Volume-4 , Issue-6 , Dec 2017, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  Normal Half Normal Model for the Incorporation of exogenous factors on Efficiency analysis and its application

  Shameena.H. Khan, L.Mary Louis

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.4 , Issue.6 , pp.1-6, Dec-2017

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v4i6.16

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  Abstract
  Present study focused on the effect of exogenous factors on the efficiency level of a firm. In this paper we have derived a model by assuming normal-half normal distribution for the error terms and .Parameter estimation was done using maximum likelihood estimates. In order to assess the impact of exogenous factors on the efficiencies of a firm the model is applied to a data of 155 maize farmers. Weather, Economic conditions of farmer, Market status and damages to the crop due to bird attack are considered as exogenous factors for the study. Results showed that damages had a significant effect on the efficiency of production output. Goodness of fit test showed that our model is fitted with baseline comparison values. Null hypothesis is rejected. Computational analysis was done using SEM in Stata.

  Key-Words / Index Term
  Normal half normal, Exogenous factors, Cost efficiency, Goodness of fit, maximum likelihood estimates, Null hypothesis

  References
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  [3] Kai Sun and Subal C Kumbhakar, “Semiparametric smooth-coefficient stochastic frontier model”, Economic letters,Vol.120,Issue.2,pp. 305-309,2013.
  [4] Lukas Meub, Till Proeger and Hendrik Hüning, “A comparison of endogenous and exogenous timing in a social learning experiment”, Centre for European Governance and Economic Development Research, Discussion paper,Number.167,pp.1-26,2013.
  [5] D.Reifschneider and R.Stevenson, “Systematic departures from the frontier: A framework for the analysis of firm inefficiency”, International Economic Review,Vol.32,Issue.3,pp.715–23,1991.
  [6] Roberto Zotti and Cristian Barra, “How students’ exogenous characteristics affect faculties’ inefficiency, A heteroscedastic stochastic frontier approach”, Munich Personal RePEc Archive Paper No. 54011,pp.1-13,2014.
  [7] L.Simar, C.A.K.Lovell and van den Eeckaut, “P.Stochastic frontiers incorporating exogenous influences on efficiency,Institut de Statistique”, Universit´e Catholique de Louvain, Louvain-la-Neuve, Belgium, Discussion Paper No.9403,1994.
  
  [8] Subal C Kumbhakar, Hung-Jen wang and Alan P Horncastle, “A Practitioner’s guide to stochastic frontier analysis using Stata”,Cambridge University Press,ISBN:978-1-107-60946-4,2015.
  [9] Wang and Schmidt, “One-Step and Two-Step Estimation of the Effects of Exogenous Variables on Technical Efficiency Levels”, Journal of Productivity Analysis, Vol.18, pp.129–144,2002.
  [10] A.C Zoghbi, F.Rocha and E.Mattos, “Education production efficiency: Evidence from Brazilian universities”. Economic Modelling, Vol.31, pp. 94–103,2013.
  

  Citation
  Shameena.H. Khan, L.Mary Louis , "Normal Half Normal Model for the Incorporation of exogenous factors on Efficiency analysis and its application," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, Issue.6, pp.1-6, 2017

• Open Access   Article

  Zagreb Radio Indices of Some Graphs with Diameter Two

  A.T. Raj, J. V. Kureethara

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.4 , Issue.6 , pp.7-11, Dec-2017

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v4i6.711

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  Abstract
  A good amount of studies are there to explore the possibilities of non-laboratory characterization of molecules. In the field of quantitative structure-activity relationships (QSAR), topological indices play an important role. This paper is a perusal of the recently introduced topological indices called Zagreb radio indices. The Zagreb radio indices make use of the labeling of the vertices from the multi-level distance labeling of vertices called radio coloring. This is a vertex labeling with the condition on the distance between the vertices. Radio coloring is a non-negative integer labeling of the vertices of a graph such that difference of the colors of any pair of vertices is at least the difference between the diameter of the graph and the distance between those vertices plus one. This condition forces every vertex to have distinct labels. If the diameter of the graph is one, then radio coloring is nothing but the proper coloring. The Zagreb indices were originally introduced for the degrees of the vertices. Here, the Zagreb radio indices of some graphs of diameter two are computed replacing the degrees of the vertices with radio labels of the vertices originated from the minimal radio coloring.

  Key-Words / Index Term
  Zagreb Indices, Zagreb Radio Indices, Distance Labeling, Mathematical Chemistry, Diameter 2 graphs

  References
  [1] D. B. West, "Introduction to Graph Theory", 2 ed., New Delhi: PHI Learning Private Ltd, 2012.
  [2] H. Hosaya, "Topological Index. A Newly Proposed Quantity Characterizing the Topological Nature of Structural Isomers of Saturated Hydrocarbons," "Bulletin of the Chemical Society of Japan", vol. 44, no. 9, pp. 2332-2339, 1971.
  [3] I. Gutman, "Degree-based topological indices," "Croatica Chemica Acta", vol. 86, no. 4, pp. 351-361, 2013.
  [4] I. Gutman and N. Trinajstić, "Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons," "Chemical Physics Letters", vol. 17, no. 4, pp. 535-538, 1972.
  [5] A. T. Balaban, I. Motoc, D. Bonchev and O. Mekenyan, "Topological indices for structure-activity correlations," in "Steric Effects in Drug Design", Berlin, Springer-Verlag, pp. 21-55, 1983.
  [6] A. T. Raj and J. V. Kureethara, "Zagreb Radio Indices of Graphs," unpublished, 2017.
  [7] G. Chartrand, D. Erwin, F. Harary and P. Zhang, "Radio labelings of graphs," "Bulletin of the Institute of Combinatorics and its Applications", vol. 33, pp. 77-85, 2001.
  [8] G. Chartrand and P. Zhang, "Colorings, Distance and Domination," in "Chromatic Graph Theory", Florida, CRC Press, p. 415, 2009.
  [9] R. K. Yeh, "Labeling graphs with a condition at distance two", Columbia, SC: Department of Mathematics, University of South Carolina, 1990.
  
  

  Citation
  A.T. Raj, J. V. Kureethara, "Zagreb Radio Indices of Some Graphs with Diameter Two," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, Issue.6, pp.7-11, 2017

• Open Access   Article

  Use of R² and Its Shortcomings

  R. K. Borah, K. K. Singh Meitei, S. C. Kakaty

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.4 , Issue.6 , pp.12-16, Dec-2017

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v4i6.1216

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  Abstract
  The coefficient of determination R2 is a general measure of usefulness of the regression model. It shows the percentage of the total variation in the response variable which can be explained by the explanatory variable and is considered as the most commonly used measure of goodness of fit for regression models. It is demonstrated by many statisticians and practitioners that expression for the coefficient of determination is generally not equivalent. However it is widely misused. The primary source of the problem is that except for linear models with an intercept term, the several R2 statistics are not equivalent.

  Key-Words / Index Term
  Coefficient of determination, Regression model, Regression analysis, Resistant or robust models

  References
  [1] Draper, N. R., and Smith. H. (1981), Applied Regression Analysis (2nded.).New York: John Wiley.
  [2] Hahn, G. J. (1973), ‟The Coefficient of Determination Exposed,” Chemtech, 3, 609-612.
  [3] Hahn, G. J. (1977), “Fitting Regression Models With No Intercept Term.” Journal of Quality Technology, 9, 56-61.
  [4] Hawkins, D. M. (1980), ‟ A Note on Fitting a Regression Without an Intercept Term,” The American Statistician, 34, 233.
  [5] Healy, M. J. R. (1984), ‟The Use of R2 as a Measure of Goodness of Fit,” Journal of Royal Statistical Society ,Ser. A ,147 , 608-609.
  [6] Kvalseth, T. O. (1985). ‟Cautionary Note about R2,”The American Statistician, Vol. 39, No.4, Part 1(Nov., 1985), pp. 279-285.
  [7] Montgomery, D. C. and Peck, E. A. (2003), Introduction to Linear Regression Analysis(3rded.). New York :John Wiley.
  [8] Marquardt, D. W., and Snee, R. D. (1974), “ Test Statistics for Mixture Models,” Technometrics, 16, 533-537.
  [9] Scott, A. and Wild, C. (1991), “Transformations and R2” The American Statistician, Vol. 45, No. 2 (1991), pp. 127-129.
  [10] Theil, H. (1971), Principles of Econometrics, New York: John Willy.
  [11] Willet, J. B., and Singer, J. D. (1998), “Another Cautionary Note about R2: Its Use in Weighted Least-Squares Regression analysis,” The American Statistician, Vol. 42, No. 3 (1991), pp. 236-238.
  

  Citation
  R. K. Borah, K. K. Singh Meitei, S. C. Kakaty, "Use of R² and Its Shortcomings," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, Issue.6, pp.12-16, 2017

• Open Access   Article

  Design of Attribute Control Chart based on Inverse Rayleigh Distribution under Type-I Censoring

  C. Nanthakumar, T. Kavitha

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.4 , Issue.6 , pp.17-22, Dec-2017

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v4i6.1722

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  Control charts are one of the most common techniques that have been used to observe and control the process deviations in the industry. A control chart provides information about the performance or capability of a process. Lifetime considered as a quality characteristics for some products. Industries are routinely performing suitable life tests for their products. In life testing, censoring schemes are adopted to save time and cost of life test. Time censoring (type-I), product censoring (type-II) and hybrid censoring (Mixture of type-I and type-II censoring) are some of the censoring schemes employed in the life tests. The main objective of this paper is to design an life test based attribute control chart for inverse Rayleigh distribution under type-I censoring scheme. The performance of the control chart is studied using average run length (ARL). Designed control chart is illustrated through numerical examples.

  Key-Words / Index Term
  Inverse Rayleigh distribution, attribute control chart, type-I censoring, average run length

  References
  [1] E. K. Epprecht, A. F. B. Costa, F. C. T. Mendes, “Adaptive control charts for attributes”, IIE Transction, Vol. 35, No. 6, pp. 567-582, 2003.
  [2] A. F. B. Costa, M. A. Rahim, “Joint X bar and R charts with two stages samplings”, Quality and Reliability Engineering International, Vol. 20, No. 7, pp. 699-708, 2004.
  [3] L. F. Hsu, “Note on Design of Double and Triple Sampling Control Charts Using Genetic Algorithms”, International Journal of Production Research, Vol. 42, No. 5, pp. 1043-1047, 2004.
  [4] L. F. Hsu, “Note on Construction of Double Sampling s -Control Charts for Agile Manufacturing”, Quality and Reliability Engineering International, Vol. 23, pp. 269-272, 2007.
  [5] Z. Wu, H. Luo, X. Zhang, “Optimal np control chart with curtailment”, European Journal of Operational Research, Vol. 174, pp. 1723-1741, 2006.
  [6] Z. Wu, Q. Wang, “An np control chart using double inspections”, Journal of Applied Statistics, Vol. 34, No. 7, pp. 843-855, 2007.
  [7] E. P. Barbosa, S. Joekes, “An improved attribute control chart for monitoring non-conforming proportion in high quality process”, Control Engineering Practice, Vol. 21, pp. 407-412, 2013.
  [8] Mohammad Aslam, Chi-Hyuck Jun, “Attribute Control Charts for the Weibull Distribution under Truncated Life Tests”, Quality Engineering, Vol. 27, No. 3, pp.283-288, 2015.
  [9] Muhammad Aslam, Nasrullah Khan, Chi-Hyuck Jun, “A control chart for time truncated life tests using Pareto distribution of second kind”, Journal of Statistical Computation and Simulation, Vol. 86, No. 11, pp. 2113-2122, 2016.
  [10] V. N. Treyer, “Doklady Acad”, Nauk, Belorus, U.S.S.R, 1964.
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  [12] M. K. Gharrap, “Comparison of estimators of location measures of an inverse Rayleigh distribution”, The Egyptian Statistical Journal, Vol. 37, No. 2, pp. 295-309, 1993.
  [13] S. P. Mukarjee, S. S. Maitim, “A percentile Estimator of the Inverse Rayleigh Parameter”, IAPQR Transactions, Vol.21, pp. 63-65, 1996.
  [14] A. Soliman, E. A. Amin, A. A. Abd-Ei Aziz, “Estimation and Prediction from Inverse Rayleigh Distribution based on Lower Record Values”, Applied Mathematical Sciences, Vol. 4, No. 62, pp. 3057-3066, 2010.
  

  Citation
  C. Nanthakumar, T. Kavitha, "Design of Attribute Control Chart based on Inverse Rayleigh Distribution under Type-I Censoring," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, Issue.6, pp.17-22, 2017

• Open Access   Article

  L(t, 1)-Colouring of Wheel Graphs

  P. Pandey, J. V. Kureethara

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.4 , Issue.6 , pp.23-25, Dec-2017

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v4i6.2325

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  Abstract
  An L(t, 1)-Colouring of graph is the colouring of the vertices of a graph with non negative integers such that the vertices which are adjacent to each other receives colour with their colour difference not belonging to set T with integers including 0 and the vertices which are at distance 2 gets distinct colours. This is a type of channel assignment problem. Allotting frequencies to the radio channels in a region is determined by non-overlapping nature of the transmissions. The L(t, 1)-Colouring takes the inspiration from the famous T-Colouring and L(h, k)-Colouring of graphs. Both are celebrated colouring schemes. The L(t, 1)-span of the graph is the minimum of the highest colour used to colour the vertices of a graph out of all the possible L(t, 1)-colourings. We study the L(t, 1)-span of wheel graphs with respect a set T with consecutive integers and a set T whose elements are in AP with common difference d.

  Key-Words / Index Term
  L(t, 1)-colouring, Communication networks, Channel assignment, Radio frequency, Colour span, Wheel Graphs

  References
  [1] B. H. Metzger, “Spectrum management technique,” in 38th National ORSA meeting, Detroit, MI, US, 1970.
  [2] W. K. Hale, “Frequency assignment: Theory and applications,” in “Proc. IEEE”, Vol. 68, pp. 1497-1514, 1980.
  [3] F. S. Roberts, “T-colorings of graphs: recent results and open problems,” “Discrete Mathematics”, Vol. 93, pp. 229-245, 1991.
  [4] R. K. Yeh, “Labelling graphs with a condition at distance two,” Ph. D. Thesis, University of South Carolina, 1990.
  [5] P. Pandey, J. V. Kureethara, “L(t, 1)-colouring of graphs,” arXiv:1711.03096.
  [6] D. B. West, “Introduction to Graph Theory”, 2nd ed. Prentice Hall, US, 2001.
  [7] F. Harary, “Graph Theory”, Addison-Wesley, US, 1969.
  [8] S. Zhang and Q. Ma, “Labelling of some planar graphs with a condition at distance two,” Journal of Applied Mathematics and Computing, Vol. 24, pp. 421-426, 2007.
  [9] P. Pandey, J. V. Kureethara, “L(t, 1)-colouring of cycles”, in ICCTCEEC, Mysore, India, pp. 185-190, 2017.
  

  Citation
  P. Pandey, J. V. Kureethara, "L(t, 1)-Colouring of Wheel Graphs," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, Issue.6, pp.23-25, 2017

• Open Access   Article

  Two Phase Sampling Exponential Type Estimators for Ratio and Product of two Population Means in the Presence of Non-response

  Kamlesh Kumar, Mukesh Kumar

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.4 , Issue.6 , pp.26-34, Dec-2017

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v4i6.2634

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  Abstract
  In this paper, two phase sampling exponential type estimators for ratio and product of two population means in the presence of non-response have been proposed and the expressions for the mean suare error of the proposed estimators for ratio and product of two population means in case of fixed sample sizes and also in case of fixed cost, are obtained. The expressions for optimum values of sample sizes are obtained in case of fixed cost and also in case of specified variance. The proposed estimators have been found to be more efficient than the relevant estimators for the fixed values of sample sizes, under the specified conditions. The proposed estimators are also more efficient than the relevant estimators in case of the fixed cost and have less total cost in comparison to the cost incurred in case of relevant estimators for the specified variance. Empirical studies have been given in support of the problem under investigation.

  Key-Words / Index Term
  Two phase sampling, Non-response, Mean square error, Study character, Auxiliary characte

  References
  [1] M.P. Singh, “On the estimation of ratio and product of population parameters”, Sankhya B, 27, 321-328, 1965.
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  [4] S.M. Shah, D.N. Shah, “Ratio cum product estimator for estima-tion ratio (product) of two population parameters”, Sankhya C, 40,156-166, 1978.
  [5] T.P. Tripathi, “A general class of estimators of population ratio”, Sankhya C, 42, 63-75,1980.
  [6] R.K. Singh, “On estimating ratio and product of population parameters”, Calcutta Statist. Assoc. Bull., 20, 39-49,1982.
  [7] H.P. Singh, “On the estimation of ratio and product of two finite populations means”, Proc. Nat. Acad. Sci. India. Sec. A, 58, 399-402,1998.
  [8] R.S. Biradar, H.P. Singh, “A class of estimators for population parameters using supplementary information”, Aligarh J. Statist., 17 & 18, 54-71,1997-98.
  [9] L.N. Upadhyaya, G.N. Singh, H.P. Singh, “Use of transformed auxiliary variable in the estimation of population ratio in sample survey”, Statistics in Transition, 4, 1019-1027, 2000.
  [10] M.H. Hansen, W.N. Hurwitz, “The problem of non response in sample surveys”, J. Amer. Statis. Assoc., 41, 517-529, 1946.
  [11] P.S.R.S. Rao, “Ratio estimation with sub sampling the non-respondents”, Survey Methodology, 12, 217–230, 1986.
  [12] P.S.R.S. Rao, “Ratio and regression estimates with sub sampling the non- respondents”, Paper presented at a special contributed session of the International Statistical Association Meeting, Sept. 2–16, Tokyo, Japan,1987.
  [13] B.B. Khare, S. Srivastava, “Transformed product type estimators for population mean in presence of soft-core observations”, Proc. Math. Soci. B.H.U., 12, 29-34, 1996.
  [14] B.B. Khare, S. Srivastava, “Transformed ratio type estimators for the population mean in the presence of non-response”, Communi. Stat.–Theory and Methods, 26, 1779–1791,1997.
  
  
  [15] R. Singh, M. Kumar, M.K. Chaudhary, F. Smarandache, “Estimation of population mean in presence of non-response using exponential estimator”, Paper published in the Book Multispace & Multistructure Neutrosophic Transdisciplinarity 4, 758-768, 2010.
  [16] S. Kumar, S. Bhougal, “Estimation of the population mean in presence of non-response”, Communi. Kore. Stat. Soci., 18, 537–548 , 2011.
  [17] K. Kumar, M. Kumar, “Improved exponential ratio and product type estimators for population mean in the presence of non-response”, Bullen. Math. Stats. Rese., 5, 68-76 , 2017.
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  [19] B.B. Khare, S. Srivastava, “Study of conventional and alternative two phase sampling ratio, product and regression estimators in presence of non-response”, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences India, 65 (A) II, 195-203, 1995.
  [20] H.P. Singh, S. Kumar, “Estimation of mean in presence of non-response using two phase sampling scheme”, Statistical Papers, 50, 559–582, 2010.
  [21] B.B. Khare, U. Srivastava, K. Kumar, “ An improved class of estimators for population mean using auxiliary character in the presence of non-response”, The National Academy Science Letters, India, 35, 361-366, 2012.
  [22] B.B. Khare, S.K. Pandey, “ A class of estimators for ratio of two population means using auxiliary character in presence of non- response”, J. Sc. Res. B.H.U., 50, 115-124, 2000.
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  Citation
  Kamlesh Kumar, Mukesh Kumar, "Two Phase Sampling Exponential Type Estimators for Ratio and Product of two Population Means in the Presence of Non-response," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, Issue.6, pp.26-34, 2017

• Open Access   Article

  Upper and Lower Control Limits for Monitoring Markoff’s Model and Non-Normal Variation with Known CV

  Bhayare Unnati, Singh Jais Raj

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.4 , Issue.6 , pp.35-42, Dec-2017

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v4i6.3542

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  Abstract
  Control charts are essential tools for quality monitoring and construction of this charts were based on the assumption that observations were independent and normally distributed. The assumption of independence of quality characteristic is questionable, as autocorrelation among the observations becomes an inherent characteristic in quality control data. This phenomenon of inherent autocorrelation can cause significant deterioration of control charting performance. Autocorrelation had a substantial and detrimental effect on the statistical properties of control charts. The setting of control limits to utilize on a control chart assumes the assumption of normality. However, in many situation the condition does not hold. The objective of this paper is to investigate the upper and lower control limit properties of the control charts when the Markoff`s model and non-normality exists in the process.

  Key-Words / Index Term
  Mean chart, Autocorrelation, Non-Normality, Markoff’s Model, Coefficient of Variation

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  Citation
  Bhayare Unnati, Singh Jais Raj, "Upper and Lower Control Limits for Monitoring Markoff’s Model and Non-Normal Variation with Known CV," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, Issue.6, pp.35-42, 2017