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• Open Access   Article

  An Analysis of Email-Eu-Core Network

  A. Bharali

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.100-104, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.100104

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  Abstract
  In this paper a complex network approach is adopted to analyze the Email-Eu-Core Network. This communication network displays small-world (SW) properties with an average path length of 2.0834 and a clustering coefficient of 0.372, and it also exhibits assortative mixing on degree of nodes, that means the high-degree nodes in the network tend to have connections with high-degree nodes. Being an assortative network, it does percolate more easily but less robust to targeted node removal. A study of the robustness of Email-Eu-Core network is also carried out for random and targeted node failures.

  Key-Words / Index Term
  Network measures, Complex Network, Email-Eu Network, Small-world, Assortative mixing, Scale-free Network.

  References
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  Placement. Journal of Software-Practice and Experience, 21 (11), 1129-1164.
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  [8] Latora, V., et. al., (2001) Efficient Behavior of Small-World Networks. Phys. Rev. Lett., 87: 198701.
  [9] Leskovec, J., Krevil, A., SNAP Datasets: Large Network Dataset Collection. http://snap.stanford.edu/data.
  [10] Newman, M. E. J., (2002) Assortative mixing in networks. Phys. Rev. E, 89(20): 208701.
  [11] Newman, M. E. J., (2003) Mixing patterns in networks. Phys. Rev. E, 67(2): 026126.
  [12] Newman, M. E. J., (2003) The structure and function of complex networks. SIAM Rev., 45(2), 167-256.
  [13] Wang, X., et. al., (2003) Complex networks: small-world, scale-free and beyond. IEEE Circuits and Systems Magazine, 3(1), 6-20.
  [14] Watts, D.J., Strogatz, S.H., (1998) Collective dynamics of ’small-world’ networks. Nature, 393, 440-442.
  [15] Wu, J., et. al., (2013) Analysis of Communication Network Performance From a Complex Network Perspective. IEEE Transactions on Circuits and Systems I: Regular Papers, 60(12), 3303-3316.
  [16] Wu, J., (2014) Study of Communication Network Performance From A Complex Network Perspective. A Doctoral Thesis (The Hong Kong Polytechnic University), http://ira.lib.polyu.edu.hk/handle/10397/7429.
  [17] Xia, J., et. al., (2008) Attack Vulnerability of Complex Communication Networks. IEEE Transactions on Circuits and Systems II: Express Briefs, 55(1), 65-69.
  [18] Yin, H., et. al., (2017) Local Higher-order Graph Clustering. In Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining.
  

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  A. Bharali, "An Analysis of Email-Eu-Core Network," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.100-104, 2018

• Open Access   Article

  Comparative Studies of Educational Level on Boys and Girls from Thanjavur District, Tamil Nadu, India

  S. Stella Mani

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.105-108, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.105108

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  Abstract
  These paper main goals, the first analyze the level of education in boys and girls from Thanjavur district, Tamil Nadu, India. Here we have concentrated on the effects of family background, economic and poverty status of the family, schooling supply effects, government programms and demographic composition of the family. Next objective is the second factors which may affect gender differences in education. It may be concluded the present study, the variables which affect the families invest in boys and girls education were calculated in Income level Vs Educational qualification and Community Vs Educational qualification are dependent in determined chi square effects of goodness of fit test.

  Key-Words / Index Term
  gender, educational qualification, chi square test

  References
  [1]. Londono, Jose Luis (1996). Pobreza, Desigualdad y Formacion de Capital Humano en América Latina, 1950-2025” Banco International de Reconstruction of Fomento/Banco Mundial, Washington, D.C., Larson, D.K. and Sung, C.H., (2009). Comparing student performance: Online versus blended versus face-to-face. J. Asynchronous Learn Netw.; 13: 31–42.
  [2]. Schultz, T.P., (1993). Investments in schooling and health of women and men: quantities and returns in T.P Schultz (ed.), Investments in Women’s Human Capital University of Chicago Press, Chicago, IL.
  [3]. King, E. and Hill, Anne (eds.) (1993). Women´s education in developing countries: barriers, benefits and policies. Johns Hopkins University Press, Baltimore.
  [4]. Parveen, A., Noor-Ul-Amin, S. and Nazir, S.K., (2013). Comparative study of the academic achievement of 10th class boys and girls studying in different high schools of District Pulwama of (J&K). J. of Education Research and Behavioral Sci.; 2(2): 020-027.
  [5]. Kapur, Devesh and Pratap Bhanu Mehta. “Indian Higher Education Reform: From Half-Baked Socialism to Half-Baked Capitalism.” Working Paper, Center for International Development at Harvard University. September 2004
  [6]. Osterman, K. F. (2000). Students’ need for belonging in the school community. Review of Educational Research; 70(3): 323–367.
  [7]. Parish, W.L. and Robert Willis. (1992). Daughters, Education and Family Budgets. Taiwan Experiences” en Journal of Human Resources, XXVIII, 4.
  [8]. Garasky, S., (1995). The effects of family structure on educational attainment: Do the effects vary by the age of the child. American Journal of Economics and Sociology; 54(1): 89-105.
  [9]. Larson DK, Sung CH. Comparing student performance: Online versus blended versus face-to-face. J Asynchronous Learn Netw. 2009; 13: 31–42
  [10]. Anderson, K. and May, F.A., (2010). Does the Method of Instruction Matter? An Experimental Examination of Information Literacy Instruction in the Online, Blended, and Face-to-Face Classrooms. J Acad Librariansh.; 36: 495–500.
  [11]. Bains, M., Reynolds, P.A., McDonald, F. and Sherriff, M., (2011). Effectiveness and acceptability of face-to-face, blended and e-learning: a randomised trial of orthodontic undergraduates. Eur J Dent Educ.; 15: 110–117.
  [12]. Xu, D. and Jaggars, S.S., (2011). Online and hybrid course enrollment and performance in Washington State community and technical colleges. Community College Research Center, Columbia University. New York, NY;
  

  Citation
  S. Stella Mani, "Comparative Studies of Educational Level on Boys and Girls from Thanjavur District, Tamil Nadu, India," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.105-108, 2018

• Open Access   Article

  Design and Evaluation of Skiplot Sampling Plans Under Life Tests Based on Percentiles of Exponentiated Rayleigh Distribution

  K.Pradeepa Veerakumari, P. Ponneeswari, P. Umamaheswari

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.109-117, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.109117

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  Abstract
  This paper presents a designing procedure of Skip lot sampling plan of type SkSP-2 with SSP and DSP for the life tests based on the percentiles of Exponentiated Rayleigh Distribution (ERD) as reference plan. This work also provides a comparative study on SkSP-2 with SSP and DSP for life tests based on the percentiles of ERD as reference plan over SSP and DSP for life tests based on the percentiles of ERD as reference plan respectively. The operating characteristic values of the plan are tabulated and the curve is drawn. Illustrations are given for the better understanding of the plan.

  Key-Words / Index Term
  Exponentiated Rayleigh Distribution, percentiles, life tests, SSP, DSP, SkSP-2

  References
  [1] Dodge H F, Perry R L. ( “A system of skip-lot plans for lot-by-lot inspection.” American Society for Quality Control Technical Conference Transactions, Chicago, Illinois, pp. 469-477, 1971.
  [2] Dodge H F. “Skip-lot sampling plan.” Industrial Quality Control, 11(5):3-5. Also reprinted in Journal of Quality Technology 9(3): 143–145, 1955.
  [3] Dodge H. F., Romig H G. . “A method of sampling inspection”. Bell system Technical Journal, 8: 613-631 1929.
  [4] Perry R L.“Skip-lot sampling plans.” Journal of Quality Technology, 5(3): 123-130, 1973a.
  [5] Perry R L. “Two-Level Skip-Lot Sampling Plans - Operating Characteristic Properties.” Journal of Quality Technology, 5(4): 160 – 166, 1973b.
  [6] Pradeepa Veerakumari K and Ponneeswari P. “Designing of Acceptance Sampling Plan for life tests based on Percentiles of Exponentiated Rayleigh Distribution..” International Journal of Current Engineering and Technology,6(4): 1148-1153, 2016.
  [7] Pradeepa Veerakumari K and Ponneeswari P. “Designing of Acceptance Double Sampling Plan for Life Test Based on Percentiles of Exponentiated Rayleigh Distribution.” International Journal of Statistics and Systems,12(3): 475-484, 2017
  [8] Schilling E G. “Acceptance Sampling in Quality Control.” Marcel Dekker, Inc., New York, 1982.
  

  Citation
  K.Pradeepa Veerakumari, P. Ponneeswari, P. Umamaheswari, "Design and Evaluation of Skiplot Sampling Plans Under Life Tests Based on Percentiles of Exponentiated Rayleigh Distribution," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.109-117, 2018

• Open Access   Article

  Estimation of expected time for the development of aids under two modes of infection

  R. Jaisankar, A. Saberunnisa

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.118-121, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.118121

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  Abstract
  Progression of the HIV infection toward AIDS is the significant one in the study HIV infected. It is believed that when the antigenic diversity exists in the infected individual crosses a threshold value the AIDS condition begins to occur. The successive sexual contacts with an infected partner may give rise in their antigenic diversity level. In this paper, Antigenic diversity threshold is assumed to be a random variable. Taking two modes of getting the infection, namely, heterosexual and homosexual contacts with randomly selected partners, the expected time to get AIDS is derived with its variance. Numerical illustrations are provided using simulation techniques to substantiate the results.

  Key-Words / Index Term
  Acquired Immuno Deficiency Syndrome, Human Immunodeficiency virus, Antigenic Diversity Threshold

  References
  REFERENCE
  [1]Barbara Bittner et. al.“Virus Load and Antigenic Diversity”.,Bulletin of Mathematical biology, Vol 59:881-896,1997.
  [2]P.ChristopherLocher, VolkerHeinrichs, Doris Apt, G .Robert Whalen , “Overcoming antigenic diversity and improving vaccines using DNA shuffling and screening technologies”, Expert Opinion on Biological Therapy, 4:589-597,2004.
  [3]R. J.De Boer, and M.C.Boerlijst,“Diversity and Virulence threshold in AIDS”. Applied Mathematics. Vol.94. 544-548,1994.
  [4]M.A .Nowak. and R.M .May, “Mathematical Biology of HIV Infection: Antigenic Variation and Diversity threshold”, Mathematical Biosciences, 106, pp. 1-21, 1991.
  [5]M. A .Nowak, D. J.Stekeland, andR.M May,“Antigenic Diversity Thresholds and Hazard Functions”. Mathematical Bioscience, Vol.139, 59-68, 1997.
  [6]N.I.Stillnakis, D.Schenzle and K.Dietz, “On the Antigenic diversity threshold model for AIDS”, Mathematical Biosciences, 121, pp.235-247, 1994.
  

  Citation
  R. Jaisankar, A. Saberunnisa, "Estimation of expected time for the development of aids under two modes of infection," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.118-121, 2018

• Open Access   Article

  Analysis of a vaccination model for carrier dependent population with a saturated incidence rate

  S. K. Tiwari, V. K. Gupta, Lakhan Nagar, Shivram Sharma

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.122-132, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.122132

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  This study to proposed and analyzed a vaccination model for carrier dependent population with a saturated incidence rate. The equilibrium’s for the model are found and their stability investigated. Gives the numerical examples in support of results

  Key-Words / Index Term
  carrier dependent, vaccination, environmental discharge, infectious diseases, carrying capacity.

  References
  [1] D. Greenhalth, “some results for an SEIR epidemic model with density dependence in the death rate”, IMA J. Math. Appl. Med Biol., 9, 67-106, 1992.
  [2] F. Bereszovsky, G. Karev, B. Song, C. Castillo-Chavez,” A simple epidemic model with surprising dynamics”, Math. Biosc. Engg., 2(1), 133-152, 2005.
  [3] G.S. Harold, “Household and stored food insects of public health importance”, US Department of Health, Education and Welfare, Communicable Disease Center, Atlanta, GA, 1960.
  [4] H.W. Hethcote, “Qualitative analysis of communicable disease models”, Math. Biosc., 28, 335-356, 1976.
  [5] J. Zhou, H.W. Hethcote, “Population size dependent incidence in models for diseases without immunity”, J. Math. Biol. 32, 809–834,1994.
  [6] K.L. Cooke,” Stability Analysis for a vector Disease model”, Rocky Mountain J. Math., 9, 31-42, 1979.
  [7] L.Q. Gao, H.W. Hethcote, “Disease transmission model with density dependence demographics”, J. Math. Biol. 32,717-731, 1992.
  [8] L.Esteva , M. Matias, “A model for vector transmitted diseases with saturation incidence”, J. Biol. Sys., 9(4), 235-245, 2001.
  [9] M. Ghosh, P. Chandra, P. Sinha, J.B. Sukla, “An Epidemiological model for carrier dependent infectious diseases with environmental effect”, Int. J. Appl. Sc. Comp., 7, 188-204, 2000.
  [10] M. Ghosh, P. Chandra, P. Sinha, J.B. Sukla, “Modeling the spread of carrier dependent infectious disease with environmental effects”,Appl. Math. Comp., 152, 385-402, 2004.
  [11] M. Ghosh, P.Chandra, P. Sinha, J.B. Sukla,” Modeling the spread of bacterial disease: effect of service providers from an environmentally degraded region”, Appl. Math. Comp., 160, 615-647, 2005.
  [12] N.T.J. Bailey, “Spatial models in the epidemiology of infectious diseases”, Lecture Notes in Biomathematics, 38,233-261,1980.
  [13] P. Das, D. Mukharjee, A. K. Sarkar, “Study of carrier dependent infectious disease cholera”, J. Biol. Sys., 13(3),233-244, 2005.
  [14] S. Hsu, A.. Zee,” Global spread of infectious diseases”, J. Bio. Sys., 12, 289-300, 2004.
  [15] S. Singh, P. Chandra, J.B. Sukla, “Modelling and analysis of the spread of carrier dependent infectious diseases with environmental effects”, J. Biol. Sys.,11(3), 325-335, 2003.
  

  Citation
  S. K. Tiwari, V. K. Gupta, Lakhan Nagar, Shivram Sharma, "Analysis of a vaccination model for carrier dependent population with a saturated incidence rate," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.122-132, 2018

• Open Access   Article

  Comparison of Global GDP Analytics– A Statistical Perspective

  K. Sampath Kumar, G. Sunitha, S.A. JyothiRani, V.V. Haragopal

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.133-139, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.133139

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  Abstract
  Gross domestic product (GDP) is an indicator of the economic health of a country. The objective of the present paper is to make a comparative study of GDP of India, USA and Japan with various components viz., Agriculture, Mining Quarrying, Manufacturing, Electricity Gas Water Supply, Construction, Trade Hotels Transport, Finance Insurance Real Estate. For the study we evaluate the analytics by considering the yearly aggregate GDP data (Market Price) at constant prices for the period 1996-97 to 2015-16. For the study Multiple and Stepwise Regressions are applied and it is observed that, in India, Finance Insurance Real Estate, Manufacturing and Construction influences the GDP at constant prices while in USA, the independent variable, Trade Hotels Transport influences the GDP and in Japan, the independent variables, viz., Construction, Manufacturing, and Trade Hotels Transport influences the GDP. Also it is observed that there is a substantial amount of variation in GDP of Japan and USA than in India. Also, from this study we can claim that over the years India fares well in GDP as compared to the other two countries. Hence, the economy of India is very sound and consistent.

  Key-Words / Index Term
  GDP, Multiple Regression, Stepwise Regression

  References
  [1]. Anghelache, C., Sacală, C. (2016). Multiple linear regressions used toanalyse the correlation between GDP and some variables, RomanianStatistical Review, Supplement, no.9, pp. 94-99.
  [2]. Anghelache, C., Anghel, M.G. (2015). GDP Analysis Methods through the Use of Statistical – Econometric Models, „ECONOMICA”
  Scientific and didactic journal, nr. 1 (91), Chişinău, Republica Moldova,pp. 124-130.
  [3]. Anghelache, C., Anghel, M.G., Sacală, C. (2013). The Gross DomesticProduct Evolution by the End of June 2013, Romanian Statistical Review, Supplement no. 4/2013, pp. 7-11.
  [4]. Anghelache, C., Manole, A. (2012). Correlation between GDP Direct Investments – An Econometric Approach, Metalurgia International nr.8, p.96.
  [5]. Bhandari, P., Frankel, J. (2015). Nominal GDP Targeting forDeveloping Countries, National Bureau of Economic Research,Working Paper 20898, Cambridge.
  [6]. Dumitrescu, D.., Anghel, M.G., Anghelache, C. (2015). Analysis Model of GDP Dependence on the Structural Variables, Theoretical andApplied Economics, Volume XXII, No.4 (605), Winter, pp. 151-158.
  [7]. Huang, B.N., Hwang, M.J., Yang, C.W. (2008). Causal relationship between energy consumption and GDP growth revisited: A dynamic panel data approach, Ecological Economics, Volume 67, Issue 1, 15 august 2008, pp. 41–54.
  [8]. Mazurek, J. (2013). A Comparison of GDP growth of European countries during 2008-2012 period from regional and other perspectives, University Library of Munich, Germany in MPRA Paper with number 51178.
  [9]. Bureau of Foreign and Domestic Commerce and National Bureau of
  Economic Research. 1934. National Income 1929–32, Report to Congress. Washington, DC: Government Printing Office. Available at http://library.bea.gov.
  [10]. Noland, M. (1993) “The Impact of Industrial Policy on Japan’s Trade Specialisation”, Review of Economics and Statistics, Vol. 75, May, pp.241-48.
  [11]. U.S. Government Accountability Office, 2005. “International Trade: U.S. and India Data on Off shoring Show Significant Differences.” GAO- 06-116. http://www.gao.gov/new.items/d06116.
  [12]. Landefeld, J. Steven. 2000. “GDP: One of the Greatest Inventions of the 20th Century.” Survey of Current Business, 80(1): 6–14.
  

  Citation
  K. Sampath Kumar, G. Sunitha, S.A. JyothiRani, V.V. Haragopal, "Comparison of Global GDP Analytics– A Statistical Perspective," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.133-139, 2018

• Open Access   Article

  A Stochastic Model for Estimating the Statistical Measures for Time to Cross the Antigenic Diversity Threshold of HIV Infected Under Correlated Inter-Contact Times using Erlang Truncated Exponential D

  R. Kannan, G. Parthasarathi

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.140-149, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.140149

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  Abstract
  This study is based on stochastic model for estimating the seroconversion time of HIV transmission under correlated inter- contact times. In the estimation of expected time to seroconversion, there is an important role for the inter-arrival times between successive contacts and has a significant influence. In this paper, it is assumed that the inter contact times between successive contacts are correlated random variables and the threshold distribution as Erlang truncated exponential distribution. In developing this model the result of Gurland (1995) has been used. The mean time to seroconversion and its variance are derived and the numerical illustrations are provided.

  Key-Words / Index Term
  Human Immune deficiency virus, Acquired Immune Deficiency Syndrome, Intercontact times, Seroconversion, Antigenic Diversity threshold

  References
  [1] Esary, J.D.,A. W. Marshall and F. Proschan (1973). Shock model and wear processes.Ann. Probability,1(4), 627-649.
  [2] Gurland, J. (1955). Distribution of maximum of the arithmetic mean of correlation random vriables. Ann. Mathematical Statistics, 26,294-300.
  [3] Kannan,R.,Vanimalini.R and RSathiyamoorthi (2012). A Stochastic Model With Antigenic Diversity Threshold Of Hiv Transmission Under Correlated Intercontact Times
  [4] Kannan, R.,Parthasarathi.G (2017). A stochastic model for the estimation of time to seroconversion of HIV transmission using Erlang Truncated Exponentail distribution. International Journal of Statistics and Applied Mathematics , 2(6), 211-215.
  [5] Kannan,R and R. Sathiyamoorthy(2006). Stochastic Model for time to seroconversion of HIV transmission under correlated intercontact times, Annamalai University Science Journal, Vol.143,1-12.
  [6] Nowak, M.A. and R.M. May (1991). Mathematical biology of HIV infection antigenic variation and diversity threshold. Mathematical Biosciences, 106,1-21.
  [7] Sathiyamoorthi, R. (1979). Cumulative Damage Model with correlated Interarrival Times of Shocks IEEE. Transactions on Reliability, R 25, No.23.
  [8] Stilianakis, N.D. Schenzle and K.Dietz (1994). On the antigenic diversity threshold model for AIDS. Mathematical Biosciences, 121, 235-247.
  

  Citation
  R. Kannan, G. Parthasarathi, "A Stochastic Model for Estimating the Statistical Measures for Time to Cross the Antigenic Diversity Threshold of HIV Infected Under Correlated Inter-Contact Times using Erlang Truncated Exponential D," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.140-149, 2018

• Open Access   Article

  Optimal Replenishment Strategy under Combined Criteria

  P.K. Tripathy, Bhabani S. Mohanty

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.150-162, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.150162

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  Abstract
  This article focuses on determining an optimal replenishment policy for items with three-parameter Weibull distribution deterioration where it represents the time to deterioration of a product. It is also observed that the demand of a consumer product usually varies with its cost and hence, the demand rate should be taken as price dependent. Holding cost is a linear function of time. Here replenishment strategy is developed under combined criteria of demand, deterioration and holding cost. The applicability of the model lies in the management of inventories of deteriorating products and for the particular items for which demand falls due to increase of its cost. Numerical illustrations and sensitivity analysis are provided to illuminate the effect of change of model parameters.

  Key-Words / Index Term
  Weibull Distribution, Time-varying Holding Cost, Price Dependent Demand, Deterioration

  References
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  [14] S. Banerjee, S. Agrawal, “A two-warehouse inventory model for items with three-parameter Weibull distribution deterioration, shortages and linear trend in demand”, International Transactions in Operational Research, Vol.15, pp.755–775, 2008.
  [15] S. K. Ghosh, K. S. Chaudhuri, “An order-level Inventory model for a deteriorating item with Weibull distribution deterioration, time-quadratic demand and shortages”, Advanced Modeling Optimization, Vol.6, Issue.1, pp.21–35, 2004.
  [16] S. K. Ghosh, S. K. Goyal, K. S. Chaudhuri, “An inventory model with weibull demand rate, finite rate of production and shortages”, International Journal of System Science, Vol.37, Issue.14, pp.1004-1009, 2006.
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  Citation
  P.K. Tripathy, Bhabani S. Mohanty, "Optimal Replenishment Strategy under Combined Criteria," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.150-162, 2018

• Open Access   Article

  Transmuted Half Normal Distribution

  S. Balaswamy

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.163-170, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.163170

  Abstract

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  Abstract
  The accumulation of large amounts of data nowadays and the necessity to characterize it leads to the birth of new statistical distributions. The current paper focuses on proposing a new distribution based on the quadratic rank transmutation map using the half normal distribution. Further, properties such as moments, Estimation of parameters, order statistics are derived for the proposed distribution along with the hazard and survival functions.

  Key-Words / Index Term
  Half Normal Distribution, Transmuted Distributions, Maximum Likelihood Estimation, Reliability Function, Quantile Function

  References
  [1]. Ayman Alzaatreh and Kristen Knight. On The Gamma-Half Normal Distribution and Its Applications. Journal of Modern Applied Statistical Methods, 12 (2013), no. 1, 103-119.
  [2]. Bland, J. M. and Altman, D. G. Measuring agreement in method comparison studies. Statistical Methods in Medical Research, 8 (1999), 135-160.
  [3]. Castro, L., Gomez, H., and Valenzuela, M. (2012). Epsilon half normal model: properties and inference. Computational Statistics and Data Analysis, 56 (2012), no. 12, 4338-4347.
  [4]. Shaw W.T. and Buckley I.R.C. The alchemy of probability distributions: beyond gram-charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. arXiv preprint, page arXiv:0901.0434, (2007).
  [5]. Bland, J. M. The half-normal distribution method for measurement error: two case studies. Unpublished lecture available on http://wwwusers.york.ac.uk/ mb55/talks/halfnor.pdf. (2005).
  

  Citation
  S. Balaswamy, "Transmuted Half Normal Distribution," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.163-170, 2018

• Open Access   Article

  Nonparametric Moving Average Control Charts Using Sign and Signed-Rank Statistics

  Vilas Yashwant Pawar, Digambar Tukaram Shirke and Shashikant Kuber Khilare

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.171-178, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.171178

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  Abstract
  In this paper, we provide two nonparametric moving average control charts based on well-known nonparametric statistics namely sign and signed-rank statistic. These control charts are useful in detecting shifts in the median of the symmetric process distributions. Average run length of these control charts has been studied for various symmetric process distributions. These include the normal, double exponential and Cauchy distributions. Performance of the proposed nonparametric moving average control chart based on the sign statistic is compared with the nonparametric sign chart and the Shewhart X-bar chart. Also, the performance of the proposed nonparametric control chart based on signed-rank statistic is compared with the Shewhart X-bar chart and the 2-of-2 control chart based on the signed-rank statistic. The study reveals that the proposed nonparametric moving average control chart based on sign statistic perform significantly better than the nonparametric sign chart and Shewhart X-bar chart. Also, the performance of the proposed nonparametric moving average control chart based on the signed-rank statistic perform significantly better than the Shewhart X-bar chart and the 2-of-2 chart based on the signed-rank statistics. The gain in the performance is substantial for heavy-tail distributions as compared to light-tail distribution. Robustness study against contamination by outliers for both the proposed charts show satisfactory performance. These chars can be used in practice, since they are simple to use and do not need any distributional assumptions, except symmetry.

  Key-Words / Index Term
  Nonparametric, Sign Statistic, Sign-Rank Statistic, Average Run Length.

  References
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  Citation
  Vilas Yashwant Pawar, Digambar Tukaram Shirke and Shashikant Kuber Khilare, "Nonparametric Moving Average Control Charts Using Sign and Signed-Rank Statistics," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.171-178, 2018