Volume-5 , Issue-5 , Oct 2018, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  Properties of New Parametric Generalized Entropy of Order Statistics

  Rifat Nisa and M.A.K. Baig

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.82-87, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.8287

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  Abstract
  In this article, we introduce a new two parametric generalized uncertainty measure based on order statistics and also its residual version. Some general expressions of this proposed measure corresponding to particular probability distributions are derived. Finally, we study a lower bound for the proposed dynamic measure.

  Key-Words / Index Term
  Shannon’s Entropy; Order Statistics; Probability Integral Transformation; Residual Entropy; Generalized Information

  References
  B. C. Arnold, N. Blakrishan and N. H. Nagraja, “A First Course in Order Statistics”, John Wiley and Sons, New York, 1992.
  S. Baratpour, J. Ahmadi and N.R. Arghami, “Some Characterizations Based On Entropy of Order Statistics and Record Values”, Communications in Statistics-Theory and Methods, Vol.36, Issue.1, pp.47–57, 2007.
  J. Beirlant, E. J. Dudewicz, L. Gyorfi and E. C. Van Der Meulen, “Non Parametric Entropy Estimation: An Overview”, International Journal of the Mathematical Statistics Sciences, Vol.6, Issue 1, pp.17-39, 1997.
  H. A. David and H. N. Nagaraja, “Order Statistics,” Wiley New York, 2003.
  N. Ebrahimi, “How to Measure Uncertainty in the Residual Lifetime Distribution” Sankhya Series. A, Vol.58 pp.48-56, 1996.
  N. Ebrahimi, E. S. Soofi and H. Zahedi, “Information Properties of Order Statistics and Spacing”. IEEE Trans. Information Theory: Vol.50, pp.177-183, 2004.
  S. Kullback, “Information Theory and Statistics”, Wiley New York, 1959.
  C. E. Shannon, “A Mathematical Theory of Communication”. Bell System Technical Journal. Vol.27, Issue 3, pp.379-423,1948.
  R. Thapliyal, H.C. Taneja, “Generalized Entropy of Order Statistics” Applied Mathematics, Vol.3, pp.1977-1982, 2012.
  R.S. Verma, “Generalization of Renyi’s Entropy of Order α,” Journal of Mathematical Sciences, Vol.1, pp.34-48, 1966.
  

  Citation
  Rifat Nisa and M.A.K. Baig, "Properties of New Parametric Generalized Entropy of Order Statistics," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.82-87, 2018

• Open Access   Article

  L1 Penalized Regression Procedures for Feature Selection

  Muthukrishnan. R and Mahalakshmi. P

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.88-91, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.8891

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  Abstract
  In high dimensional regression analysis, a greater number of independent variables occur in many scientific fields and machine learning applications. To select predictors that are relevant to the response, statistical feature selection should be performed. In the study on variable selection in regression analysis, specifically when there are a greater number of predictor variables or highly correlated variables (or both), traditional method includes forward-backward and mixed stepwise variable selection procedure fails. There is need of alternatives, that is, L1 penalized regression procedures which provide higher prediction accuracy and computational efficiency. This paper demonstrates such procedures, particularly least absolute shrinkage and selection operator (LASSO) which does shrinkage and variable selection simultaneously and its variants. In case of extreme observations in the data set, robust regression estimators that are adopted in LASSO tolerate outliers with comparatively greater accuracy. In this paper, the performance of these procedures has been analyzed using the performance measure Median Squared Error (MSE) with numerical illustrations.

  Key-Words / Index Term
  Variable selection, LASSO, Huber, outlier, Robust, R Software

  References
  [1] A. Alfons, C. Croux, S. Gelper, “Sparse least trimmed squares regression for analyzing high-dimensional large data sets”, Annals of Applied Statistics, Vol.7, No.1, pp.226-248, 2013.
  [2] A. C. Lozano, N. Meinshausen, E. Yang, “Minimum distance lasso for robust high-dimensional regression”, Electronic Journal of Statistics, Vol.10, No.1, pp.1296-1340, 2016.
  [3] H. Wang, C. Leng, “A note on adaptive group lasso”, Computational Statistics and Data Analysis, pp.5277-5286, 2008.
  [4] H. Wang, G. Li, G. Jiang, “Robust regression shrinkage and consistent variable selection through the LAD-lasso”, Journal of Business & Economic Statistics, Vol.25, pp.347-355, 2007.
  [5] H. Zou, “The adaptive lasso and its oracle properties”, Journal of the American Statistical Association, Vol.101, No.476, pp.1418-1429, 2006.
  [6] H. Zou, M. Yuan, “Composite quantile regression and the oracle model selection theory”, Annals of Statistics, Vol.36, No.3, pp.1108-1126, 2008.
  [7] J. Fan, Q. Li, Y. Wang, “Estimation of high dimensional mean regression in the absence of symmetry and light tail assumptions”. J.R.Statist.Soc. B (Statistical Methodology), In Press, 2016.
  [8] K. Knight, W. Fu, “Asymptotics of lasso-type estimators”, Annals of statistics, Vol.28, pp.1346-1378, 2000.
  [9] Lambert-Lacroix, Zwald, “Robust Regression through the Huber`s criterion and adaptive lasso penalty”, Electron. J. Stat., Vol.5, pp.1015-1053, 2011.
  [10] M. Mohanadevi, V. Vinothini, “Accurate Error Prediction of Sugarcane Yeild Using a Regression Model”, International Journal of Computer Science and Engineering, Vol.6, Issue.7, pp.66-71, 2018.
  [11] M. Yuan, Y. Lin, “Model selection and estimation in regression with grouped variables”, J.R.Statist.Soc. B, Vol.68, pp.49-67, 2006.
  [12] R Core Team, “R: A language and environment for statistical computing”, R Foundation for Statistical Computing, Vienna, Austria, 2018.
  [13] R. Tibshirani, “Regression shrinkage and selection via the lasso”, J.R.Statist.Soc. B, Vol.58, pp.267-288, 1996.
  [14] R. Tibshirani, M. Saunders, S. Rosset, J. Zhu, K. Knight, “Sparsity and smoothness via the Fused Lasso”, J.R.Statist.Soc. B, Vol.67, pp.91-108, 2005.
  [15] S. Li and Y. Qin, “MTE: Maximum Tangent Likelihood and Other Robust Estimators for High-Dimensional Regression”, R package version 1.0.0.
  [16] S. N. Negahban, P. Ravikumar, “A unified framework for high-dimensional analysis of M-estimators with decomposable regularizes”, Statistical Science, Vol.27, No.4, 538-557, 2010.
  [17] X. Wang, Y. Jiang, M. Huang, H. Zhang, “Robust variable selection with exponential squared loss”, Journal of the American Statistical Association, Vol.108, Issue.502, pp.632-643, 2013.
  [18] Y. Qin, Shaobo Li, Yang Li, Yan Yu, “Penalized maximum tangent likelihood estimation and robust variable selection”, Unpublished, 2017.
  

  Citation
  Muthukrishnan. R and Mahalakshmi. P, "L1 Penalized Regression Procedures for Feature Selection," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.88-91, 2018

• Open Access   Article

  A New Inverse Rayleigh Distribution: Properties and Application

  A.S. Malik, S.P. Ahmad

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.92-96, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.9296

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  Abstract
  In this paper, a new generalization of inverse Rayleigh Distribution known as Alpha Power inverse Rayleigh distribution is proposed using Alpha Power Transformation. Some mathematical properties of the Alpha Power inverse Rayleigh distribution have been derived and the parameters are estimated using Maximum Likelihood estimation method. Two real life data sets have been incorporated to illustrate the applicability of the proposed distribution.

  Key-Words / Index Term
  Alpha power inverse Rayleigh Distribution, Alpha Power Transformation, Entropy, Reliability, MLE

  References
  [1] N. Trayer. Doklady Acad, Nauk, Belorus, U.S.S.R, 1964.
  [2] R. Gh. Voda, (1972), “On the inverse Rayleigh variable”, Rep. Stat. Apph. Res. Juse, Vol. 19, Issue., 4, pp.15-21, 1972.
  [3] A. Mahadavi, D. Kundu, “A new method of generating distribution with an application to exponential distribution”, Communications in Statistics-Theory and Methods, Vol. 46, Issue., 13, 2015.
  [4] M. Nassar, A. Alzaatreh, M. Mead &O. Abo-Kasem, “Alpha Power Weibull distribution: Properties and application”, Communications in Statistics-Theory and Methods, Vol. 46, Issue., 20, 2017.
  [5] A. S. Malik, S.P. Ahmad, “Alpha Power Rayleigh Distribution and Its Application to Life Time Data”, International Journal of Enhanced Research in Management & Computer Applications, Vol. 6, Issue., 11, pp. 212-219, 2017.
  [6] R. L. Smith, J. C. Naylor, “A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution”, Appl Stat ,Vol. 36,pp. 358–369, 1987.
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  [8] C. D. Devi, S. Thaddeus, “Information Retrieval Mechanism for Dynamic Health Care”, International Journal of Computer Sciences and Engineering, Vol. 6 (9), pp. 105-107, 2018.
  

  Citation
  A.S. Malik, S.P. Ahmad, "A New Inverse Rayleigh Distribution: Properties and Application," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.92-96, 2018

• Open Access   Article

  Some Solutions of Einstein-Maxwell Field Equations for Charged Fluid Sphere

  Abhishek Kumar Singh

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.97-103, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.97103

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  Abstract
  In the present paper we have found some solutions of Einstein-Maxwell Field equations for some charged fluid sphere. Assuming that the spin of the individual particles compositing the fluids are all aligned along radial direction, we have obtained solutions by choosing metric potentials as λ(r) and υ(r) on different suitable forms or conditions. Pressure and density have been also calculated for the distribution and the physical constants appearing in the solution have been evaluated by matching the solutions to the Reissner-Nordstrom metric at the boundary. It is found that our metric give the solutions to only that value of constants for which pressure and density are positive. Also some physical and kinematical properties of the models are discussed.

  Key-Words / Index Term
  Einstein-Cartan theory, Charged fluid sphere, Metric potential, boundary conditions, pressure, matter density, charged density

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  Citation
  Abhishek Kumar Singh, "Some Solutions of Einstein-Maxwell Field Equations for Charged Fluid Sphere," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.97-103, 2018

• Open Access   Article

  Discriminatiing Between Dagum Distribution and Burr-III Distribution

  B.Srinivasa Rao, P. Sricharani

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.104-107, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.104107

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  Abstract
  Test statistics based on Likelihood function , population Quantiles are suggested to discriminate between Dagum distribution and Burr-III distribution. Because of the non tractability of their exact sampling distributions, the percentiles of the proposed test statistics are tabulated with the help of simulated sampling distributions of the test statistics . The power of the test statistics are also tabulated and a comparative study w.r.t the powers for a given sample and the level of significance are worked out.

  Key-Words / Index Term
  Dagum distribution(DD), Burr-III distribution(BD), Likelihood function , Quantiles , power of the test.

  References
  [1] Arabin.K.D. and Kundu.D., “Discriminating between the log normal and log logistic distributions”,Communications in Statistics Theory and Methods,Vol 39, pp.280-290, 2010.
  [2] Chambers.E.A. and Cox.D.R “Discriminating Between alternative binary response models”, Biometrika, Vol.54, pp 573-578, 1967.
  [3] Dumonceaux.R. and Antle.C. E., “Discriminating between the log-normal and weibull distributions”, Technometrics, Vol.15, pp 923-926, 1973.
  [4] Gupta.D.R., Kundu.D., “Discriminating between gamma and generalized exponential distributions” , Journal of Statistical computation and Simulation, Vol.74,No.2,pp 107–121,2004.
  [5] Gupta.D.R., Kundu.D.,Manglic.A., Discriminating between log normal and generalized exponential distributions , Journal of Statistical planning and Inference, Vol.127: pp 213–227, 2005.
  [6] Rao.B.S. and Kantam.R.R.L., “Discriminating between generalized exponential distribution and some life test models based on population quantiles”, Journal of Modern Applied StatisticalMethods, Vol.12 No.2, pp.336-343, 2013.
  [7] Rao.B.S. and Kantam.R.R.L., “Discriminating between log-logistic and Rayleigh distributions”, Pakistan Journal of Statistics and Operations Research, Vol. 10,No.1, pp. 1-7, 2014.
  

  Citation
  B.Srinivasa Rao, P. Sricharani, "Discriminatiing Between Dagum Distribution and Burr-III Distribution," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.104-107, 2018

• Open Access   Article

  Volatility of daily and Weekly Crude Oil Prices – A Statistical Perspective

  Kanthala Sampath Kumar, V. Swapna, S.A. JyothiRani and V.V. Hara Gopal

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.108-113, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.108113

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  Abstract
  Crude oil is a key commodity for the economy of any country. The changes in Crude oil prices are very complex and therefore, seem to be unpredictable. The effect of increasing price and its daily fluctuations affects not only the economies and financial markets but extends to reach individuals. This is because an increase in oil prices has a direct effect on petrol prices, in addition, it also affects the prices of other goods and services. Therefore, forecasting crude oil is a very important task to reduce the impact of price fluctuations, and help investors, hedgers, and individuals to make decisions when dealing with energy markets. However, one of the main challenges of the econometric models is to forecast such a seemingly unpredictable economic series. The econometric models have not been promising when used for forecasting, particularly in the case of complex series such as oil prices. Although linear and nonlinear time series models have performed much better job in forecasting oil prices, there is yet room for an improvement. If the data generating process is nonlinear, applying linear models could result in large forecast errors. Model specification in nonlinear modeling can also be very case dependent and time-consuming. This article proposes a novel technique for forecasting crude oil price based on Neural Networks. The study adopts the data on crude oil price of West Texas Intermediate (WTI). To evaluate the performance of the model, the study employs three measures, RMSE, MAE and MAPE. In this study, the forecasting accuracy of two models of neural networks, BPN and RNN are compared with the traditional econometric model. The results reveal that the proposed method outperforms the other in terms of forecast accuracy

  Key-Words / Index Term
  Neural networks, root mean squared error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE),Recurrent Neural Networks(RNN),Multi-Layer Perceptron (MLP),Oil Price and ARIMA.

  References
  [1] Bashar Al-hnaity and MaysamAbbod (2016), Predicting Financial Time Series Data Using Hybrid Model, © Springer International Publishing Switzerland.
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  [7] Haidar, Imad, Siddhivinayak Kulkarni, and Heping Pan. "Forecasting model for crude oil prices based on artificial neural networks." Intelligent Sensors, Sensor Networks and Information Processing, 2008. ISSNIP 2008. International Conference on. IEEE, 2008.
  [8] Hamdi, Manel, and ChakerAloui. "Forecasting crude oil price using artificial neural networks: a literature survey." Econ Bull 3.2 (2015): 1339-1359.
  [9] Koutroumanidis, Theodoros, Konstantinos Ioannou, and GaryfallosArabatzis. "
  Predicting fuelwood prices in Greece with the use of ARIMA models, artificial neural
  networks and a hybrid ARIMA–ANN model." Energy Policy 37.9 (2009): 3627-3634.
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  forecasting." Review of Economic Sciences 6 (2004): 161-176.
  [11] Mohamed A. Hmilad(2015), Regression analysis to forecast Malaysia’s imports of crude material, International Journal of Management and Applied Science, ISSN: 23947926, Volume-1, Issue-4.
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  [13] Rana Abdullah Ahmed (2014), Daily crude oil price forecasting model using ARIMA, Generalised autoregressive Conditional Heteroscedastic and support vector Machines, American Journal of Applied Sciences, 11 (3): 425-432
  [14] Rani, SA Jyothi, V. V. Haragopal, and M. Krishna Reddy. "Forecasting Inflation Rate
  of India using Neural Networks." International Journal of Computer Applications
  158.5 (2017).
  [15] Rani, SA Jyothi, and V. V. Haragopal. "Forecasting Exchange Rates using Neural
  Neworks."
  [16] S. Moshiri and F. Foroutan, "Forecasting nonlinear crude oilfutures prices,
  " The Energy Journal, vol. 27, pp. 81-95, 2005.
  [17] Yadav, S., & Meshram, S. (2013). Brain tumor detection using clustering method. International Journal of Computational Engineering Research, 3(4), 11-14.
  

  Citation
  Kanthala Sampath Kumar, V. Swapna, S.A. JyothiRani and V.V. Hara Gopal, "Volatility of daily and Weekly Crude Oil Prices – A Statistical Perspective," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.108-113, 2018

• Open Access   Article

  Hamiltonian Decomposition of Special Class of Ladder Graphs

  L.T. Cherin Monish Femila and S. Asha

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.114-120, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.114120

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  Abstract
  A path in a graph G that contains every vertex of G is called Hamiltonian path. A cycle in a graph G that contains every vertex of G is called a Hamiltonian cycle of G. A Hamiltonian graph is a graph that contains a Hamiltonian cycle. A graph is uniquely Hamiltonian if it contains exactly one Hamiltonian cycle. A decomposition of a graph G into Hamiltonian cycles will be called Hamiltonian decomposition of G. In this paper, we decompose some families of graphs such as ladder, triangular ladder, diagonal ladder, and circular ladder using the concept of Hamiltonian decomposition. Also using the concept of Hamiltonian decomposition of ladder graphs we decompose the diagonal ladder graph.

  Key-Words / Index Term
  Hamiltonian cycle, Hamiltonian graph, uniquely Hamiltonian, Hamiltonian decomposition, Ladder Graph.

  References
  [1] Klas Markstrom, “Even cycle decomposition of 4-regular graphs and line graphs”.
  [2] Murugesan N., Vanadhi T., “Hamiltonian decomposition of complete graphs and complete digraphs”, Global Journal of theoretical and applied Mathematics Sciences, Vol 1, No 1, (2011), ISSN 2248-9916.
  [3] Bermond J.C., “ Hamiltonian Decompositions of Graphs, Directed Graphs and Hypergraphs”, Advances in Graph Theory, Annals of Discrete Mathematics 3 (1978) 21-28.
  [4] Bondy J.A., Murty U.S.R., “Graph Theory with Applications”, 1976, Elsevier, New York.
  [5] Bosak J., “Decompositions of Graphs”, 1990, Kluwer Academic Press, Dordrecht.
  [6] Seoud. M.A., Shakir M. Salman, “On Difference Cordial Graphs”, Mathematica Aeterna, Vol. 5, 2015, no. 1, 105 – 124.
  

  Citation
  L.T. Cherin Monish Femila and S. Asha, "Hamiltonian Decomposition of Special Class of Ladder Graphs," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.114-120, 2018

• Open Access   Article

  Weibull Survival Model and Its Posterior Analysis

  G. Venkatesan, P. Saranya

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.121-137, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.121137

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  Abstract
  In this paper, the two parameter Weibull distribution is considered for estimating the Bayes risk of survival function assuming non-informative and informative priors such as Jeffrey’s, Extension of Jeffrey’s, Lognormal-Inverted Gamma and Gamma-Gamma using various type of loss functions with Squared error loss, Linex loss, General entropy loss, Quadratic loss, Weighted loss, Precautionary loss and Squared logarithmic loss. Posterior analysis done through estimating Bayes risk of survival function for combination of priors with loss functions. To illustrate the methodology, simulation study is carried out and done the parametric analysis.

  Key-Words / Index Term
  Bayes risk, Weibull distribution, Squared error loss function, General entropy loss function, Linex loss function, Precautionary loss function, Quadratic loss function, Squared logarithmic loss function, Weighted loss

  References
  [1] A.O.M. Ahmed and N.A. Ibrahim, “Bayesian Survival Estimator for Weibull Distribtuion with Censored Data”, Journal of Applied
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  [10]G. Venkatesan and P. Saranya, “Bayesian Survival Analysis of Weibull Distribution Assuming Various Loss Structure”,
  International Journal of Interdisciplinary Research and Innovations, Vol.6, issue 2, pp: 339- 353, 2018b.
  [11]G. Venkatesan and P. Saranya, “Posterior Risk Analysis of Survival Function of Weibull Distribution”, International Journal of
  Research and Analytical Reviews, Vol.5, issue 3, pp: 705-716, 2018c.
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  Citation
  G. Venkatesan, P. Saranya, "Weibull Survival Model and Its Posterior Analysis," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.121-137, 2018

• Open Access   Article

  On Neutrosophic Semi-preopen Sets and Semi-preclosed Sets in a Neutrosophic Topological Space

  Renu Thomas, Anila. S

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.138-143, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.138143

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  Abstract
  In this paper we introduce the concept of Neutrosophic semi-preopen sets and Neutrosophic semi-preclosed sets in Neutrosophic topological spaces. After giving the fundamental definitions of neutrosophic set, operations on a neutrosophic set and neutrosophic topology, we introduce Neutrosophic semi-preopen sets and Neutrosophic semi-preclosed sets and some of their properties are derived.

  Key-Words / Index Term
  Neutrosophic set, Neutrosophic topology, Neutrosophic semi-preopen sets, Neutrosophic semi-preclosed sets

  References
  [1]. K.Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 1986: 20: 87-96.
  [2]. K.Atanassov, Intuitionistic fuzzy sets, in V.Sgurev, ed., ⅶ ITKRS Session, Sofia (June 1983 central Sci. and Techn. Library, Bulg.Academy of Sciences (1984)).
  [3]. K.Atanassov, Review and new result on intuitionistic fuzzy sets, preprint IM-MFAIS-1-88, 1988.
  [4]. Florentine Smarandache A Unifying Field in Logic, Neutrosophic Logic, Neutrosophy, Neutrosophic Set, Neutrosophic Probability, American Research Press, Rehoboth, NM, 1999.
  [5]. Florentine Smarandache, Neutrosophy and Neutrosophic Logic, First International Conference on Neutrosophy, Neutrosophic Logic, Set, Probability and statistics, University of New Mexico, Gallup, NM 87301, USA(2002), smarand@unm.edu .
  [6]. P. Iswarya., Dr. K. Bageerathi, On Neutrosophic Semi-open Sets in Neutrosophic Topological Spaces, IJMTT, Vol (37) Number 3 –Sep 2016 214-223.
  [7]. A.A.Salama and S.A.Albowi, Generalized Neutrosophic sets and Generalized Neutrosophic topological spaces, Journal of Computer science and Engineering Vol(2) no:7 (2012)
  [8]. A.A.Salama and S.A.Albowi, Neutrosophic set and Neutrosophic Topological spaces, IOSR.JM. Vol (3) (2012), 31-35.
  [9]. V.Venkateswara Rao, Y. Srinivasa Rao, Neutrosophic Preopen sets and Preclosed sets in Neutrosophic Topological spaces, International journal of ChemTech Research, Vol 10 No:10, 449-458
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  Citation
  Renu Thomas, Anila. S, "On Neutrosophic Semi-preopen Sets and Semi-preclosed Sets in a Neutrosophic Topological Space," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.138-143, 2018

• Open Access   Article

  Regression-type Estimators Based on Two Auxiliary Variables of a Finite Population Mean in Two-phase Sampling

  P. A. Patel and F. H. Shah

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.5 , pp.144-152, Oct-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.144152

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  Abstract
  This paper suggests a class of regression-type estimators of a finite population mean incorporating auxiliary information on two variables at estimation stage in two-phase sampling. This class of estimators includes many known estimators. Up to the first order of approximation the mean square error (MSE) and optimal MSE are obtained and compared with the MSEs of the estimators included in this paper. Also, an empirical comparison is carried out using a Monte Carlo simulation over three natural populations.

  Key-Words / Index Term
  Auxiliary variables, mean square error, optimum estimation, regression-type estimator, simulation, two-phase sampling

  References
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  Citation
  P. A. Patel and F. H. Shah, "Regression-type Estimators Based on Two Auxiliary Variables of a Finite Population Mean in Two-phase Sampling," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.144-152, 2018