Volume-4 , Issue-5 , Oct 2017, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  Dual to Ratio and Product Type Exponential Estimators of Finite Population Mean in Double Sampling for Stratification

  Arpita Lakhre

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.4 , Issue.5 , pp.1-8, Oct-2017

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v4i5.18

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  Abstract
  For estimating the finite population mean, two exponential type estimators in double sampling for stratification have been suggested with their properties. The biases and mean squared errors of the suggested estimators are obtained upto the first degree of approximation. The suggested estimators have been compared with usual unbiased estimator of population mean, ratio and product estimators, dual to ratio and product type estimators and ratio and product type exponential estimators in double sampling for stratification. To judge the merits of the suggested estimators, an empirical study has been carried out.

  Key-Words / Index Term
  double sampling, two exponential type estimators in double sampling, dual to ratio and product type estimators, Bias, mean squared error

  References
  [1] Bahl, S. and Tuteja, R.K. (1991). Ratio and product type exponential estimators. Info. & Opti. Sci. XIII, 159-163.
  [2] Bandyopadhyay (1980). Improved ratio and product estimators. Sa nkhya, 42, C, 45-49.
  [3] Ige, A.F. and Tripathi. T.P. (1987). On double sampling for stratification and use of auxiliary information. J. Ind. Soc. Agri. Statist., 39, 191-201.
  [4] Neyman, J. (1938). Contribution to the theory of sampling human population. J. Amer. Statist. Assoc., 33, 101-116.
  [5] Srivenkataramana , T. (1980). A dual of ratio estimator in sample surveys. Biometrika, 67, 1, 199-204.
  [6] Tailor, R., Chouhan, S. and Kim, J.M. (2014). Ratio and product type exponential estimators of population mean in double sampling for stratification. Comm. Statist. Appl. & Meth. 21, 1, 1–9.
  

  Citation
  Arpita Lakhre, "Dual to Ratio and Product Type Exponential Estimators of Finite Population Mean in Double Sampling for Stratification," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, Issue.5, pp.1-8, 2017

• Open Access   Article

  A Simple Sirs Mathematical Model with Mass Action Type Incidence

  Amit kumar, Pardeep Porwal, V. H. Badshah

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.4 , Issue.5 , pp.9-12, Oct-2017

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v4i5.912

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  In this paper a simple SIRS mathematical model with mass action type incidence is formulated and studied. Steady state, equilibrium point and the basic reproduction number are obtained for the system of differential equation. Existence and stability of the diseases free and endemic stages are investigated. An example is also furnished which demonstrates validity of main result.

  Key-Words / Index Term
  Mathematical Model, Equilibrium point, Stability, Incidence

  References
  [1]. A. Kumar., P. Porwal, and V. H. Badshah., “Modified SIRS Epidemic Model with Immigration and Saturated Incidence rate”, MAYFEB Journal of Mathematics ISSN,2371-6193,(4) , 7-12, 2016.
  [2]. H. W. Hethcote., “Qualitative Analysis for Communicable Disease Models”, Math., Bio science, 28, 335-356, 1976.
  [3]. H. W. Hethcote., “Three Basic Epidemiological Models”, In Applied Mathematical Ecology, L. Gross, T.G. Hallam and S.A. Levin , Springer, Berlin, 119-144, 1989.
  [4]. H. W. Hethcote., and P. Driessch Van Den., “Some Epidemiological models with Non-linear Incidence”. J. Math. Boil., 29, 271-287, 1991.
  [5]. H. W. Hethchote., “The Mathematics of Infectious Disease”, SIAM Review 42, 599 -653, 2000.
  [6]. J. M. Mena Lorca., and H. W. Hethcote., “Dynamic Models of Infectious Disease as Regulators of Population Sizes’, Journal Math. Bio. 30, 693 – 716, 1992.
  [7]. P. Porwal., P. Ausif., and S. K. Tiwari., “An SIS Model for Human and Bacterial Population with Modified Saturated Incidence Rate and Logistic Growth”, International Journal of Modern Mathematical Science, 12(2), 98-111, 2011.
  [8]. P. Porwal., and V. H. Badshah., “A Study of Avion Influenza (Birds- Flu) Epidemic with Vaccinated Human Population”, International Journal of Mathematical Modeling Simulation and Application 5(12),75.
  [9]. P. Porwal., and V. H. Badshah., “Modified Epidemic Model with Saturated Incidence rate and Reduced Transmission Under Treatment”, International Journal of Mathematics Archieve, 4(12), 106-111, 2013.
  [10]. P. Porwal., and V. H. Badshah., “Dynamical study of SIRS Epidemic Model with Vaccinated Susceptibilit”, Canadian Journal of Basic and Applied Science 2(4), 90-96, 2014.
  [11]. P. Porwal., P. Shrivastava, and S. K. Tiwari., “Study of Single SIR Epidemic Model”, Plegia Library Advance in Applied Science Research, 6(4),1- 4,2014.
  [12]. R. M. Anderson, and R.M. May., “ Population Biology of Infectious Disease”, Nature, Springer Verlag, Berlin , Heidelberg, New York, 180, 361-367, 1979.
  [13]. R. K. Miller., and AN. Michal., “Ordinary Differential equations” New York, Academic Press (1982)
  [14]. V. H. Badshah., and A. Kumar., “A Study of Mathematical Modeling in Mathematics”, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.3, Issue.1, pp.1-3, 2016.
  [15]. V. Capasso., and G. Serio., “A Generalization of the Kermack and Mc Kendrick Deterministic Epidemic Model”, Math Bio science. 42, 41 – 61, 1978.
  [16]. W. O. Kermack., and A. G. Mc Kendrick., “Contribution to the Mathematical Theory of Epidemics”, Part1. Royal Society, London, 115, 700 – 721, 1927.
  

  Citation
  Amit kumar, Pardeep Porwal, V. H. Badshah, "A Simple Sirs Mathematical Model with Mass Action Type Incidence," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, Issue.5, pp.9-12, 2017

• Open Access   Article

  Bayes Estimation of Parameter in Inverse Maxwell Distribution under Weighted Quadratic Loss Function

  A. Loganathan, S. Mari Chelvi, M. Uma

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.4 , Issue.5 , pp.13-16, Oct-2017

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v4i5.1316

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  The inverse Maxwell distribution is the probability distribution of the reciprocal of the Maxwell random variable. This distribution has applications in reliability and life testing. In this paper, Bayes estimator of the parameter in the inverse Maxwell distribution is derived employing Jeffreys non-informative prior under weighted quadratic loss function. The Bayes estimator in this case is the minimax estimator. Efficiency of the Bayes estimator is compared with the maximum likelihood estimator. Application of the inverse Maxwell distribution to a real life situation is also studied.

  Key-Words / Index Term
  Bayes estimator, Inverse Maxwell distribution, Jeffreys prior, Maximum likelihood estimator

  References
  [1] L. Boltzmann, “Further Studies on Thermal Equilibrium among Gas Molecule” Conference Reports of the Imperial Academy of Sciences, Vienna, Mathematical and Natural Sciences class, 66, pp. 275-370, 1872.
  [2] I.J. Good., R.A. Gaskins., “Density Estimation and Bump-hunting by the Penalized Likelihood Method Exemplified by Scattering and Meteorite Data”, Journal of the American Statistical Association, 75, pp.42-56, 1980.
  [3] P.M. Lee, “ Bayesian Statistics: An Introduction”, Second Edition, Arnold Publication, 1997.
  [4] E.L. Lehmann, “Theory of Point Estimation”, John Wiley, New York, 1983.
  [5] A. Loganathan., S. Mari Chelvi., “Estimation of Parameter in Inverse Maxwell Distribution”, Communications in Statistics - Simulation and Computation (communicated), 2017a.
  [6] J.C. Maxwell, “Illustrations of the Dynamical Theory of Gases. Part I. On the Motions and Collisions of Perfectly Elastic Spheres”, The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, 4th Series, Vol.19, pp.19-32, 1860a.
  [7] M. Rajagopalan., P. Dhanavanthan., “Statistical Inference”, PHI Learning Private Limited, India, 2012.
  [8] K.L. Singh., R.S. Srivastava., “Inverse Maxwell Distribution as a Survival Model, Genesis and Parameter Estimation”, Research Journal of Mathematical and Statistical Sciences, Vol.2 (7), pp.23-28, 2014.
  

  Citation
  A. Loganathan, S. Mari Chelvi, M. Uma, "Bayes Estimation of Parameter in Inverse Maxwell Distribution under Weighted Quadratic Loss Function," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, Issue.5, pp.13-16, 2017

• Open Access   Article

  Numerical Study Of an Unsteady 2-D Compressible Inviscid Flow with Heat Transfer with Slip Boundary Conditions Using MacCormack Technique

  Arti Kaushik

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.4 , Issue.5 , pp.17-26, Oct-2017

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v4i5.1726

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  In this paper the problem of an unsteady 2-D compressible inviscid flow with heat transfer with slip boundary conditions is analyzed. Numerical solutions of the governing equations are obtained by using Mac Cormack technique. The numerical computations of u-velocity, v-velocity, pressure and temperature are done at different times for different positions along x- axis and y- axis. The numerical solutions of the u-velocity, v-velocity, pressure and temperature obtained in this analysis have been ensured to be stable based on stability requirements. The significant findings from the present analysis have been given under conclusion.

  Key-Words / Index Term
  Inviscid flow, Heat transfers, Euler’s equations, MacCormack technique, slips boundary conditions

  References
  [1]. R.W. MacCormack,”The effect of viscosity in hypervelocity impact crartering”, AIAA paper, pp. 69-354, 1969.
  [2]. Robert S. Bernard, “A MacCormack scheme for incompressible flow”, Computers and mathematics with applications, Vol. 24, Issue 5-6, pp 151-168, 1992.
  [3]. F. Payri, A.J. Torregrosa and M.D. Chust, “Applicationof MacCormack scheme to IC engine exhaust noise prediction”, Journal of sound and vibration, Vol. 195, Issue 5, pp 757-773, 1996.
  [4]. R. Hixon and E. Turkel,” High accuracy compact MCT scheme for computational acoustics”,36 Aerospace Sciences Meeting and exhibition, Reno, NV. 1998.
  [5]. R. Hixon and E. Turkel,” Compact implicit MC type scheme with high accuracy”, Journal of computational physics, Vol 158, Issue 1, pp. 51-70, 2000.
  [6]. A.Perrin and H.H.Hu,:An explicit finite difference scheme for simulation of moving particle”, Journal of computational physics, Vol. 212, Issue 1, pp 166-187, 2006.
  [7]. Li Guoyuan and C. Rhett Jackson,”Simple, accurate andefficieny revisions to McCormack and Saulyev Schemes: High Peclet number”, Applied mathematics and Computations, Vol. 186, Issue 1, pp 610-622. ,2007.
  [8]. Noppart Pochai, “Numerical treatment of a modified MacCormack scheme in a non dimensional form of water quality models in a non uniform flow stream”, Journal of applied mathematics, Vol. 2014. Article ID 274263
  [9]. Samir K. Das and Jafar Bagheri,” Modeling of shallow water equations by using compact MacCormack type scheme with applications on dam break problem”, International Journal of Advance Applied Mathematics and Mechanics Vol. 2 ,Issue 3, pp 60-71, 2015.
  [10]. T.P. Gallagher, M. Akiki, S. Menon, V. Sankaran, V. Sankaran,” Development of generalized MacCormack scheme and its extension to low mach number flows”, International Journal for numerical methods in fluids. Vol. 85, Issue 3, pp 165-188. 2017.
  [11]. J. D. Anderson,”Computational Fluid Dynamics: The Basics with Applications”, McGraw-Hill Publications, First(Ist) Edition, April 1995.
  [12]. H.K. Versteeg, W. Malalsekra, “An Introduction to Computational Fluid Dynamics: The Finite Volume Method”, Prentice Hall, Second (2nd) Edition, February 2007.
  [13]. Prabhjot Singh and Anjana Sharma,” Face Recognition Using Principal Component Analysis in MATLAB”, International Journal of Scientific Research in Computer Science and Engineering, Vol.3, Issue 1, pp.1-5, 2015.
  

  Citation
  Arti Kaushik, "Numerical Study Of an Unsteady 2-D Compressible Inviscid Flow with Heat Transfer with Slip Boundary Conditions Using MacCormack Technique," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, Issue.5, pp.17-26, 2017

• Open Access   Article

  MCA (Information Science and Management): The Next Generation Interdisciplinary specialization for Social, Business, Health & Mathematical Sciences—A Step for promoting Digital Humanities

  P.K. Paul, P.S. Aithal, A. Bhuimali

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.4 , Issue.5 , pp.27-32, Oct-2017

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v4i5.2732

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  Information Science is an important domain for building healthy information infrastructure for almost all kind of organization and institutions for almost all kind of organization and institutions and sector. Information and its growing number is the main reason behind the requirement of information and similar domain. Information Science is actually an interdisciplinary domain combines with so many subjects related to information and processing of data and similar facet. Computer is one of the important gradients in Information Science for healthy and sophisticated information system designing and development. In the education sector, there are so many courses available which are related to computers such as Computer Science, Computer Application, Computer Science and Engineering, IT and so on and comes with so many nomenclatures and levels. Information Science is also a computer related subject but having information concentration. MCA is one of the important and popular courses in computing applications in India; which deals with IT applications in the industrial and society problems. This paper talks about MCA in respect of possibilities of Information Science specialization in such programme for better information infrastructure development. Several contents of this paper are directly included in the thesis of the author (for obtaining research degree) and the fact is hereby acknowledged. Paper deals with many aspects of Information Science including its need and characteristics, educational situation in India and globally in brief manner and way to introduce this proposal in contemporary Indian MCA programme.

  Key-Words / Index Term
  Information, Information Science, IST, Knowledge, Social Development, Digital Divide, Information Literacy, Information Divide, Information Development, Academics, Information Systems

  References
  [1] Cohen, E. B. (2004). Applying the Informing Science Framework to Higher Education: Knowledge Development, Management, and Dissemination. Konferencja Pozyskiwanie wiedzy i zarządzanie wiedzą (Proceedings of the Knowledge Acquisition and Management Conference) May 13-15, 2004 Kule, Poland.
  [2] Cohen, Eli B. and Nycz Malgorzata (2006). Learning Objects and E-Learning: an Informing Science Perspective. Interdisciplinary Journal of Knowledge and Learning Objects Volume 2, 2006.
  [3] Martin, S.B. (1998). Information technology, employment, and the information sector: Trends in information employment 1970–1995. Journal of the American Society for Information Science, 49(12), 1053–1069.
  [4] Michael Buckland and Ziming liu (1995).History of information science. Annual Review of Information Science and Technology vol. 30: 385-416.
  [5] Paul, P. K. (2012). Information Scientist: Roles and Values with special Reference to their Appropriate Academic Programme and its availability in India:” International Journal of Information Dissemination and Technology, Vol. 2, No. 4, October-December-2012, Page-245-248, ISSN-2229-5984
  [6] Paul, P. K., D Chaterjee,R Bhatnagar, Uma Pricilda (2012). Information Scientist: Contemporary innovative techno management roles with special reference to Information Scientist Vs Information Technologist: A Study” , Indian Journal of Information Science and Applications [IJISA], Vol. 2. No. 1, Jan-Jun-2012, Academic Research Publication, New Delhi, Page-47-50, ISSN-2249-3689.
  [7] Paul, P.K., R Rajesh, D Chatterjee, M K Ghose (2013). Information Scientist: Technological and Managerial Skill requirement in 21st century” in ‘Information Studies’ Vol. 19, No. 1, RCIS,Chennai, Page-29-36, ISSN-0971-6726.
  [8] Paul, P. K., (2013). MSc-Information Science [Geo Informatics]: Overview emphasizing twoproposed curriculum for sophisticated Geo Spatial development. International Journal of Pharmaceutical and Biological Research (IJPBR), Vol 4 Issue 5, ISSN : 0976- 285X, Vol-218-227.
  [9] Paul, P. K., (2013). Environment and Sustainable Development with Cloud Based Green Computing:A Case Study” Scholars Academic Journal of Biosciences (SAJB), 1(6):337-341 ISSN 2321-6883.
  [10] Paul, Prantosh Kumar, (2013). Nutrition Information Networks: Possible domain and Future Potentials. Scholars Academic Journal of Biosciences (SAJB), 1(6):342-345, ISSN 2321-6883.
  [11] Paul, P.K., K L Dangwal (2014). Cloud Computing Based Educational Systems and iits challenges and opportunities and issues” Turkish Online Journal of Distance Education-TOJDE, ISSN 1302-6488 Volume: 15 Number: 1, Page-89-98.
  [12] Paul, P.K., K L Dangwal, B Karn, (2013). Engineering Academics, Departments and Community : Emphasizing Some Educational Perspective of Information Science [IS], EDUCATIONAL QUEST: An International Journal of Education and Applied Social Sciences, 4(2), 141-146.
  [13] Paul, P.K., K L Dangwal, A Kumar (2013). Information Infrastructure and Academic and Education World: The Role and Opportunities in Contemporary Perspective. International Journal of Education for Peace and Development: Vol. 1 No. 1, Page-31-36.
  [14] Reichman, F. (1961). Notched Cards. In R. Shaw (Ed.), The state of the library art04(01), pp. 11–55). New Brunswick, NJ: Rutgers, The State University, Graduate School of Library Service.
  [15] Saracevic, T. (1996). Relevance reconsidered. Information science: Integration in perspectives. In Proceedings of the Second Conference on Conceptions of Library and Information Science (pp. 201–218), Copenhagen, Denmark: Royal School of Library and Information Science.
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  [17] Saracevic, T. (1979a). An essay on the past and future of information science education. I. Historical overview. Information Processing &Management, 15(1), 1–15.
  [18] Saracevic, T. (1979b). An essay on the past and future of information science education. II. Unresolved problems of ‘extemalities’ of education Information Processing & Management, 15(4), 291–301.
  [19] Vakkari, S.P. (1996). Library and information science: Content and scope. In J. Olaisen, E. Munch-Petersen, & P. Wilson (Eds.), Information science: From development of the discipline to social interaction. Oslo, Norway: Scandinavian University Press.
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  [23] www.en.wikipedia.org
  [24] www.infosci.cornell.edu/
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  [26] http://www.libsci.sc.edu/bob/istchron/iscnet/ischron.html
  

  Citation
  P.K. Paul, P.S. Aithal, A. Bhuimali , "MCA (Information Science and Management): The Next Generation Interdisciplinary specialization for Social, Business, Health & Mathematical Sciences—A Step for promoting Digital Humanities," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, Issue.5, pp.27-32, 2017

• Open Access   Article

  The Effect of Measurement Error on the Power of X Charts with Known Coefficient of variation

  Bhayare Unnati, Singh Jais Raj

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.4 , Issue.5 , pp.33-39, Oct-2017

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v4i5.3339

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  Abstract
  Measurement error often exists in quality control applications. This error has an adverse effect on the chart’s performance. Measurement error (ME) is a source of variation that may considerably affect the performance of control charts applied within a statistical process control scheme. While the consequences of ME on the actual performance of various control charts has been studied in recent publications, the more important inverse problem of how to specify ME requirements to achieve desirable control chart performance characteristics has not been addressed in the literature. In this paper, we develop guidelines regarding the formulation of power function to distribution-related ME characteristics with known coefficient of variation and investigate the effect of ME and cv on power of mean chart.

  Key-Words / Index Term
  Mean chart, Power, Measurement Error, Coefficient of Variation

  References
  [1] Automotive Industry Action Group, Chrysler, Ford, GM, Measurement Systems Analysis, AIAG, Detroit, MI, 1995.
  [2] K. Linna and W.H.Woodall, Effect of measurement error on shewhart control charts, J. Qual. Technol. 33(2) (2001), pp. 213–222.
  [3] K. Linna and W.H.Woodall, The performance of multivariate control charts in the presence of measurement error, J. Qual. Technol. 33(3) (2001), pp. 349–355.
  [4] P.E. Maravelakis, J. Panaretos, and S. Psarakis, EWMA chart and measurement error, J. Appl. Stat. 31(4) (2004), pp. 445–455.
  [5] D.C. Montgomery, Statistical Process Control, JohnWiley & Sons, NewYork, 2009.
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  [8] D. T. Searls, The utilization of a known coefficient of variation in the estimation procedure, Journal of the American Statistical Association, 59,( 1964), pp. 1225-1226.
  

  Citation
  Bhayare Unnati, Singh Jais Raj, "The Effect of Measurement Error on the Power of X Charts with Known Coefficient of variation," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, Issue.5, pp.33-39, 2017