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• Open Access   Article

  Proposed Indian squad for ICC-T20 World Cup-2020 by using a new “HD-CLFPR with E-DNIT” Mathematical model

  Udaykumar S. Kashid, Archana U. Kashid, Saurabh N. Mehta, Vineeta Basotia

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.5 , pp.1-15, Oct-2020

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  In sports entity, especially in Indian Premier League (IPL) the performance evaluation and ranking of the players is a process often with data of incomplete information under uncertain environment. Mainly due to the evolution of the new auction rules and development in advanced new technologies in sports field, the complexity of the decision problem is increased for every year. Hence, the prevailing MCDM methodologies fail to handle such situations. Hence, in this paper we have proposed balanced Indian men’s team for ICC-T20 WC to be held in Australia from 18 October to 15 November 2020((Recently ICC confirmed that the Men’s T20 WC in Australia 2020 has been postponed due to the ongoing COVID-19 Pandemic and now India will host it as ‘ICC Men’s T20 World Cup 2021’) by applying new developed hybrid D-Numbers extended Consistent Linguistic Fuzzy Preference Relation with Enhanced D-Numbers Integral Theorem (HD-CLFPR with E-DNIT) as a Mathematical model[1]. The main objective of this paper is in three folds: In first fold , the weight of selected criteria for the players performance evaluation is prioritized by applying a new proposed MCDM model “ HD-CLFPR with E-DNIT” to allocate incomplete information data to complete information data under uncertain situation[1]. In second fold, we have applied MCDM model “TOPSIS” based on Euclidean distance measurement to select the best alternatives for ranking of the players. In third fold, we have predicted Indian squad of 16 members with 2 reserved players for ICC-T20-WC-2020 as per the ranking obtained from proposed model[1].

  Key-Words / Index Term
  HD-CLFPR with E-DNIT; MCDM, Decision Theory; Fuzzy Preference Relations; D-Numbers Theory; IPL

  References
  [1] Udaykumar S. Kashid, Archana U. Kashid, Saurabh N. Mehta, Vineeta Basotia “A New Hybrid D-Numbers extended Consistent Linguistic Fuzzy Preference Relation with Enhanced DNIT model for selection of Bowlers in IPL-2019”, ISROSET’s “International Journal of Scientific Research in Mathematical and Statistical Sciences”(IJSRMSS), Vol.7, Issue.3, pp.08-22, June 2020.
  DOI: https://doi.org/10.26438/ijsrmss/v7i3.822
  [2] Carlsson, C., Fuller, R., “Fuzzy multiple criteria decision making: Recent developments,” Elsevier,Fuzzy Sets and Systems, Vol.78, Issue.2, pp.139-153 ,1996. https://doi.org/10.1016/0165-0114(95)00165-4.
  [3] Deng Yong.,“D Numbers: Theory and Applications,” Journal of Information and Computational Science, Vol. 9, pp. 2421-2428, 2012.
  [4] Dibyojyoti Bhattacharjee, Hemanta Saikia,“On Performance Measurement of Cricketers and Selecting an Optimum Balanced Team,” Taylor & Francis Journals- International Journal of Performance Analysis in Sport,Vol.14, pp. 262-275, 2014. DOI: 10.1080/24748668.2014.11868720.
  [5] E. H-Viedma, F. Herrera, F. Chiclana, M. Luque, “Some issues on consistency of fuzzy preference relations,” Elsevier, European Journal of Operational Research, Vol.154, Issue.1, pp. 98-109, 2004. https://doi.org/10.1016/S0377-2217(02)00725-7.
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  [7] Hermanus H. LEMMER, “An analysis of players’ performances in the first cricket twenty20 world cup series,” South African Journal for Research in Sport, Physical Education and Recreation, Vol. 30, Issue. 2, pp. 71-77, 2008.DOI:10.4314/sajrs.v30i2.25990 .
  [8] Huan-Jyh Shyurb, E. Stanley Lee, “An extension of TOPSIS for group decision making,” Elsevier, Mathematical and Computer Modelling, Vol.45 pp. 801–813, 2007. doi:10.1016/j.mcm.2006.03.023.
  [9] Lotfi A Zadeh, “A simple view of the Dempster-Shafer theory of evidence and its implication for the rule of combination,” Journal AI Magazine archive,Vol. 7, Issue. 2, pp. 85 – 90, 1986. DOI: https://doi.org/10.1609/aimag.v7i2.542.
  [10] T.C.Wang, Y.-H. Chen, “Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP,” Elsevier, Information Sciences,Vol. 178, Issue.19, pp. 3755–3765, 2008. doi:10.1016/j.ins.2008.05.028
  [11] Udaykumar S. Kashid, Archana Kashid, Saurabh Mehta, “A Review of Mathematical Multi-Criteria Decision Models with A case study,” International Journal of Research and Analytical Reviews (IJRAR) , Vol. 6, special Issue, pp. 110-124, 2019. HTTP://DOI.ONE/10.1729/JOURNAL.20927
  [12] Udaykumar S. Kashid, Saurabh N. Mehta, Vineeta Basotia, “A Hybrid ‘AHP-TOPSIS’ Mathematical Multi Criteria Decision-Making model for players performance evaluation and selection in IPL: A case study”, International Journal AU-FAIT, Vol.5, Issue.2, pp. 922-933, 2019.
  [13] Xinyang Deng, Xi Lua, Felix T.S. Chan, Rehan Sadiq, Sankaran Mahadevan , “Yong Deng, D-CFPR: D numbers extended consistent fuzzy preference relations,” Elsevier, Knowledge-Based Systems, Vol. 73, pp. 61–68, 2014.
  [14] Xinyang Denga, Yong Deng, “D-Numbers theory- a generalization of Dempster-Shafer theory,” The Scientific World Journal, Vol.1402, pp. 1-37, 2014. http://dx.doi.org/10.1155/2014/358057.
  [15] Y. Dong, Yinfeng Xu, Hongyi Li., “On consistency measures of linguistic preference relations,” Elsevier, European Journal of Operational Research,” Vol. 189, Issue. 2, pp. 430-444, 2008. doi:10.1016/j.ejor.2007.06.013.
  [16] Yong Deng, Felix T.S. Chan. “A new fuzzy dempster MCDM method and its application in supplier selection,” Elsevier,Expert Systems with Applications,Vol. 38, Issue.8, pp. 9854–9861, 2011. https://doi.org/10.1016/j.eswa.2011.02.017 .

  Citation
  Udaykumar S. Kashid, Archana U. Kashid, Saurabh N. Mehta, Vineeta Basotia, "Proposed Indian squad for ICC-T20 World Cup-2020 by using a new “HD-CLFPR with E-DNIT” Mathematical model," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.5, pp.1-15, 2020

• Open Access   Article

  Improved Estimator for Estimating the Population Mean In Simple Random Sampling

  Khalid Ul Islam Rather, Rizwan Yousuf

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.5 , pp.16-18, Oct-2020

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  This paper proposes some improvement in estimators for the population mean using the ratio estimators presented in [C. Kadilar,H. Cingi, Ratio estimators in simple random sampling, Applied Mathematics and Computation 151 (2004)893–902] and shows that all proposed estimators are always more efficient than the ratio estimators. This result is also supported by a numerical example

  Key-Words / Index Term
  Ratio-type estimators; Simple random sampling; Mean square error; Auxiliary information; Efficiency

  References
  [1] C. Kadilar, H. Cingi, Ratio estimators in simple random sampling, Applied Mathematics and Computation 151 (2004) 893–902.
  [2] B.V.S. Sisodia, V.K. Dwivedi, A modified ratio estimator using coefficient of variation of auxiliary variable, Journal of Indian Society Agricultural Statistics 33 (1981) 13–18.
  [3] H.P. Singh, M.S. Kakran, A modified ratio estimator using known coefficient of kurtosis of an auxiliary character, 1993 (unpublished).
  [4] L.N. Upadhyaya, H.P. Singh, Use of transformed auxiliary variable in estimating the finite population mean, Biometrical Journal 41 (1999) 627–636.
  [5] C. Kadilar, H. Cingi, Ratio estimators in stratified random sampling, Biometrical Journal 45 (2003) 218–225.
  [6] C. Kadilar, H. Cingi, A new ratio estimator in stratified random sampling, Communications in Statistics: Theory and Methods 34 (2005) 597–602.
  [7] K.M. Wolter, Introduction to Variance Estimation, Springer-Verlag, 1985.
  [8] W.G. Cochran, Sampling Techniques, John Wiley and Sons, 1977.
  [9] H. Cingi, Sampling Theory, Hacettepe University Press, 1994.

  Citation
  Khalid Ul Islam Rather, Rizwan Yousuf, "Improved Estimator for Estimating the Population Mean In Simple Random Sampling," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.5, pp.16-18, 2020

• Open Access   Article

  Stochastic Application of Gumbel Distribution in Flood Frequency Analysis of Lingadzi River

  S.M. Chikabvumbwa, C.C. Banda, D.A. Worku, A. Kone

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.5 , pp.19-23, Oct-2020

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  The study of flood frequency analysis is important as it guides hydraulic engineers and policy makers to design flood control structures, and prepare flood risk management plans. This paper discussed how Gumbel statistical distribution can be applied in analyzing peak floods in Lingadzi River Basin. Annual peak flood data for 37 years (1970–2006) for Lingadzi River was analyzed using Excel and Hydrognomon software applications. Practically, peak flows at return periods of 2,5,10,20,25,50,100 and 500 years were determined for Lingadzi river. Statistical results at 95% confidence interval indicated the appropriateness of Gumbel’s distribution in predicting maximum floods. The estimated maximum floods obtained at the stated return periods above are: 169.69, 296.77, 380.9, 487.2, 566.01, 644.35 and 825.24 m3/s respectively. These values are useful for designing flood control structures such as bridges, reservoirs and culverts in the Lingadzi River basin. These results can be used to establish and advance reliable flood risk management models for river basins. This study further recommends that flood analysis studies should be intensified in the country so as to develop and explore recommendable models, strategies and procedures for flood control based on the type of flood in different watersheds as the effects of climate change are predicted to increase in the near future.

  Key-Words / Index Term
  Probability distributions, Lingadzi River basin, Hydrognomon, Urban floods, Return period

  References
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  Citation
  S.M. Chikabvumbwa, C.C. Banda, D.A. Worku, A. Kone, "Stochastic Application of Gumbel Distribution in Flood Frequency Analysis of Lingadzi River," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.5, pp.19-23, 2020

• Open Access   Article

  Population Projection of India using decennial time series data: A Bayesian Study

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

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.5 , pp.24-30, Oct-2020

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  Abstract
  This paper explores the use of Markov chain Monte Carlo simulation technique in the Bayesian inference through WinBUGS software to project the future population of India using the logistics growth model under the Bayesian framework. The purpose of this study is to illustrate the Bayesian approach to population forecasting. It also summarizes the benefits of this approach. In addition to this new and possibly improved form of logistics growth model for population, projections has been proposed in the Bayesian setup. This model was featured in the historical time series from 1901 to 2011 and is used to predict future population data till the year 2101. These results are compared to the latest projections made in other studies. These studies have shown that our projections provide a stable and narrow credible interval accordingly. This paper concludes with some conclusions and suggestions for future work.

  Key-Words / Index Term
  Population forecasting; Bayesian forecasting; Highest posterior density; non-linear regression model; Monte Carlo error

  References
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  Citation
  Anurag Verma, Abhinav Singh, Gyan Prakash Singh, Pramendra Singh Pundir, "Population Projection of India using decennial time series data: A Bayesian Study," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.5, pp.24-30, 2020

• Open Access   Article

  Corrected Analysis of Microcanonical Ensemble Model of Mixture of Fermions and Bosons at the Low-Temperature Limit

  Ritesh Purushottam Harshe, Rupsa De

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.5 , pp.31-38, Oct-2020

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  Abstract
  In a microcanonical ensemble of bosons dominated by fermions, a statistical distribution model is developed based on pair interaction between the fermions and bosons. The phase space volume is calculated and maximized. Corrected expressions for entropy, total internal energy and specific heat of the model are derived using simple thermodynamic relations. Total internal energy and specific heat are plotted as a function of temperature. The natures of the curves obtained are studied. The abrupt jump of internal energy is at 0.007063 K and that of specific heat is at 0.006443K. We see oscillations in specific heat and quantization in internal energy before their corresponding abrupt jumps.

  Key-Words / Index Term
  Microcanonical, Ensembles, Pair interaction, Entropy, Internal energy, Specific heat

  References
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  Citation
  Ritesh Purushottam Harshe, Rupsa De, "Corrected Analysis of Microcanonical Ensemble Model of Mixture of Fermions and Bosons at the Low-Temperature Limit," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.5, pp.31-38, 2020

• Open Access   Article

  Introduction to Continuous Squares Spiral

  Toyesh Prakash Sharma, Ankush Kumar Parcha

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.5 , pp.39-47, Oct-2020

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  Abstract
  In this paper, there is a new spiral has been introducing by authors, they call their spiral as Continuous Squares Spiral (CSS) due to its basic structural background. Most of the time peoples are engaged in finding extra properties and applications of well know spirals as Fibonacci spiral, logarithmic spiral, golden spiral, Spiral of Theodorus, Archimedean spiral, Euler’s spiral, Fermat’s spiral, etc.. with it we can understand spirals is a very vast subject in mathematics and may peoples work to understand spirals, their properties, their applications and discovering inside them and hence they can’t think toward discovering a new spiral.

  Key-Words / Index Term
  Spiral, Triangles, Squares, Continuous Squares Spiral (CSS), Prime numbers, Pythagoras Theorem, Basel Problem, Wallis Product

  References
  [1] “List of Spirals” list on wikipedia, link is https://en.wikipedia.org/wiki/List_of_spirals
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  [7] Guillera, J. and Sondow, J. "Double Integrals and Infinite Products for Some Classical Constants Via Analytic Continuations of Lerch`s Transcendent." 16 June 2005. https://arxiv.org/abs/math.NT/0506319

  Citation
  Toyesh Prakash Sharma, Ankush Kumar Parcha, "Introduction to Continuous Squares Spiral," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.5, pp.39-47, 2020

• Open Access   Article

  Differential Incidence of Type 2 Diabetes Mellitus Using Beta-Binomial and Negative Binomial Models

  M. Aina, T.O. Aro, D. Tukur, O.A. Olukiran, T.A. Oyelakun

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.5 , pp.48-52, Oct-2020

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  Abstract
  This paper entails, the differential incidence between males and females using Beta-Binomial and Negative Binomial models for type 2 diabetes mellitus. From the previous studies, it was discovered that type 2 diabetes mellitus incidence is at an increased level in the region and localities across the countries. In view of this, gender sensitivity to type 2 diabetes was considered. Secondary data for 10 years were collected from medical records of General Hospital, Ifaki-Ekiti, Ekiti State, Nigeria. The Beta-Binomial and Negative Binomial models were applied to test the incidence of type 2 diabetes in both female and male patients. .The two models were compared with the use of goodness of fit and Akaike information criterion (AIC) for the two fitted models. The experimental results showed that Beta-Binomial outperformed the Negative Binomial model in fitting the incidence of male and female patients in type 2 diabetes.

  Key-Words / Index Term
  Beta-Binomial, Differential Incidence, Negative Binomial, Type 2 Diabetes Mellitus

  References
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  Citation
  M. Aina, T.O. Aro, D. Tukur, O.A. Olukiran, T.A. Oyelakun, "Differential Incidence of Type 2 Diabetes Mellitus Using Beta-Binomial and Negative Binomial Models," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.5, pp.48-52, 2020

• Open Access   Article

  Comparison of Estimators of Five Probability Distributions for Estimation of Peak Flood

  N. Vivekanandan

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.5 , pp.53-59, Oct-2020

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  Estimation of Peak Flood (PF) for a given return period is of utmost importance for planning, design and management of civil and hydraulic structures. Depending on the design-life of the structure, the estimated PF with a desired return period is used. This can be achieved through Flood Frequency Analysis (FFA) that involves fitting probability distribution to the series of observed Annual Peak Flood (APF) data. In this paper, a study on comparison of estimators of 2-parameter Log Normal, Log Pearson Type-3 (LP3), Generalized Extreme Value (GEV), Extreme Value Type-1 and Extreme Value Type-2 distributions adopted in FFA for river Tapi at Bhusawal and Savkheda sites is carried out. Based on the intended applications and the variate under consideration, standard parameter estimation procedures such as Method of Moments (MoM), Maximum Likelihood Method (MLM) and L-Moments (LMO) are used for determination of parameters of the probability distributions. The adequacy of probability distributions applied in FFA is quantitatively assessed by Goodness-of-Fit (GoF) tests viz., Chi-square and Kolmogorov-Smirnov, and diagnostic test using D-index. The paper presents the GEV (LMO) distribution is better suited for estimation of PF at Bhusawal whereas LP3 (MLM) for Savkheda.

  Key-Words / Index Term
  Chi-Square, D-index, Generalized Extreme Value, Kolmogorov-Smirnov, L-Moments, Log Pearson Type-3, Maximum Likelihood Method, Peak Flood

  References
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  Citation
  N. Vivekanandan, "Comparison of Estimators of Five Probability Distributions for Estimation of Peak Flood," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.5, pp.53-59, 2020