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In this paper we consider a set of T repeated measurements on p characteristics on each of n individuals. The n individuals themselves may be divided and randomly assigned to K groups. These data are analyzed using a mixed effect MANOVA model, assuming that the data on an individual have a covariance matrix which is a Kronecker product of two positive definite matrices. Results are illustrated on a data set obtained from experiments with varieties of winter rye.

calculation of the most probable values of frequency constants for data arranged according to equidistant divisions of a scale, in: Proc. Lond. Math. Soc. 29 (1897), 353-380. [10] SKEEL, R.: Roundoff error and the Patriot missile, SIAM News 25 (1992), 11. [11] STAM, A.-COGGER, K. O.: Rounding errors in autoregressive processes, Internat. J. Forecast. 9 (1993), 487-508. [12] TALLIS, G. M.: Approximate maximum likelihood estimates from grouped data, Techno- metrics 9 (1967), 599-606. [13] TRICKER, T.: Effects of rounding data sampled from the exponential distribution, J. Appl


The present work proposes hybridization of Expectation-Maximization (EM) and K-means techniques as an attempt to speed-up the clustering process. Even though both the K-means and EM techniques look into different areas, K-means can be viewed as an approximate way to obtain maximum likelihood estimates for the means. Along with the proposed algorithm for hybridization, the present work also experiments with the Standard EM algorithm. Six different datasets, three of which synthetic datasets, are used for the experiments. Clustering fitness and Sum of Squared Errors (SSE) are computed for measuring the clustering performance. In all the experiments it is observed that the proposed algorithm for hybridization of EM and K-means techniques is consistently taking less execution time with acceptable Clustering Fitness value and less SSE than the standard EM algorithm. It is also observed that the proposed algorithm is producing better clustering results than the Cluster package of Purdue University.


The problem of estimating lifetime distribution parameters under progressively Type-II censoring originated in the context of reliability. But traditionally it is assumed that the available data from this censoring scheme are performed in exact numbers. However, some collected lifetime data might be imprecise and are represented in the form of fuzzy numbers. Thus, it is necessary to generalize classical statistical estimation methods for real numbers to fuzzy numbers. This paper deals with the estimation of lifetime distribution parameters under progressively Type-II censoring scheme when the lifetime observations are reported by means of fuzzy numbers. A new method is proposed to determine the maximum likelihood estimates of the parameters of interest. The methodology is illustrated with two popular models in lifetime analysis, the Rayleigh and Lognormal lifetime distributions.


The nucleotide binding site (NBS) domain sequences were iso­lated from genomic DNA in black bamboo, using the degenerate primer designed according to the conserved motifs of the NBS resistance gene. The expected size of the PCR product was about 700 bp. Among 55 positive clones, the amino acid sequence alignment identified 33 black bamboo resistance gene analogs (RGAs) that contain the NBS conserved motifs. All of the 33 RGAs ORFs were constructed in an NJ (Neighbor-joi­ning) tree, and divided into 10 groups. This analysis demonstrated the diversity of the NBS class RGA in black bamboo. The maximum likelihood estimates of various evolutionary models were analyzed; the result showed that 2 groups with a total of 10 sequences and 12 sites demonstrated statistically significant positive selection. Most of the positive selected sites were not located in the NBS conserved motifs. Two groups of gene conversion events had been discovered, which provide a mate­rial basis and research direction in isolating black bamboo R genes.


This research was undertaken to examine the gender perspective of the technical efficiency of catfish farming in Alimosho Local Government Area of Lagos State. Primary data elicited from a sample size of 70 catfish farmers (38 male and 32 female catfish farmers) were employed in the study. Analysis of the data was done using descriptive statistics and stochastic frontier production function. The maximum likelihood estimates of the stochastic frontier production function revealed that the mean technical efficiency of the male catfish farmers (86%) was higher than that of the female catfish farmers (20%) and this implies that the male and female catfish farmers have the scope of improving their efficiency by 14% and 80%, respectively, through the use of farming practices used by the most efficient male and female catfish farmers. The factors that were significant in influencing the technical efficiency of the female catfish farmers were farming experience and credit while in the case of the male catfish farmers, farming experience significantly influenced their technical efficiency. In the light of the low technical efficiency of the female catfish farmers relative to the male catfish farmers, it was recommended that gender equality infishery training, extension delivery, distribution of resources and access to supportive services should be encouraged in a bid to improve the technical efficiency of the catfish farmers especially that of the female catfish farmers.

References [1] ACHCAR, J. A.-COELHO-BARROS, E.-MAZUCHELI, J.: Cure fraction models using mixture and non-mixture models, Tatra Mt. Math. Publ. 51 (2012), 1-9. [2] BERKSON, J.-GAGE, R.: Survival curve for cancer patients following treatment, J. Amer. Statist. Assoc. 47 (1952), 501-515. [3] BOAG, J. W.: Maximum likelihood estimates of the proportion of patients cured by cancer therapy, J. R. Stat. Soc. Ser. B Stat. Methodol. 11 (1949), 15-44. [4] CHIEN-LIN, S.-ADAM DING, A.-WANG, W.: Analysis of clustered survival data in the presence of cure with the Gompertz

: 19–31. Doi: . Pledger, S.A. 2000. “Unified Maximum Likelihood Estimates for Closed Capture-Recapture Models Using Mixtures.” Biometrics 56: 434–442. Doi: . Stanghellini, E. and P.G. Van der Heijden. 2004. “A Multiple-Record Systems Estimation Method that Takes Observed and Unobserved Heterogeneity into Account.” Biometrics 60: 510–516. Doi: . Sutherland, J.M. 2003. Multi-List Methods in Closed Populations with

-15, Department of Mathematical Modelling, DTU, (revised Oct. 2004). Nørgaard M., Poulsen N., Ravn O., (2000) „New Developments in State Estimation for Nonlinear Systems”, Automatica, 36. Rauch, H. E., Tung, F., Striebel, C. T., (1965) „Maximum likelihood estimates of linear dynamic systems”. AIAA Journal, 3(8):1445–1450. Rogers, R.M. (2007). „Applied Mathematics in Integrated Navigation Systems.” 3rd ed. Blacksburg, VA, USA: American Institute of Aeronautics and Astronautics , Inc. Särkkä, S. (2006) „Recursive Bayesian Inference on Stochastic Differential Equations

computed (overall and according to ward specialties). Univariate and multivariate analyses of association of having any HAI acquired during current hospitalization with selected risk factors studied were performed. Univariate analyses were first performed using the classical method for analyses of 2×k contingency tables and then repeated using logistic regression. Maximum likelihood estimates of odds ratios (ORs) together with 95% CIs and results of likelihood ratio tests for significance were computed. Risk factors that were found to be significantly associated with any