statistic for assessing univariate normality of datasets.
This paper aims at obtaining the optimum number of states for a hidden Markov manpower model, whi... more 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 comparison tests on the N hidden Markov manpower models ordered according to their level of parsimony. The illustration shows the usefulness of the procedure in choosing the right number of states for a hidden Markov manpower model to avoid wrong specification of such models. The proposed procedure can be useful in other areas of research, such as in biological, medical and social sciences, where application of hidden Markov model may require the determination of number of hidden states based on unobserved data with latent heterogeneity. The procedure has a straightforward formulation and its application in other areas requires mainly the adaptat...
In this research work we introduce a new sampling design, namely a two-stage cluster sampling, wh... more 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 obtained an unbiased estimator of the population mean and total, as well as the variance of the mean estimator. We calculated the relative efficiency of the new sampling design to the two-stage cluster sampling with simple random sampling in the first stage and ranked set sampling in the second stage. The results demonstrated that the new sampling design is more efficient than the competing design when a significant variation is observed in the first stage units.
Journal of Advances in Mathematics and Computer Science
In this paper, a more robust estimator of the Shannon entropy is applied in place of an earlier e... more 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 those of a competing statistic as well as their power comparisons are obtained through extensive simulation study. The result of the power comparison showed that the statistic can be recommended as a good test for normality especially at small samples and against symmetric alternative distributions.
In recent works in manpower planning interest has been awakened in modelling manpower systems in ... more 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-departmentalized) manpower models. In this paper a multinomial Markov-switching model is formulated for investigating latent heterogeneity in intra-departmental and interdepartmental transitions in departmentalized manpower systems. The model incorporates the mover-mediocre-stayer principle. The use of EM algorithm for estimation of the model parameters and a validity test for assessing the model performance in comparison to the classical Markov manpower model are presented.
Type III beta phosphatidylinositol 4-kinase (PI4KIIIβ) is the only clinically validated drug targ... more 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 the development of new antimalarial drugs by building a PPI4K homology model since there was no available three-dimensional structure of PfPI4K and virtually screened a small library of ~ 22 000 fragments against it. Sixteen compounds from the fragment-based virtual screening (FBVS) were selected based on ≤ − 9.0 kcal/mol binding free energy cut-off value. These were subjected to similarity and sub-structure searching after they had passed PAINS screening and the obtained derivatives showed improved binding affinity for PfPI4K (− 10.00 to − 13.80 kcal/mol). Moreover, binding hypothesis of the top-scoring compound (31) was confirmed in a 100 ...
This paper compares the empirical power performances of eight tests for multivariate normality cl... more 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 sensitive to distributional differences with respect to their power performances than others. Also, some tests are generally more powerful than others. The generally most powerful ones are therefore recommended.
This paper presents an adaptive technique for assessing multivariate normality (MVN). It is shown... more This paper presents an adaptive technique for assessing multivariate normality (MVN). It is shown that the squared L2¬ norm otherwise known as the squared Euclidean distance of a standard d-variate normal distribution is chi-squared distributed with d degrees of freedom. Based on this, an adaptive test for MVN was proposed as the sum of squared differences between the ordered set of the squared normalized L2 norms of the observation vectors and the set of the population pth quantiles from the chi-squared distribution with d degrees of freedom. The critical values of the test were evaluated for different sample sizes and different number of random variables contained in the multivariate data through extensive simulations. For some selected sample sizes and number of random variables, the empirical power of the proposed test was compared with those of some other widely used techniques for assessing multivariate normality. The results showed that the test can be recommended as a good t...
International journal of statistics and applications, 2019
A new technique for testing whether or not a set of data is drawn from an exponential distributio... more 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 empirical type-I-error rates and powers of the proposed test were compared with those of some other well known tests for exponentiality and the result showed that the proposed technique can be recommended as a good test for exponentiality.
In this paper, the equivalence of the sample p th quantile of a distribution and the k th order s... more In this paper, the equivalence of the sample p th quantile of a distribution and the k th 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 k th order statistic to the p th quantile was obtained without proof. Through an extensive Monte Carlo simulation, the extreme as well as the central k th order statistics of five different continuous distributions were obtained at different sample sizes and the asymptotic normality of the order statistics were investigated with the use of the Anderson – Darling (AD) statistic for normality test. The result showed among other things that asymptotic normality holds only for the central order statistics.
A new technique for assessing multivariate normality (MVN) is proposed in this work based on a be... more 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 invariant. The critical values of the test were evaluated for different sample sizes and different random vector dimensions through extensive simulations. For some selected sample sizes and random vector dimensions, the empirical type-I-error rates and powers of the proposed test were compared with those of other already in use tests for MVN. The results showed that the test is a good and competitive tool for testing MVN.
In this paper, 91 different tests for exponentiality are reviewed. Some of the tests are universa... more 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 performanc...
Plasmodium species that cause malaria, a disease responsible for about half a million deaths per ... more 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 effective both in vitro and in vivo. In this work, a small library of ~22 000 fragments was virtually screened using PPI4K homology model to discover potential ligands of the enzyme. 16 virtual hits were selected based on ≤ -9.0 kcal/mol binding energy cut off and were subjected to similarity and substructure searching after they had passed PAINS screening. The derivatives obtained showed improved binding energies, which ranged from -10.00 to -13.80 kcal/mol. Moreover, the topmost ranking compound 31, with interesting drug-like quality was stable within the protein’s binding cavity during the 10 ns molecular dynamics simulation period. In ...
This paper proposes a new goodness-of-fit for the two-parameter distribution. It is based on a fu... more 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 the unit-scaled gamma distributions and computations. The empirical powers of the statistic are obtained and compared with some well-known tests for the gamma distribution, and the results show that the proposed statistic can be recommended as a test for the gamma distribution.
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Papers by Mbanefo Madukaife