iosr-Jm   Volume-13 ~ Issue-3 ~ May-June 2017

Abstract: The aim of this paper is to discuss on Transport of O2 in a Red Blood Cell involving A-function

[1] Forester, R. E.: Rate of Gas uptake by Red cells, Chapter 32 in Handbook of Physiology, Section 3, Respiration 1 (W. O. Fenn and H. Rohneds) Am. Physiol. Soc. Washington D. C., (1964 b).
[2] Gautam, G. P. and Goyal, A. N.:On Fourier Kernels and Asymptotic Expansion, Ind. J. Pure and Appl. Math. ,1981, 12(9), 1094-1105.
[3] Kutchai, H.: Numerical study of oxygen uptake by layers of hemoglobin solution, Respir, physiol. 10 273 (1970).
[4] Luke, Y. L.: The Special Functions and their Approximations, Vol.II, Academic Press, New York (1969).
[5] Moll W.: The influence of hemoglobin diffusion on oxygen uptake and releaseby red cells, respire Physiol, 6 1 (1968)..

Abstract: Decades after its discussion in (Koenker and Bassett, 1978), quantile regression (QR) has been the topic of great practical applications in many areas: economics, ecology, biology and so on. In this paper, we present Bayesian quantile regression using two level prior distributions. Specifically, we assume that the prior distribution of each regression coefficient is a zero mean normal prior distribution with unknown variance. Then, we assign noninformative Jeffreys prior distributions for the variances assuming they are independent. A Gibbs sampler algorithm is developed for the posterior inference. The new method is illustrated via simulations and a real dataset..

Keywords: Bayesian, Jeffreys prior, Noninformative, MCMC.

[1] Alhamzawi, R. (2014). Bayesian elastic net tobit quantile regression. Communications in Statistics-Simulation and Computation (just-accepted), 00-00.
[2] Alhamzawi, R. (2015). Model selection in quantile regression models. Journal of Applied Statistics 42 (2), 445-458.
[3] Alhamzawi, R. (2017). Brq: Bayesian Analysis of Quantile Regression Models. R package version 2.0.
[4] Alhamzawi, R. and H. T. M. Ali (2017). Bayesian quantile regression for ordinal longitudinal data. Journal of Applied Statistics, 1-14.
[5] Alhamzawi, R. and K. Yu (2013). Conjugate priors and variable selection for bayesian quantile regression. Computational Statistics & Data Analysis 64, 209-219..

Abstract: In this paper, we prove some common fixed point results for pair of rational type of contractive mappings in the setting of complex valued b-metric spaces. Our results extend, generalize and improve the corresponding results of A. K .Dubey' [48].

Keywords: Complex valued b-metric space; common fixed point; Rational expression type of contractive mappings.

[1] R. Kannan, some results on Fixed Points, Bull. Calcutta math. Soc; 60,(1968),71-76.
[2] A. Azam ,B.Fisher and m.khan, common fixed point theorem in complex valued metric space, Numerical complex Analysis & Optimization 32(3)(2011),243-253.
[3] B.K. Dass and S. Gupta, An extension of Banach contraction principle through rational expressions, Indian J. Pure Appl. Math. 6(1975),1455-1458
[4] S. Banach, Sur les operation dans les ensembles abstraits et leur application aux equations integrals, Fundamental mathematics 3(1922), 133-181.
[5] S. Bhatt, S. Chaukiyal and R. Dimri, Common fixed point of mappings satisfying rational inequality in complex valued metric spaces, International Journal of Pure and Applied Mathematics 73 (2) (2011),159-164.

Abstract: Gamma regression is a member of generalized liner models and often used when the phenomenon under study is skewed and the mean is proportional to the standard deviation. It can find applications in several areas such as life-testing problems, forecasting cancer incidences, weather extremes and quality control. Also it is a natural candidate when modeling the variance and it has been increasingly used over the past decade. paper attempts to introduce readers with the concept of the gamma regression model, in which the dependent variable has the gamma distribution, and the use of the paired bootstrapping resampling associated with the"boot" package in R program. Three confidence intervals were computed.

Keywords: Gamma distribution, gamma regression, paired bootstrapping, confidence intervals.

[1] Carroll, R., J., Ruppert, D., Stefanski, L., A., and Crainiceanu, C., M.,(2006),"Measurement Error in Nonlinear Models, A Modern
Prespective", 2nd ed., Chapman & Hall/CRC, Florida.
[2] Davison, A., D. and Kuonen, D.,(2002), " An Introduction to Bootstrap with Applications in R", Statistical computing & Statistical
Graphics Newsletter, Vol.13, No.1, pp.6-11.
[3] Efron, B. (1979) "Bootstrap Methods: Another look at Jackknife", Annals of Statistics,Vol.7, pp.1-26.
[4] Efron, B. and Tibshirani, R., (1993), "An introduction to the bootstrap", Chapman and Hall , New York.
[5] Everitt, B., S. and Hothorm, T., (2010), " A Handbook of Statistical Analysis Using R", 2nd ed., Chapman & Hall/CRC, Florida.

Abstract: Plants, animals and humans live in close association with microbial organisms. Increasingly, biologists have come to appreciate that microbes make up an important part of an organism's phenotype. This microbial community contains a unique complexity that makes it difficult to study their diversity. However, for many questions on the structure of the microbial community one only needs to know the relative order of diversity among samples rather than the total diversity. Unfortunately the culture of microorganisms can be complex but this has prompted the development of new scientific methodologies for their study. One of these methodologies is metagenomics. An important problem in metagenomics is measuring the dissimilarity between distributions of features, such as taxons or groups...........

Keywords: Multivariate methods, applied statistical methods, data analysis, multidimensional scaling, metagenomics, cluster, biology, microbiology, metrical distances

[1] Pollan, M. (2013). Some of My Best Friends Are Germs. New York Time magazine. (Retrieved May 03, 2016, from http://www.nytimes.com/2013/05/19/magazine/say-hello-to-the-100-trillion-bacteria-that-make-up-your-microbiome.html?_r=1)
[2] Handelsman J. 2004. Metagenomics: Application of Genomics to Uncultured Microorganisms Microbiology and Molecular Biology Review 68(4): 669–685.
[3] Rodríguez CI, Monleón-Getino T. 2016. A new R library for discriminating groups based on abundance profile and biodiversity in microbiome metagenomic matrices. Article in International Journal of Scientific and Engineering Research 7(10):243-253
[4] Wikipedia (a), 2016. Metagenomics. (From https://en.wikipedia.org/wiki/Metagenomics )
[5] Holmes I, Harris K, Quince C (2012) Dirichlet Multinomial Mixtures: Generative Models for Microbial Metagenomics. PLoS ONE 7(2):

Abstract: In the presence of outliers least square estimation is insufficient and can be biased. Adaptive estimation is robust estimation that can be used to improve the accuracy of the estimate by reducing the influence of outliers. Adaptive estimators can be effective in achieving low mean squared error for a variety of non normal distributions of errors. M estimation is the extension of the maximum likelihood estimation and is also a robust estimation. In this paper, comparison is made between OLS Estimation, Adaptive estimation and M estimation under a particular situation (An example).

Keywords: OLS estimation, Adaptive estimation, M estimation, Robust regression,.

[1] Badan Pusat Statistik, Production of Paddy Maize and Soybeans, www.bps.go.id/release/Production of Paddy Maize and Soybeans, 2012.
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[3] Chen,C., Robust Regression and Outlier Detection with the ROBUSTREG Procedure, Statistics and Data Analysis, paper 265-27, SAS Institute Inc., Cary, NC.
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Abstract: Based on the Bayesian adaptive Lasso quantile regression (Alhamzawi et al., 2012), we propose the iterative adaptive Lasso quantile regression, which is an extension to the Expectation Conditional Maximization (ECM) algorithm (Sun et al., 2010). The proposed method is demonstrated via simulation studies and a real data set. Results indicate that the new algorithm performs quite good in comparison to the other existing methods.

Keywords: ECM, Bayesian inference, Prior distribution, Posterior inference, Quantile regression.

[1] Akaike, H. (1998). "Information theory and an extension of the maximum likelihood principle." In Selected Papers of Hirotugu Akaike, 199–213. Springer.
[2] Alhamzawi, R. (2014). Bayesian elastic net tobit quantile regression. Communications in Statistics-Simulation and Computation (just-accepted), 00-00.
[3] Alhamzawi, R. (2015). Model selection in quantile regression models. Journal of Applied Statistics 42 (2), 445-458.
[4] Alhamzawi, R. (2017). Brq: Bayesian Analysis of Quantile Regression Models. R package version 2.0.
[5] Alhamzawi, R. and H. T. M. Ali (2017). Bayesian quantile regression for ordinal longitudinal data. Journal of Applied Statistics, 1-14.

Abstract: The least squares method has been in use in regression analysis mainly because of tradition and ease of computation, but this method may suffer a huge setback in the presence of unusual observation such as outliers and high leverage point. In this paper our main objective was to use jackknife after bootstrap procedure in most of robust regression method like, M-estimator and MM-estimator. Analytical examples are presented to show the effective of the deleted observation on the coefficients, and the behavior of jackknife after bootstrap in robust regression.

Keywords: Robust Regression, Outlier, Leverage point, Bootstrap, Jackknife after Bootstrap

[1] Bancayrin,C.,(2009)."Performance of Median and Least squares Regression for slightly skewed Data", world Academy of
science, Engineering and Technology Vol.53, PP.226-230.
[2] Draper, N. R. and Smith, l.,(1998),"Applied Regression Analysis", 3rd ed., John Wiley & Sons, Inc., Canada.
[3] Efron, B. and Tibshirni, R.,(1993),"An introduction to the bootstrap", Chapman & Hall Inc. USA.
[4] Efron, B.,(1992),"Jackknife-After-Bootstrap standard Errors and Influence Functions", Journal of the Royal statistical. Series
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[5] Huber, P. J. and Ronchetti, E. M.,(2009),"Robust statistics" 2nd ,John Wiley & Sons, Inc., New Jersey.

Abstract: The present theory a consistent estimators of the parameters of stationary Gaussian statistical structures in Hilbert space of measures can be used, for example, in the reliability predication of different engineering designs. In the paper there are discussed Gaussian stationary statistical structuresE S i I i , , ,  in Hilbert space of measures. We prove necessary and sufficient conditions for existence of such estimators in Hilbert space of measures..........

Keywords:consistent estimators, orthogonal, weakly separable, strongly separable statistical structures.
Ceassificationcocles 62HO5, 62H12

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Abstract: In this note, some fluctuation results for renormalized number of ancestors of a stationary quadratic continuous-state branching process are given. We consider three different cases: same time, different step width; different time, the same step width; adjacent time with the same step width. The Laplace transform of some related quantities is derived to prove this result.

Keywords: and phrases.Fluctuation, stationary CB process, number of ancestor.

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Inst. H. Poincare Probab. Statist., 52(3):1321–1350, 2016.
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