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• Open Access   Article

  A New Life Time Model: The Generalized Rayleigh-Truncated Negative Binomial Distribution

  J. Gillariose, L. Tomy

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.5 , Issue.6 , pp.1-12, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.112

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  Abstract
  In this paper, we introduced a generalized form of Rayleigh distribution. Shapes of probability density function and hazard rate function along with sub-models and statistical properties of the proposed distribution are provided. The usefulness of the new distribution is illustrated through real data set by comparing with other generalizations of the Rayleigh distribution. A reliability test plan for acceptance or rejection of a lot of products submitted for inspection with lifetimes governed by this distribution is developed and illustrated with real data set.

  Key-Words / Index Term
  Generalized family, Maximum likelihood estimation, Rayleigh distribution, Truncated negative binomial distribution

  References
  [1] V.G., Voda ̆, “Inferential procedures on a generalized Rayleigh variate (I)", Aplikace Matematiky, Vol.21, Issue.6, pp.395-–412, 1976.
  [2] V.G., Voda ̆, “Inferential procedures on a generalized Rayleigh variate (II)", Aplikace Matematiky, Vol.21, Issue.6, pp.413-–419, 1976.
  [3] G.M., Cordeiro, C.T., Cristino, E.M., Hashimoto, E.M.M, Ortega, “The beta generalized Rayleigh distribution with applications to lifetime data", Statistical Papers, Vol.54, Issue.1, pp.113–161, 2013.
  [4] A.E., Gomes, C.Q., Da-Silva, G.M., Cordeiro, E.M.M, Ortega, “A new lifetime model: The Kumaraswamy generalized Rayleigh distribution", Journal of Statistical Computation and Simulation, Vol.84, Issue.2, pp.290–309, 2014.
  [5] S.M.T.K., MirMostafaee, M., Mahdizadeh, A.J. Lemonte, “The Marshall–Olkin extended generalized Rayleigh distribution: Properties and applications", Journal of Statistical Computation and Simulation, Vol.46, Issue.2, pp.653–671, 2017.
  [6] S., Nadarajah, K., Jayakumar, M.M, Ristić, “A new family of lifetime models", Journal of Statistical Computation and Simulation, Vol.83, Issue.8, pp.1–16, 2012.
  [7] A.W., Marshall, I., Olkin, “A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families", Biometrica, Vol.84, No.3, pp.641–652, 1997.
  [8] K., Jayakumar, K.K, Sankaran, “On a generalization of Uniform distribution and its Properties", Statistica, Vol.6, Issue.3, pp.83–91, 2016.
  [9] M.G., Babu, “On a generalization of Weibull distribution and its applications", International Journal of Statistics and Applications, Vol.6, Issue.2, pp.168–176, 2016.
  [10] K., Jayakumar, K. K., Sankaran, “Generalized Exponential Truncated Negative Binomial distribution", American Journal of Mathematical and Management Sciences, Vol.36, Issue.2, pp.98–111, 2017.
  [11] K.K., Jose, R., Sivadas, “Negative binomial Marshall-Olkin Rayleigh distribution and its applications", Economic Quality Control, Vol.30, Issue.2, pp.89–98, 2015.
  [12] M.G, Badar, A.M., Priest, “Statistical aspects of fiber and bundle strength in hybrid composites", In: Hayashi T, Kawata K, Umekawa S (eds) Progress in Science and Engineering Composites, ICCM-IV, Tokyo, pp.1129–-1136, 1982.
  [13] G.M, Cordeiro, E.M.M., Ortega, D.C.C, Cunha, “The Exponentiated Generalized Class of Distributions", Journal of Data Science, Vol.11, No.1, pp.1–27, 2013.
  [14] A.J., Lemonte, W., Barreto-Souza, G.M., Cordeiro, “The Exponentiated Kumaraswamy Distribution and Its Log-Transform", Brazilian Journal of Probability and Statistics, Vol.27, No.1, pp.31–53, 2013.
  [15] A., Alzaatreh, C., Lee, F., Famoye, “A New Method for Generating Families of Continuous Distributions", Metron, Vol.71, Issue.1, pp.63–79., 2013.
  [16] M., Amini, S., MirMostafaee, J., Ahmadi, “Log-Gamma-Generated Families of Distributions", Statistics: A Journal of Theoretical and Applied Statistics, Vol.48, Issue.4, pp.913–932., 2013.
  [17] S. Rajagopal, K. Vijayadevi, "A Hybrid Group Acceptance Sampling Plan for Lifetimes Based on Transmuted Rayleigh Distribution", International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.77-94, 2018
  [18] A., Wood, “Predicting software reliability", IEEE Transactions on Software Engineering, Vol.22, pp.69–77., 1996
  

  Citation
  J. Gillariose, L. Tomy, "A New Life Time Model: The Generalized Rayleigh-Truncated Negative Binomial Distribution," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.1-12, 2018

• Open Access   Article

  A Mathematical Core and Peripheral Layer Model of Blood Flow Through Stenosed Artery

  Rajesh Shrivastava, R.S. Chandel, Ajay Kumar, Keerty Shrivastava, Sanjeet Kumar

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.13-20, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.1320

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  Abstract
  In this paper we investigate a mathematical model on the peripheral layer model for blood flow through stenosed artery has been developed. The information about the geometry has been presented to analysis the severity of stenosis, so we have proposed a trapezium-shaped geometry of mild asymmetric stenosis. The blood flow with artery has been represented by a two-layered model consisting of a core layer and a peripheral layer. It has been observed that the resistance to flow and wall shear stress increase as the peripheral layer viscosity increases. In this paper, the analytical expressions have been obtained for resistance to flow and wall shear stress. The impact of concerned parameters has been examined and depicted through the graphs for different values of interest. The model can be used for approximation of diseased arterial system.

  Key-Words / Index Term
  Physiological flow, Stenosis, arterial wall, blood flow, peripheral layer viscosity

  References
  [1] D. Biswas, “Blood Flow Models- A Comparative Study”, Mittal Publication, New- Delhi. (2000).
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  [8] H. Kumar, R. S. Chandel, S. Kumar and S. Kumar, “A mathematical model for blood flow and cross-sectional area of an artery”, International Journal of Mathematical Sciences & Engg. Applications, vol. 7 (6), pp. 389-400, (2013).
  [8] H. Kumar, R. S. Chandel, S. Kumar and S. Kumar, “A mathematical model for different shapes of stenosis and slip velocity at the wall through mild stenosis artery”, Advances in Applied Mathematical Biosciences, vol.5 (1), pp. 9-18, (2014).
  [9] R. N. Pralhad and T. J.Schultz, “Two-layered blood flow in stenosed tube for different diseases”, Biorheology, vol.25, pp. 715-726, (1988).
  [10] Sarifuddin, S. Chakravarty, P. K. Mandal and G. C Layek, “Numerical simulation of unsteady generalized Newtonian blood flow through differently shaped distensible arterial stenoses”, Journal of Medical Engineering & Technology, vol. 32, pp. 385-399, (2008).
  [11] J. B. Shukla, R. S. Parihar and S.P. Gupta, “Effects of peripheral layer viscosity on blood flow through the artery with mild stenosis”, Bulletin of Mathematical Biology, vol.42, pp. 797-805, (1980) (a).
  [12] J. B. Shukla, R. S. Parihar and B.R.P. Rao, “Effects of stenosis on non-Newtonian flow of the blood in an artery”, Bulletin of Mathematical Biology, vol. 42, pp. 283-294, (1980) (b).
  [13] A. M. Siddiqui, T. Haroon, A. Mirza and A. R. Ansari, “Steady Non-isothermal two-dimensional flow of Newtonian fluid in a stenosed channel”, Theory and Applications of Mathematics & Computer Science, vol. 3(2), pp. 75-92, (2013).
  [14] L.M. Srivastava, and V.P. Srivastava, “On two phase model of pulsatile blood flow with entrance effects”, Biorheology, vol.20, pp. 761-777, (1983).
  [15] V.P. Srivastava, (1996): “Two-phase model of blood flow through stenosed tubes in the presence of a peripheral layer: Applications”, Journal of Biomechanics, vol.29 (10), pp. 1377-1382, (1996).
  [16] V.K. Sud, R. S. Srinivasan J. B. Charles, J.B. and M. W. M. S. Bungo, “Mathematical modeling of the human cardiovascular system in the presence of stenosis”, Phys. Med. Biol., vol.38, pp. 369-378, (1993).
  

  Citation
  Rajesh Shrivastava, R.S. Chandel, Ajay Kumar, Keerty Shrivastava, Sanjeet Kumar, "A Mathematical Core and Peripheral Layer Model of Blood Flow Through Stenosed Artery," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.13-20, 2018

• Open Access   Article

  Bayesian Methods of Estimation of HIV Replication in a 〖CD〗_4^+ T Using Rayleigh Distribution under the Various Loss Function Approach

  G. Meenakshi, S. Lakshmi Priya

  Review Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.21-37, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.2137

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  Abstract
  Human Immuno Deficiency Virus (HIV) infection of humans represents a complex biological system and a great challenge to public health. Novel approaches for analysis and prediction of the infection dynamics based on a multi-scale integration of virus ontogeny and immune reactions are needed to deal with the system complexity. It is known from the literature survey that HIV replication models are represented as first order differential equations. It gives only rate of change of HIV replication with respect to time. But, the parameter estimation and analytical solution of the differential equations are very difficult. So, in this paper, the Bayesian Methodology is used to estimate the HIV replication for the future period per infected CD_4^+ T cell. In the Bayesian Methodology, the prior and current sample information simultaneously is used to obtain the posterior estimation of the parameter which gives effective information for future. In the HIV life cycle, there are seven different stages, such as binding, fusion, reverse transcription, integration, replication, assembly and budding. At the stage of binding, the various viral components bind with the CD_4^+ T cell. Such as a-Surface glycoprotein (gp120),b - transmembrane glycoprotein (gp41) CCR5, c - reverse transcriptase (P66 /P51) are considered to estimate the HIV replication. Therefore, in this paper, a new risk function derived to use the components a, b and c. Finally, posterior parameter of HIV replication in a CD_4^+ T cell is estimated. The estimated parameter is compared with some standard parameter using various loss functions.

  Key-Words / Index Term
  HIV Replication, New loss function, Bayes estimator, Risk function

  References
  [1]. Siddiqui, M.M. Some problems connected with Rayleigh distribution. J. Res. National Bureau of Standards, vol 66D, pp167-174, 1962.
  [2]. Polovko, A.M. (1968) Fundamentals of reliability theory, New York: Academic Press.
  [3]. Dyer, D.D. & Whisenand, C.W. Linear unbiased estimator of the Rayleigh distribution – Part-I: Small sample theory for censored order statistics. IEEE Transactions on Reliability R-22 (1), pp27-32, 1973.
  [4]. Grossman, Z.; Meier-Schellersheim, M.; Sousa, A.E.; Victorino, R.M.; Paul, W.E. CD4+ T cell depletion in HIV infection: Are we closer to understanding the cause? Nat. Med., vol 8, pp 319–323, 2002.
  [5]. R. Paul Duffin And Richard H. Tullis “Mathematical Models of the Complete Course of HIV Infection and AIDS” Journal of Theoretical Medicine, 2002 Vol. 4 (4), pp. 215–221, 2002.
  [6]. Dominik Wodarz1 and Martin A. Nowak “Mathematical models of HIV pathogenesis and treatment” BioEssays 24:1178–1187, _ 2002 Wiley Periodicals, Inc.
  [7]. Rebecca V. Culshaw “Mathematical Modeling of AIDS Progression: Limitations, Expectations, and Future Directions” Journal of American Physicians and Surgeons Volume 11 Number 4 Winter 2006.
  [8]. Grossman, Z.; Meier-Schellersheim, M.; Paul,W.E.; Picker, L.J. Pathogenesis of HIV infection: What the virus spares is as important as what it destroys. Nat. Med., vol 12, pp 289–295, 2006
  [9]. Levy, J.A. HIV and the Pathogenesis of AIDS, 3rd ed.; ASN Press: Washington, DC, USA, 2007.
  [10]. Sanku Dey “Minimax Estimation of the Parameter of the Rayleigh Distribution under Quadratic Loss Function”data science journal volume 7DOI: 10.2481/dsj.7.23 • Source: DBLP,2008.
  [11]. Chereshnev, V.A.; Bocharov, G.; Bazhan, S.; Bachmetyev, B.; Gainova, I.; Likhoshvai, V.; Argilaguet, J.M.; Martinez, J.P.; Rump, J.A.; Mothe, B.; et al. Pathogenesis and treatment of HIV infection: The cellular, the immune system and the neuroendocrine systems perspective. Int. Rev. Immunol., vol 32, pp 282–306, 2013.
  [12]. Kent, S.J.; Reece, J.C.; Petravic, J.; Martyushev, A.; Kramski, M.; De Rose, R.; Cooper, D.A.; Kelleher, A.D.;Emery, S.; Cameron, P.U.; et al. The search for an HIV cure: Tackling latent infection. Lancet Infect. Dis.,vol 13, pp 614–621, 2013.
  [13]. Esteban A.Hernandez-Vargas , RichardH.Middleton (2013) “Modeling the three stages in HIV infection” Journal of Theoretical Biology 320 (2013) 33–40.
  [14]. A. Ahmed and S.P Ahmad at.el. “Bayesian Analysis of Rayleigh Distribution” International Journal of Scientific and Research Publications, Volume 3, Issue 10, October 2013 1 ISSN 2250-3153, 2013.
  [15]. R. Lakshmajayam and G.Meenakshi “HIV Replication Model for the Succeeding Period of Viral Dynamic Studies In Aids Clinical Trials” International Journal Of Mathematics And Statistics Invention (IJMSI) Volume 2 Issue 10 PP-28-36, 2014.
  [16]. R. Lakshmajayam and G. Meenakshi “A Statistical Model for HIV Replication in the Infected CD4+T – Cells” International Journal of Recent Scientific Research Vol. 6, Issue 6, pp.4858-4868, 2015.
  [17]. R. Lakshmajayam and G.Meenakshi “Determination of Average HIV Replication in the Blood Plasma Using Truncated Logistic Distribution” International Journal of Recent Research in Interdisciplinary Sciences (IJRRIS) Vol. 2, Issue 4, pp: (48-58), 2015.
  [18]. Paresh Sanat and R. S. Srivastava “Bayesian Analysis of Rayleigh Distribution Under Quasi-Prior for Different Loss Functions” International Journal of Science and Research (IJSR) Volume 5 Issue 6, June 2016.
  [19]. J.T. Ferreira et.al “Objective Bayesian Estimators For The Right Censored Rayleigh Distribution:Evaluating The Al-Bayyati Loss Function” Statistical Journal ,Volume 14, Number 4, October, 433–454, 2016
  [20]. Melkova, Z.; Shankaran, P.; Madlenakova, M.; Bodor, J. Current views on HIV-1 latency, persistence, and cure. Folia Microbiol., pp1–15, 2016.
  [21]. G Meenakshi and S Lakshmi Priya “A statistical modelling for viral replication in the CD4+Tcells dynamic by bayesian methodology” International journal of statistics and applied mathematics, vol 2, issue 2, pp43-49, 2017.
  [22]. Isha Gupta “Bayesian and E- Bayesian Method of Estimation of Parameter of Rayleigh Distribution- A Bayesian Approach under Linex Loss Function” International Journal of Statistics and Systems ISSN 0973-2675 Volume 12, Number 4, pp. 791-796, 2017.
  [23]. G Meenakshi and S Lakshmi Priya “Statistical model for HIV replication in the CD4+Tcells” Scholars Journal of Applied Medical Sciences (SJAMS), Vol6 (3):PP., 1123-1130, 2018.
  [24]. Silvia Pagliariniand and Andrei Korobeinikov “A mathematical model of marine bacteriophage evolution” Royal society open science rsos.royalsocietypublishing.org R. Soc. open sci. 5: 171661, 2018.
  

  Citation
  G. Meenakshi, S. Lakshmi Priya, "Bayesian Methods of Estimation of HIV Replication in a 〖CD〗_4^+ T Using Rayleigh Distribution under the Various Loss Function Approach," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.21-37, 2018

• Open Access   Article

  Mixture of Exponential and Weighted Exponential Distribution: Properties and Applications

  A. A. Bhat, Sofi Mudasir, S.P. Ahmad

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.38-46, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.3846

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  Abstract
  In this paper, a new model entitled as “Mixture of Exponential and Weighted Exponential Distribution (MEWED): Properties and Applications” is obtained. Some statistical properties of the new model are unfolded. The method of maximum likelihood is used to estimate the parameters of the proposed model. The usefulness of the proposed model is illustrated by using real life data sets.

  Key-Words / Index Term
  Exponential Distribution, Weighted Exponential Distribution, Maximum Likelihood Estimation and Real Life Data

  References
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  [3] Adnan, M.A.S. and H. Kiser, “Some Laplace Mixture Distributions”, Journal of Applied Statistics and Sciences, Vol. 17, pp.549-560, 2009.
  [4] Z. A. Kamaruzzaman, Z. Isa, and M. T. Ismail, “Mixtures of Normal Distributions, Application to Bursa Malaysia Stock Market Indices”, World Applied Science Journal, Vol. 16, pp.781-790, 2012.
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  [6] B. Marco, B. Roberto and E. Giuseppe, “On Maximum Likelihood Estimation of a Pareto Mixture”, Computational Statistics, Vol. 28, pp.161-178, 2013.
  [7] P.G. Sankaran and M.T. Nair, “On a Finite Mixture of Pareto Distribution”, Calcutta Statistical Association Bulletin, Vol.57, pp.67-83, 2005.
  [8] S. Suksaengrakcharoen, W. Bodhisuwan, “A New Family of Generalized Gamma Distribution and its Application”, Journal of Mathematical Statistics, Vol. 10, No.2, pp.211-220, 2014.
  [9] M. K. Roy, M. F. Imam, and J. C. Paul, “Gamma Mixture of Normal Moment Distribution”, International Journal of Statistical Sciences, Vol. 1, pp.20–24, 2002.
  [10] M. K. Roy, M. R. Zaman, and N. Akter, “Chi-square Mixture of Gamma Distribution”, Journal of Applied Sciences, Vol. 5, No.9, pp.1632–1635, 2005.
  [11] M. K. Roy, M. E. Haque, and B. C. Paul, “Erlang Mixture of Normal Moment Distribution”, International Journal of Statistical Sciences, Vol. 6, pp.29–37, 2007.
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  [14] M. H. Tahir, G. M. Cordeiro, M. Mansoor and M. Zubair, “The Weibull-Lomax Distribution: Properties and Applications”, Hacettepe Journal of Mathematics and Statistics, Vol. 44, No.2, pp.461-460, 2015.
  [15] M. E. Ghitany, B. Atieh and S. Nadarajah, “Lindley Distribution and its Application”, Mathematics and Computers in Simulation, Vol.78, pp.493-506, 2008.
  

  Citation
  A. A. Bhat, Sofi Mudasir, S.P. Ahmad, "Mixture of Exponential and Weighted Exponential Distribution: Properties and Applications," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.38-46, 2018

• Open Access   Article

  Can India Achieve SDGs target related to IMR level till 2030? : A Bayesian Study

  Abhinav Singh, Anurag Verma, Gyan Prakash Singh, Pramendra Singh Pundir

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.47-52, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.4752

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  Abstract
  India is playing an important role in shaping sustainable development in the world. In this article, is an attempt to explore, the Bayesian inference with the application of projection for future levels of Infant Mortality Rates (IMR) for India, through the Markov chain Monte Carlo simulation technique, using a nonlinear growth model. The main aim of the study is to examine the preparation of India to evaluate its progress towards Sustainable Development Goals (SDGs) target related to IMR under Bayesian Approach. The findings of this study show that India is not in a position to achieve the IMR target in the SDGs.

  Key-Words / Index Term
  IMR, MCMC, Bayesian Approach, SDGs, Probability, OpenBUGS

  References
  [1] Reidpath, D. D., & Allotey, P. (2003). Infant mortality rate as an indicator of population health. Journal of Epidemiology & Community Health, 57(5), 344-346.
  [2] Registrar General, I. (2018). Compendium of India’s fertility and mortality indicators 1971-2013 based on The Sample Registration System (SRS). New Delhi Registrar General: India.
  [3] Registrar General, India. (2014). Sample Registration System Statistical Report, 2013. Report No. 1 of 2013. New Delhi: Controller of Publications.
  [4] Registrar General, India. (2015). Sample Registration System Statistical Report, 2014. Report No. 1 of 2014. New Delhi: Controller of Publications.
  [5] Registrar General, India. (2016). Sample Registration System Statistical Report, 2015. Report No. 1 of 2015. New Delhi: Controller of Publications.
  [6] Registrar General, India. (2017). Sample Registration System Statistical Report, 2016. Report No. 1 of 2016. New Delhi: Controller of Publications.
  [7] United Nations Sustainable Development (2017). The Sustainable Development Goals Report 2017.
  [8] United Nations Children`s Fund(UNICEF) The state of the world`s children 2008: Child survival. New York: UNICEF; 2008. Available: http://www.unicef.org/sowc08/docs/sowc08.pdf. Accessed 2011 Jan 13.
  [9] Singh, A., Pathak, P. K., Chauhan, R. K., & Pan, W. (2011). Infant and child mortality in India in the last two decades: a geospatial analysis. PLoS One, 6(11), e26856.
  [10] Ramachandran, P. (2010). Nutrition and child survival in India. The Indian Journal of Pediatrics, 77(3), 301-305.
  [11] International Institute for Population Sciences. (2017). India National Family Health Survey (NFHS-4), 2015-16 (Vol. 1). International Institute for Population Sciences.
  [12] Singh, O. P., Pandey, G. S., & Rahul. (2007). Population Projection of India (2001–2051) Using MCMC Technique in Bayesian Inference. American Journal of Mathematical and Management Sciences, 27(1-2), 139-152.
  [13] Rahul, S. G., & Singh, O. P. (2009). Population projection of Kerala using Bayesian methodology. Asian Journal of Applied Sciences, 2(4), 402-413.
  [14] Lunn, D., Jackson, C., Best, N., Thomas, A., & Spiegelhalter, D. (2012). The BUGS book: A practical introduction to Bayesian analysis. CRC press.
  [15] Gelman, A., Stern, H. S., Carlin, J. B., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. Chapman and Hall/CRC.
  

  Citation
  Abhinav Singh, Anurag Verma, Gyan Prakash Singh, Pramendra Singh Pundir, "Can India Achieve SDGs target related to IMR level till 2030? : A Bayesian Study," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.47-52, 2018

• Open Access   Article

  A Generalized Form of G^*-Open Sets

  Rajesh Kumar Tiwari, J. K. Maitra, Ravi Vishwakarma

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.53-58, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.5358

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  Abstract
  Generalization of sets in topological space is a very important concept in modern mathematics for structural oriented techniques. To enrich the structure and properties of generalized open sets, we define the notion of p^*-open sets by using topological space and generalized topological space both on the set X. The main aim of this paper is to define p^*-open sets and its generalized sets p^*-I-open sets, I_(p^* )-open sets and weakly I_(p^* )-open sets in a space (both topological space and generalized topological space) via ideal with illustrative examples. Also, we study the significant properties of newly defined open sets in the set X.

  Key-Words / Index Term
  Generalized topology, ideal topological spaces, G-open sets, p^*-open sets, I_(p^* )-open sets

  References
  Levin, N., Semi-open sets and Semi-continuity in topological spaces, Amer. Math. Monthly, 70, 36-41, 1963.
  Dontchev, J., On pre-I-open sets and a decomposition of I-continuity, Banyan Math. J., 2, 1996.
  Njasted, O., On some classes of nearly open sets, Pacific J. Math. Sci., 10(3), 393-396, 1965.
  Abd El-Monsef, M. E., El-Deep, S.N., & Mahmoud, R.A., β-open set and β-continuous mapping. Bull. Fac. Sci. Assiut univ., 12, 77-90, 1983.
  Csaszar, A., Generalized topology, generalized continuity. Acta Math. Hungar., 96, 351-357, 2002.
  Csaszar, A., Generalized open sets in generalized topologies. Acta Math. Hungar, 106, 53-66, 2005.
  Dontchev, J., On pre-I-open sets and a decomposition of I-continuity, Banyan Math. J., 2, 1996.
  Roy B., Sen R., Generalized semi-open and pre-semi-open sets via ideals, Transactions of A. Razmadze Mathematical institute, 127, 95–100, 2015.
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  Hatir E., T. Noiri, On semi-I-open set and semi-I-continuous functions, Acta Math. Hungar. 107, 345–353, 2005.
  Mukherjee M. N., B. Roy, R. Sen, On extension of topological spaces in terms of ideals, Topology Appl. 154, 3167–3172, 2007.
  Jankovic D., Hamlett T.R., New topologies from old via ideals, Amer. Math. Monthly 97 295–310, 1990.
  Roy B., Sen R., On a type of decomposition of continuity, Afr. Math. 26, 153–158, 2015.
  

  Citation
  Rajesh Kumar Tiwari, J. K. Maitra, Ravi Vishwakarma, "A Generalized Form of G^*-Open Sets," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.53-58, 2018

• Open Access   Article

  Bioeconomic Modelling of a Low Growth Rate Fish Species Obeying Modified Logistic Growth Function: A Comparative Study With Schaefer Model

  Tarun Pradhan

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.59-67, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.5967

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  Abstract
  This paper develops a mathematical model for growth and exploitation of a fish species obeying modified logistic growth function. A low growth rate species compared to the growth rate which is directly proportional to the population density is considered. Considering the harvesting rate as the catch-per-unit-effort (CPUE) hypothesis, conditions for existence of the biological equilibrium and the bioeconomic equilibrium are studied. Maximum sustainable yield is discussed with graphical representation. The nature of stability of the dynamical and the bionomic steady states are also examined. The results are compared with those of the Schaefer model. The results are illustrated and explained with the help of numerical example.

  Key-Words / Index Term
  Modified logistic growth functions; maximum sustainable yield; bioeconomic equilibrium; catch-per-unit-effort hypothesis; Schaefer model; biotechnical productivity

  References
  [1] Schaefer, M.B., 1954. Some aspects of the dynamics of populations important to the management of the commercial marine fisheries, Bull. Inter-American Trop. Tuna Comm.I, 27-56.
  [2] Clark, C.W., 1976. Mathematical Bioeconomics: The Optimal Management of Renewable Resources, John Willy and Sons, New York.
  [3] Verhulst, P.F., 1838. Notice Sur la loi que to population suit dans son accroissment, Correspondence Mathematique et Physique, 10,113-121.
  [4] Pradhan, T., Chaudhuri, K.S.,1999. A dynamical reaction model of a rwo-species fishery with taxation as a control instrument; a capital theoretic analysis, Ecological Modelling, 121,1-16.
  [5] Ganguly, S., Chaudhuri, K.,1991. On an extension of Schaefer model, Ecological Modelling, 55, 141-150.
  [6] Ray, J., Pradhan, T., 2014. A dynamic reaction model of an inshore-offshore fishery with taxation as a control instrument, IOSR Journal of Mathematics (IOSR-JM), 10, 13-20.
  [7] Chaudhuri, Kripasindhu, Johnson Thomas, 1990. Bieconomic Dynamics of a Fishery Moleded as an S-system, Mathematical Biosciences, 99, 231-249.
  [8] Pradhan, T., Chaudhuri, K.S., 1999. Bioeconomic Modelling of Selective Harvesting in an Inshore-Offshore Fishery, Differential Equations and Dynamical Systems, 7(3), 305-320.
  [9] Smith, J.M., 1974. Models in Ecology, Cambridge University Press, England.
  [10] Pradhan, T., Chaudhuri, K.S., 1998. Bioeconomic modeling of a single species fishery with Gompertz law of growth, Journal of Biological Systems, 6(4), 393-409.
  [11] May, R.M., 1973. Stability and complexity in Model Ecosystem, Monographs in population Biology VI, Princeton University Press (Princeton, N.J.).
  [12] Ray, J., Pradhan, T., 2017. Dynamical behaviour of an exploited fish species obeying modified logistic growth function with taxation as a control instrument, Advances in Dynamical Systems and Applications, 12(2), 149-161.
  

  Citation
  Tarun Pradhan, "Bioeconomic Modelling of a Low Growth Rate Fish Species Obeying Modified Logistic Growth Function: A Comparative Study With Schaefer Model," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.59-67, 2018

• Open Access   Article

  CASP for Truncated Pareto Weibull Distribution Based on CUSUM Schemes and its Optimization

  M. C. Chandra Prasad, P. Mohammed Akhtar, G.Venkatesulu

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.68-74, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.6874

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  CUSUM charts are firstly introduced by E. S. Page, in 1954. They are used to identify a sudden and persistent change in the production average. Many researchers worked in this area and developed optimization techniques by updating the previous one. In this direction, all the optimization techniques are developed under the assumption that variable with regard to quality characteristic is distributed according to certain probability law. In the present study, we assume that variable under study follows the Truncated Pareto Weibull Distribution and its Optimization of CASP-CUSUM Schemes. Critical comparison is made based on the obtained numerical results.

  Key-Words / Index Term
  CASP – CUSUM Schemes, O C Curve, Optimal Truncated Point, Truncated Pareto Weibull Distribution

  References
  [1]. Hawkins, D.M. (1992). “A Fast Accurate Approximation for Average Lengths of CUSUM Control Charts”. Journal on Quality Technology, Vol. 24(No.1): 37-43.
  [2]. Kakoty, S and Chakravaborthy, A.B., (1990), “A Continuous Acceptance Sampling Plan for Truncated Normal distribution based on Cumulative Sums”, Journal of National Institution for Quality and Reliability, Vol.2 (No.1): 15-18.
  [3]. Vardeman, S. And Di-ou Ray. (1985). “Average Run Length for CUSUM schemes where observations are Exponentially Distributed”, Technometrics, vol. 27 (No.2):145-150.
  [4]. Lonnie, C. Vance. (1986). “Average Run Length of CUSUM Charts for Controlling Normal means”. Journal of Quality Technology”, Vol.18:189-193.
  [5]. Akhtar, P. Md. and Sarma. K.L.A.P.(2004). “Opimization of CASP-CUSUM Schemes based on Truncated Gamma Distribution”. Bulletin of Pure and applied sciences, Vol-23E (No.2):215-223.
  [6] Narayana Muthy, B. R, Akhtar, P. Md and Venkataramudu, B.(2012) “Optimization of CASP- CUSUM Schemes based on Truncated Log-Logistic Distribution”. Bulletin of Pure and Applied Sciences, Vol-31E (Math&Stat.): Issue (No.2) pp243-255.
  [7] B.Sainath, P.Mohammed Akhtar, G.Venkatesulu, and Narayana Muthy, B. R, (2016) “CASP CUSUM Schemes based on Truncated Burr Distribution using Lobatto Integration Method”. IOSR Journal of Mathematics (IOSR-JM), Vol-12, Issue 2, pp54-63.
  [8]. Venkatesulu.G, Akhtar.P.Md, Sainath.B, Narayana Murthy B.R.(2017), “Truncated Gompertz Distribution and its Optimization of CASP-CUSUM Schemes” Journal of Research in applied Mathematics, Vol-3, Issue7, pp:19-28.
  [9]. Venkatesulu.G, Akhtar.P.Md, Sainath.B, Narayana Murthy B.R.(2018), “Continuous Acceptance sampling plans for Truncated Lomax Distribution Based on CUSUM schemes” International Journal Mathematics Trends and Technology (IJMTT) – Vol -55 , No-3.
  [10]. M. H. Tahir, Gauss M. Cordeiro, Ayman Alzaatreh, M. Mansoor and M. Zubair. “A New Weibull-Pareto Distribution: Properties and Applications”. Vol-45, 2016.
  [11].Beattie, B.W.(1962). “A Continuous Acceptance Sampling procedure based upon a cumulative Sums Chart for a number of defective”. Applied Statistics, Vol. 11 (No.2): pp: 137-147.
  [12]. Page, E.S.,(1954) “Continuous Inspection Schemes”, Biometrika, Vol. XLI, pp. 104- 114.
  

  Citation
  M. C. Chandra Prasad, P. Mohammed Akhtar, G.Venkatesulu, "CASP for Truncated Pareto Weibull Distribution Based on CUSUM Schemes and its Optimization," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.68-74, 2018

• Open Access   Article

  Statistical Model for Poverty Index

  S. S. Singh, S. S. Singh, S. P. Singh

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.75-80, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.7580

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  Abstract
  The incidence of poverty measured in Poverty Gap (PG) introduced by Foster-Greer-Thorbecke (FGT) is adopted as poverty indicator and the Lorenz curve and Gini-concentration co-efficient were used to explain the income inequality of households in the selected village. A village, called Thanga Karang comprising of 257 households, is considered as selected village. Household survey was conducted to collect the data related to poverty. A statistical analysis of PG is carried out and fitted to the beta distribution with parameters α and β by method of moments and the method of maximum likelihood. The statistically significant values of α and β are respectively α ̂= 0.2989 and β ̂= 3.4722 by method of moments; α ̂= 1.459 and β ̂= 3.001 by method of maximum likelihood. Therefore the PG, an index of poverty is best fit to the assumed model (i.e. Beta distribution). The Gini-concentration co-efficient is found to be 0.5253. It suggests that income inequality among the household is observed in 52.53 percentages.

  Key-Words / Index Term
  Poverty, Head Count Ratio, Poverty Gap, Lorenz curve and Gini-concentration co-efficient

  References
  [1] Durrheim, Robyn von Maltzahn and Kevin. 2008. "Is Poverty Multidimensional? A Comparison of Income and Asset Based Measures in Five Southern African Countries." Social Indicators Research, Vol. 86, No.1, pp-149-162. doi: 10.1007/sl.
  [2] James Foster, Joel Greer and Erik Thorbecke. 1984. "A Class of Decomposable Poverty Measures." Econometrica , Vol. 52 ,No.3,pp-761-766.
  [3] Pan, Mridul Saggar and Indranil. 1994. "SCs and STs in Eastern India: Inequality and Poverty Estimates." Economic and Political Weekly ,Vol. 29, No.10, pp-567-569+571-574.
  [4] Singh, Salam Sovachandra. 2017. "Measurement of Poverty: Its nature and Dimensions." Research Line, pp-89-96.
  [5] Singh, Thiyam Bharat. 2007. "Poverty in Manipur." Economic and Political Weekly, Vol. 42, No.3, pp-251-254.
  [6] Tendulkar, K. Sundaram and Suresh D. 2003. "Poverty in India in the 1990s An Analysis of Changes in 15 Major States 2003." Economic and Political Weekly, Vol.38, No.14, pp-1385-1393.
  [7] Yu, Jiantuo. June 2013. "Multidimensional Poverty in China: Findings Based on the CHNS." Social Indicators Research Published by: Springer, Vol. 112, No.2, pp-315-336. doi: 10.1007/s.
  
  

  Citation
  S. S. Singh, S. S. Singh, S. P. Singh, "Statistical Model for Poverty Index," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.75-80, 2018

• Open Access   Article

  On Star Decomposition and Star Number of Some Graph Classes

  J.K. Sebastian, J.V. Kureethara, S.Naduvath, C. Dominic

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.6 , pp.81-85, Dec-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.8185

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  Abstract
  Graph decomposition is a partition of graph into its subgraphs. Star decomposition is the decomposition of the graph into stars. In this paper we define a parameter, the star number of graphs, as the minimum number of end vertices of stars in a star decomposition of a graph. We determine this parameter for certain fundamental graph classes.

  Key-Words / Index Term
  Decomposition, star decomposition, pendant number, star number

  References
  [1] T. Ae, S. Yamamoto, N Yoshida, “Line-disjoint Decomposition of Complete Graph into Stars”, Journal of Combinatorial Theory Series B. (to appear),1970.
  [2] P. Cain, “Decomposition of Complete Graphs into Stars”, Bulletin of the Australian Mathematical Society, Vol. 10,No.1, pp.23-30, 1974.
  [3] G. Chartrand, P. Zhang, “Introduction to Graph Theory”, Tata McGraw-Hill Publishing Limited, India, 2006.
  [4] 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, No.5, pp.114-120, 2018.
  [5] J. A. Gallian, “A Dynamic Survey of Graph Labeling”, ElectronicJournal of Combinatorics, Vol.16, No.6, pp.1-219, 2009.
  [6] F. Harary, “Graph Theory”, Addison-Wesley, Reading, MA, 1969.
  [7] F. Harary, A. J. Schwenk, “The number of Caterpillars”,Discrete Mathematics, Vol.6, No.4, pp.359-365, 1973.
  [8] P. C. Hogarth, “Decomposition of Complete Graphs into 6-stars and into 10-stars”, Combinatorial Mathematics III, pp.136-142, 1975.
  [9] T. A. Mangam, and J. V. Kureethara, “Diametral Paths in Total Graphs of Complete Graphs, Complete Bipartite Graphs and Wheels”, International Journal of Civil Engineering & Technology, Vol.8, No.5, pp.1212-1219, 2017.
  [10] B. Neggazi, M. Haddad, H. Kheddouci “A new self-stabilizing algorithm for maximal p-star decomposition of general graphs”, Information Processing Letters, Vol.115, No.11, pp.892-898, 2015.
  [11] J.K. Sebastian, J.V. Kureethara, “A Note on d-decomposition of Smaller Graphs”,communicated, 2018.
  [12] J. K. Sebastian, J. V. Kureethara,“Pendant Number of Graphs”, International Journal of Applied Mathematics,Vol.31, No.5, pp.679-689, 2018.
  [13] J. K. Sebastian, J. V. Kureethara, N.K. Sudev, C. Dominic, “A study on Pendant Number of Graphs”, communicated, 2018.
  [14] J. K. Sebastian, J. V. Kureethara, N. K. Sudev, C. Dominic, “On the Pendant Number of Some Graphs”, communicated, 2018.
  [15] J.K. Sebastian, J.V. Kureethara, N.K. Sudev, C. Dominic, “Some Properties of Pendant Number of Graphs”, communicated, 2018.
  [16] B.S. Sunoj, T.K. Mathew Varkey, "One Raised Product Prime Labeling of Some Star Related Graphs", International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, No.3, pp.18-23, 2018.
  [17] M. Tarsi, “On the Decomposition of a Graph into Stars”, Discrete Mathematics, Vol.36, No.3, pp.299-304, 1981.
  [18] J. Varghese, A. Antonysamy, “On double continuous monotonic decomposition of graphs”, Journal of Computer and Mathematical Sciences Vol.1, No.2, pp.103-273, 2010.
  [19] J. Varghese and A. Antonysamy, “On modified continuous monotonic decomposition of tensor product of graphs”, Int. J. Contemp. Math. Sciences, Vol.5, No.33, pp.1609-1614, 2010.
  [20] X. Zhang, H. Zhang, “Some Graphs Determined by Their Spectra”, Linear Algebra and its Applications,Vol.431,No.9,pp.1443-1454, 2009.
  [21] Y. Zhao, B. Wu, “Star Decomposition of Graphs”, Discrete Mathematics, Algorithms and Applications,Vol. 7, No.2, pp.1-9, 2015.
  

  Citation
  J.K. Sebastian, J.V. Kureethara, S.Naduvath, C. Dominic, "On Star Decomposition and Star Number of Some Graph Classes," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.6, pp.81-85, 2018