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### Article

Penalties for Misclassification of a Pure Diagonal Bilinear Process of Order Two as a Moving Average Process of Order Two

1Department of Statistics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria

2Department of Statistics, Federal University of Technology, Owerri, Imo State, Nigeria

American Journal of Applied Mathematics and Statistics. 2014, 2(1), 47-52
DOI: 10.12691/ajams-2-1-8
Copyright © 2014 Science and Education Publishing

Cite this paper:
O. E. Okereke, I. S. Iwueze, C. O. Omekara. Penalties for Misclassification of a Pure Diagonal Bilinear Process of Order Two as a Moving Average Process of Order Two. American Journal of Applied Mathematics and Statistics. 2014; 2(1):47-52. doi: 10.12691/ajams-2-1-8.

Correspondence to: O.  E. Okereke, Department of Statistics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria. Email: emmastat5000@yahoo.co.uk

### Abstract

The penalty function based on misclassification of a pure diagonal bilinear process of order two as a moving process of order two was derived in this study. Computation of penalties using the penalty function revealed that such misclassification increases the error variance. Regression analysis of the penalties on the parameters of the pure diagonal bilinear process suggested a second order polynomial regression model. A test of significance of each of the parameters of the fitted model showed that all the parameter estimates were statistically significant at 5% level of significance. The analysis of variance technique was also used to confirm the adequacy of the fitted model.

### References

 [1] Bessels, S. (2006). One step beyond the solvable equation. www.staff.science.uu.nc/…/Afstudeerscriptie_Sander_Bessels.pdf (This site was visited in June, 2013). [2] Box, G. E. P., Jenkins, G. M. and Reinsel, G. C.(1994). Time Series Analysis: Forecasting and Control. 3rd ed., Prentice-Hall, Englewood Cliffs, N. J. [3] Chatfield, C. (1995). The Analysis of Time Series. An Introduction. 5th ed. Chapmann and Hall, London. [4] Granger, C. W. J. and Andersen, A. (1978). An Introduction to Bilinear Time Series Models. Vanderhoeck and Ruprecht, Gottingen. [5] Hahn, K. (2005). Solving cubic and quartic polynomials. www.Karlscalculus.org/pdf/cubicquartic.pdf.
 [6] Iwueze, I. S. and Ohakwe, J. (2009). Penalties for misclassification of first order and linear moving average time series processes. Interstat Journal of Statistics, No3, http//interstatjournals.net/Year/2009/articles/0906003.pdf. [7] Okereke, O. E. (2013). Characterization of moments of pure diagonal bilinear process of order two and moving average process of order two, Unpublished Ph. D Dissertation. [8] Okereke, O. E and Iwueze, I. S. (2013). Region of comparison for the second order moving average and pure diagonal bilinear processes. International Journal of Applied Mathematics and Statistical Sciences, 2(2): 17-25. [9] Okereke, O. E, Iwueze, I. S and Johnson, O. (2013). Extrema for autocorrelation coefficients of moving average processes. Far East Journal of Theoritical Statistics, 42(2): 137-150. [10] Wei, W. W. S. (2006). Time Series Analysis, Univariate and Multivariate Methods. 2nd ed. Pearson Addision Wesley, New York.
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### Article

Effects of Automated Teller Machine on the Performance of Nigerian Banks

1Department of Accounting and finance, Lagos State University, Ojo, Nigeria

American Journal of Applied Mathematics and Statistics. 2014, 2(1), 40-46
DOI: 10.12691/ajams-2-1-7
Copyright © 2014 Science and Education Publishing

Cite this paper:
Jegede C.A.. Effects of Automated Teller Machine on the Performance of Nigerian Banks. American Journal of Applied Mathematics and Statistics. 2014; 2(1):40-46. doi: 10.12691/ajams-2-1-7.

Correspondence to: Jegede  C.A., Department of Accounting and finance, Lagos State University, Ojo, Nigeria. Email: jegede_charles@yahoo.com

### Abstract

This study investigates the effects of ATM on the performance of Nigerian banks. Available studies have concentrated on the significant dimensions of ATM (automated teller machine) service quality and its effect on customer satisfaction with a bias against ATM producers. The study is motivated by the astronomical challenges confronting the proliferation of ATM infrastructure and attendant financial losss to banks which are often under-reported. Also, there are serious debate on the relevance of ATM technology as most countries in the world are moving away from the virus technology to the more secured chip cards free of credit and debit frauds. Questionnaire was used to collect the data from a convenience sample of 125 employees of five selected banks in Lagos State with interswitch network. Therefore, data collected through the questionnaire were analyzed statistically by using the Software Package for Social Science (SPSS Version 20.0 for Student Version) and chi-square technique. The results indicate that less than the benefits, the deployment of ATMs terminals have averagely improved the performance of Nigerian banks because of the alarming rate of ATM fraud. Similarly, ATM service quality is less correlated to security and privacy of users and providers.The conclusion therefore is that banks should strive to increase their security layers to subvert the tricks of web scammers, limit the amount which customers may be allowed to withdraw at a time and provide electronic alerts to customers’phone for all transactions carried out on their bank accounts through ATMs and the provisions of extra security layer that can prevent third party to make use someone else’s ATM card for unauthorized withdrawals electronically.

### References

 [1] Mitroff, I. I. (2003). Do not Promote Religion under the Guise of Spirituality. Organization, 10(2), 375-377. [2] Thakor, A. V and Olazabal, N. (2002) Banking: The IT Paradox. McKinsey Quarterly 1(1): 45-51. [3] Ogbuji, C. N. et al. (2012). Analysis of the Negative Effects of the Automated Teller Machine (ATM) as a Channel for Delivering Banking Services in Nigeria. International Journal of Business and Management 7, No. 7; April 2012. [4] Dapo, A. A. (2008). The impact of ICT on professional practice in the Nigerian construction industry. The Electronic Journal of Information Systems in Developing Countries. 24(2), p1-19. [5] Paul, D.R. (1998). Towards a more efficient use of payment instruments. Available online at http://www.econ.kuleuven.ac.be/ew/academic/intecon/Degrauwe/PDG.
 [6] Giddens, E. (2008). A first look at communication theory. New York: McGraw Hill [7] Rose, P. S. (1999). Commercial bank management. Boston, Irwin/McGraw-Hill. [8] Aditi, O. (2013). Working of Automated Teller Machine (ATM). Avalable at http://www.techs24x7.com/blog/working-of-automated-teller-machine-atm/. [9] Ugwu, E. (2008). CBN, banks to tackle ATMs’ hitches. Retrieved April 25, 2013, from http://www.guardiannewsngr.com. [10] Siyanbola, T.T. (2013). The effect of cashless banking on nigerian economy. eCanadian Journal of Accounting and Finance, 1(2): 9-19. [11] Adeoti, J.A. (2011). Automated Teller Machine (ATM) Frauds in Nigeria: The Way Out. Journal of Social Sciences, 27(1): 53-58. [12] Ebiringa, O. T. (2010). Automated Teller Machine and Electronic Payment System in Nigeria: A Synenthesis of the Critical Success Factors. Journal of Sustainable Development in Africa, 12 (1): 71-86. [13] Maiyaki A. U. and Mokhtar S. S. M (2010) Effects of electronic banking facilities, employment sector and age – group on customers choice of banks in Nigeria. Journal of Internet Banking and Commerce, Vol. 15(1), April. [14] Lovelock, C. H. (2000). Functional integration in service: understanding the links between marketing, operations, and human resources. In Swartz, T.A. and Iacobucci, D. [15] Chung, W.C.C., A.Y.K. Yam, M.F.S. Chan. (2004). Networked enterprise: A new business model forglobal sourcing. International Journal of Production Economics 87 267-280. [16] Asif Khan, M. (2011). An Empirical Study of Automated Teller Machine Service Quality and Customer Satisfaction in Pakistani Banks. European Journal of Social Sciences, 13 (3): 333-344. [17] Cabas, M. G. (2001). A History of the Future of Banking: Predictions and Outcomes. Retrieved September 2, 2012, from http://www.hass.berkeley.edu/finance /CMWpaper.pdf. [18] Moutinho, L. and Smith, A. 2000. Modelling bank customer satisfaction through mediation of attitudes toward human and automated banking, The International Journal of Bank Marketing 18(3): 124. [19] Ihejiahi R 2009. How to fight ATM fraud online. Nigeria Daily News, June 21, P. 18. [20] Muhammad, A. K. (2009). An empirical study of automated teller machine service quality and customer satisfaction in Pakistani banks. European Journal of Social Sciences, Vol. 13 No.3, pp. 333-344. [21] Adeyemi, A. (2010). Winning customers’ confidence: The new banking focus. The Guardian, May 26 p. 25. [22] Obiano W 2009. How to fight ATM fraud. online Nigeria Daily News, June 21, P. 18 [23] Omankhanlen Odidison 2009. ATM fraud rises: Nigerians groan in Nigeria. Daily News, Sunday, June 21, pp. 8-10. [24] A Report on Global ATM Frauds (2007). Available online at http://www.icmrindia.org/casestudies/catalogue/Business%20Reports/BREP041.htm.
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### Article

A Study on New Sequence of Functions Involving -Function

1Department of Mathematics, Anand International College of Engineering, Jaipur, India

2Department of Mathematics, Fateh College for Women, RampuraPhul, Bathinda, India

3Department of Mathematics, Suresh Gyan Vihar University, Jaipur, India

American Journal of Applied Mathematics and Statistics. 2014, 2(1), 34-39
DOI: 10.12691/ajams-2-1-6
Copyright © 2014 Science and Education Publishing

Cite this paper:
Praveen Agarwal, Mehar Chand, Saket Dwivedi. A Study on New Sequence of Functions Involving -Function. American Journal of Applied Mathematics and Statistics. 2014; 2(1):34-39. doi: 10.12691/ajams-2-1-6.

Correspondence to: Praveen  Agarwal, Department of Mathematics, Anand International College of Engineering, Jaipur, India. Email: goyal.praveen2011@gmail.com

### Abstract

A remarkably large number of operational techniques have drawn the attention of several researchers in the study of sequence of functions and polynomials. Very recently, Agarwal and Chand gave certain new sequence of functions involving the special functions in their series of papers. In this sequel, here, we aim to introduce a new sequence of functions involving the Generalized Mellin-Barnes Type of Contour Integrals by using operational techniques. Some generating relations and finite summation formulae of the sequence presented here are also considered. These generating relations and finite summation formulae are unified in nature and act as key formulae from which, we can obtain as their special cases.

### References

 [1] Agarwal, P., On multiple integral relations involving generalized Mellin-Barnes type of contour integral, Tamsui O xf. J. Math. Sci. 2011, 27(4), 449-462. [2] Agarwal, P. and Chand, M., On new sequence of functions involving pFq, South Asian J Math, 2013, 3(3), 199-210. [3] Agarwal, P. and Chand, M., Graphical Interpretation of the New Sequence of Functions Involving Mittage-Leffler Function Using Matlab, American Journal of Mathematics and Statistics 2013, 3(2): 73-83. [4] Agarwal, P. and Chand, M., On new sequence of functions involving pFq, South Asian Journal of Mathematics 2013 , Vol. 3 ( 3 ) : 199-210. [5] Agarwal, P. and Jain, S., On unified finite integrals involving a multivariable polynomial and a generalized Mellin Barnes type of contour integral having general argument, Nat. Acad. Sci. Lett. 2009, 32(9-10), 281-286.
 [6] Chak, A. M., A class of polynomials and generalization of stirling numbers, Duke J. Math. 1956, 23, 45-55. [7] Chandel, R.C.S., A new class of polynomials, Indian J. Math. 1973, 15(1), 41-49. [8] Chandel, R.C.S., A further note on the class of polynomials Tnα,k(x,r,p), Indian J. Math. 1974,16(1), 39-48. [9] Chatterjea, S. K., On generalization of Laguerre polynomials, Rend. Mat. Univ. Padova. 1964, 34, 180-190. [10] Gould, H. W. and Hopper, A. T., Operational formulas connected with two generalizations of Hermite polynomials, Duck Math. J. 1962, 29, 51-63. [11] Joshi, C. M. and Prajapat, M. L., The operator Ta,k, and a generalization of certain classical polynomials, Kyungpook Math. J. 1975, 15, 191-199. [12] K.C. Gupta and R.C. Soni, On a basic integral formula involving the product of the H-function and Fox H-function, J.Raj.Acad.Phy. Sci. 2006, 4 (3), 157-164. [13] K.C. Gupta, R. Jain and R. Agarwal, On existence conditions for a generalized Mellin-Barnes type integral Natl Acad Sci Lett. 2007, 30(5-6), 169-172. [14] Meijer, C.S., On the G-function, Proc. Nat. Acad. Wetensch 1946, 49, p. 227. [15] Mittal, H. B., A generalization of Laguerre polynomial, Publ. Math. Debrecen 1971, 18, 53-58. [16] Mittal, H. B., Operational representations for the generalized Laguerre polynomial, GlasnikMat.Ser III 1971, 26(6), 45-53. [17] Mittal, H. B., Bilinear and Bilateral generating relations, American J. Math. 1977, 99, 23-45. [18] Patil, K. R. and Thakare, N. K., Operational formulas for a function defined by a generalized Rodrigues formula-II, Sci. J. Shivaji Univ.1975, 15, 1-10. [19] Prajapati , J. C. and Ajudia, N. K., On New Sequence of Functions and Their MATLAB Computation International Journal of Physical, Chemical & Mathematical Sciences, 1(2),Accepted On: 27.08.2012. [20] Rathie, A.K., A new generalization of generalized hypergeometric functions, Le Mathematic he Fasc. II 1997, 52, 297-310. [21] Shrivastava, P. N., Some operational formulas and generalized generating function, The Math. Education 1974, 8, 19-22. [22] Shukla, A. K. and Prajapati J. C., On some properties of a class of Polynomials suggested by Mittal, Proyecciones J. Math.2007, 26(2), 145-156. [23] Singh, R. P., On generalized Truesdell polynomials, Rivista de Mathematica 1968, 8, 345-353. [24] Srivastava, A. N. and Singh, S. N., Some generating relations connected with a function defined by a Generalized Rodrigues formula, Indian J. Pure Appl. Math. 1979, 10(10), 1312-1317. [25] Srivastava, H.M., Gupta, K.C. and Goyal, S.P., The H-function of one and two variables with applications, South Asian Publishers, New Dehli, Madras ,1982. [26] Srivastava, H. M. and Singh, J. P., A class of polynomials defined by generalized, Rodrigues formula, Ann. Mat. Pura Appl. 1971, 90(4), 75-85.
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### Article

Evaluation of Mean Time to System Failure of a Repairable 3-out-of-4 System with Online Preventive Maintenance

1Department of Mathematics, Usmanu Danfodio University, Sokoto, Nigeria

2Department of Mathematical Sciences, Bayero University, Kano, Nigeria

3Department of Mathematics, Federal University, Dutse, Nigeria

American Journal of Applied Mathematics and Statistics. 2014, 2(1), 29-33
DOI: 10.12691/ajams-2-1-5
Copyright © 2014 Science and Education Publishing

Cite this paper:
U.A. Ali, Saminu I. Bala, Ibrahim Yusuf. Evaluation of Mean Time to System Failure of a Repairable 3-out-of-4 System with Online Preventive Maintenance. American Journal of Applied Mathematics and Statistics. 2014; 2(1):29-33. doi: 10.12691/ajams-2-1-5.

Correspondence to: Ibrahim  Yusuf, Department of Mathematical Sciences, Bayero University, Kano, Nigeria. Email: Ibrahimyusuffagge@gmail.com

### Abstract

Most of the literature assumed that systems undergo preventive maintenance. Little literature is found on whether the preventive maintenance is online or offline. It is known that most of the engineering systems undergo both online and offline preventive maintenance. In this paper, we studied the mean time to system failure of a repairable redundant 3-out-of-4 system with online preventive maintenance involving four types of failures. We develop the explicit expressions for mean time to system failure for the system using Chapman-Kolmogorov equations. Various cases are analyzed graphically to investigate the impact of system parameters on mean time to system failure. Results have shown that system with online preventive maintenance is better in terms of mean time to system failure of system than system without preventive maintenance.

### References

 [1] Bhardwj, R.K. and Chander, S. (2007). Reliability and cost benefit analysis of 2-out-of-3 redundant system with general distribution of repair and waiting time. DIAS- Technology review- An Int. J. of business and IT. 4(1), 28-35. [2] Chander, S. and Bhardwaj, R.K. (2009). Reliability and economic analysis of 2-out-of-3 redundant system with priority to repair. African J. of Maths and comp. sci, 2(11), 230-236. [3] Bhardwj,R.K., and S.C. Malik. (2010). MTSF and Cost effectiveness of 2-out-of-3 cold standby system with probability of repair and inspection. Int. J. of Eng. Sci. and Tech. 2(1), 5882-5889. [4] Wang, k. Hsieh, C. and Liou, C (2006). Cost benefit analysis of series systems with cold standby components and a repairable service station. Journal of quality technology and quantitative management, 3(1), 77-92. [5] El-Said, K.M., (2008). Cost analysis of a system with preventive maintenance by using Kolmogorov’s forward equations method. American Journal of Applied Sciences 5(4), 405-410.
 [6] Haggag, M.Y., (2009). Cost analysis of a system involving common cause failures and preventive maintenance, Journal of Mathematics and Statistics 5(4), 305-310. [7] Haggag, M.Y., (2009). Cost analysis of k-out-of-n repairable system with dependent failure and standby support using Kolmogorov’s forward equations method .Journal of Mathematics and Statistics 5(4), 401-407. [8] Wang, K.H and Kuo, C.C. (2000). Cost and probabilistic analysis of series systems with mixed standby components. Applied Mathematical Modelling, 24, 957-967. [9] Wang, K..C., Liou, Y.C, and Pearn W. L. (2005). Cost benefit analysis of series systems with warm standby components and general repair time. Mathematical Methods of operation Research, 61, 329-343. [10] Yusuf, I. Availability and profit analysis of 3-out-of-4 repairable system with preventive maintenance, International Journal of Applied Mathematics Research, 1(4), 2012, 510-519.
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### Article

Application of Sarima Models in Modelling and Forecasting Nigeria’s Inflation Rates

1Department of Statistics, Central Bank of Nigeria, Owerri

2Department of Statistics, Nnamdi Azikiwe University, PMB 5025, Awka Anambra State Nigeria

3Department of Statistics, Imo State University, PMB 2000, Owerri Nigeria

4Department of Planning, Research and Statistics, Ministry of Petroleum and Environment Owerri Imo State Nigeria

American Journal of Applied Mathematics and Statistics. 2014, 2(1), 16-28
DOI: 10.12691/ajams-2-1-4
Copyright © 2013 Science and Education Publishing

Cite this paper:
Otu Archibong Otu, Osuji George A., Opara Jude, Mbachu Hope Ifeyinwa, Iheagwara Andrew I.. Application of Sarima Models in Modelling and Forecasting Nigeria’s Inflation Rates. American Journal of Applied Mathematics and Statistics. 2014; 2(1):16-28. doi: 10.12691/ajams-2-1-4.

Correspondence to: Opara  Jude, Department of Statistics, Imo State University, PMB 2000, Owerri Nigeria. Email: judend88@yahoo.com

### Abstract

This paper discussed the Application of SARIMA Models in Modeling and Forecasting Nigeria’s Inflation Rates. Time series analysis and forecasting is an efficient versatile tool in diverse applications such as in economics and finance, hydrology and environmental management fields just to mention a few. Among the most effective approaches for analyzing time series data, the method propounded by Box and Jenkins, the Autoregressive Integrated Moving Average (ARIMA) was employed in this study. In this paper, we used Box-Jenkins methodology to build ARIMA model for ’s monthly inflation rates for the period November 2003 to October 2013 with a total of 120 data points. In this research, ARIMA (1, 1, 1) (0, 0, 1)12 model was developed, and obtained as = 0.3587yt+0.6413yt-1-0.8840et-11 -0.7308912et-12+0.8268et. This model is used to forecast ’s monthly inflation for the upcoming year 2014. The forecasted results will help policy makers gain insight into more appropriate economic and monetary policy in other to combat the predicted rise in inflation rates beginning the first quarter of 2014.

### References

 [1] Rudiger Dornbusch and Stanley Fischer, (1993). “Moderates Inflation”, The Bank Economic Review, Vol.7, Issue 1, Pp.1-44. [2] Jack H.R, Bond M.T., and Webb J.R, (1989). “The Inflation- Hedging Effectiveness of Real Estate”. Journal of Real Estate Research, Vol.4. Pp. 45-56. [3] Hamidreza M. and Leila S. (2012). Using SARFIMA model to study and predict the Iran’s oil supply. International Journal of Energy Economics and Policy. Vol.2, No.1, 2012, pp.41-49. [4] Fritzer, F., Gabriel, M. and Johann, S. (2002). "Forecasting Austrian HICP and its Components using VAR and ARIMA Models," Working Papers 73, Oesterreichische National bank (Austrian Central Bank). [5] Gomez V., and Maravall A., (1998.) "Automatic Modelling Methods for Univariate Series," Banco de EspaÃ±a Working Papers 9808, Banco de España.
 [6] Leila S. and Masoud Y. (2012). An Empirical Study of the Usefulness of SARFIMA models in Energy Science. International Journal of Energy Science. IJES Vol.2 No.2 2012. [7] [Jeffrey J., (1990). “Business forecasting Methods”. Atlantic Publishers. [8] Box, G. E. P and Jenkins, G.M., (1976). “Time series analysis: „Forecasting and control,” Holden-Day, San Francisco. [9] Akaike, H. (1974). A New Look at the Statistical Model Identification. IEEE Transactions on Automatic Control 19 (6): 716-723.
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### Article

Paradox Algorithm in Application of a Linear Transportation Problem

1Department of Statistics, Nnamdi Azikiwe University, Awka Anambra State Nigeria

2Department of Statistics, Imo State University, Owerri Nigeria

3Department of Statistics, Abia State Polytechnic, Aba Nigeria

4Department of Planning, Research and Statistics, Ministry of Petroleum and Environment Owerri Imo State Nigeria

American Journal of Applied Mathematics and Statistics. 2014, 2(1), 10-15
DOI: 10.12691/ajams-2-1-3
Copyright © 2014 Science and Education Publishing

Cite this paper:
Osuji George A., Opara Jude, Nwobi Anderson C., Onyeze Vitus, Iheagwara Andrew I.. Paradox Algorithm in Application of a Linear Transportation Problem. American Journal of Applied Mathematics and Statistics. 2014; 2(1):10-15. doi: 10.12691/ajams-2-1-3.

### Abstract

Paradox seldom occurs in a linear transportation problem, but it is related to the classical transportation problem. For specific reasons of this problem, an increase in the quantity of goods or number of passengers (as used in this paper) to be transported may lead to a decrease in the optimal total transportation cost. Two numerical examples were used for the study. In this paper, an efficient algorithm for solving a linear programming problem was explicitly discussed, and it was concluded that paradox does not exist in the first set of data, while paradox exists in the second set of data. The Vogel’s Approximation Method (VAM) was used to obtain the initial basic feasible solution via the Statistical Software Package known as TORA. The first set of data revealed that paradox does not exist, while the second set of data showed that paradox exists. The method however gives a step by step development of the solution procedure for finding all the paradoxical pair in the second set of data.

### References

 [1] Adlakha V. and Kowalski, K. (1998): A quick sufficient solution to the more-for-less paradox in a transportation problem, Omega 26(4):541-547. [2] Appa G.M. (1973): The Transportation problem and its variants, Oper. Res. Q. 24:79-99. [3] Arora S.R. and Ahuja A. (2000): A paradox in a fixed charge transportation problem. Indian J. pure appl. Math., 31(7): 809-822, July 2000 printed in India. [4] Charnes A.; Cooper W.W. and Henderson (1953): An Introduction to Linear programming (Wiley, New Work). [5] Charnes A. and Klingman D. (1971): The more-for-less paradox in the distribution model, Cachiers du Centre Etudes de Recherche Operaionelle 13; 11-22.
 [6] Deineko, V.G; Klinz, B and Woeginger, G.J. (2003): Which Matrices are Immune against the Transportation Paradox? Discrete Applied Mathematics, 130:495-501. [7] Dantzig, G.D. (1963): Linear Programming and Extensive (Princeton University Press, NJ). [8] Dantzig G.B. (1951): Application of the simplex method to a transportation problem, in Activity Analysis of Production and Allocation (T.C. Koopmans, ed.) Wiley, New York, pp.359-373. [9] Ekezie, D.D.: Ogbonna, J.C. and Opara, J. (2013): The Determination of Paradoxical Pairs in a Linear Transportation Problem. International Journal of Mathematics and Statistics Studies. Vol. 1, No. 3, p.p.9-19, September 2013. [10] Finke, G.(1978): A unified approach to reshipment, overshipment and postoptimization problems, lecture notes in control and information science, Vol.7, Springer, Berlin, 1978, p.p.201-208. [11] Gupta, A. Khanna S and Puri, M.C. (1993): A paradox in linear fractional transportation problems with mixed constraints, Optimization 27:375-387. [12] Hadley G. (1987): Linear Programming (Narosa Publishing House, New Delhi). [13] Hitchcock, F.L. (1941): The distribution of a product from several resources to numerous localities, J. Math. Phys. 20:224-230. [14] Joshi, V. D. and Gupta, N. (2010): On a paradox in linear plus fractional transportation problem, Mathematika 26(2):167-178. [15] Opara, J. (2009): Manual on Introduction to Operation Research, Unpublished. [16] Klingman, D. and Russel, R. (1974): The transportation problem with mixed constraints, operational research quarterly, Vol. 25, No. 3: p.p. 447-455. [17] Klingman, D. and Russel, R. (1975): Solving constrained transportation problems, Oper. Res. 23(1):91-105. [18] Storoy, S. (2007): The transportation paradox revisited, N-5020 Bergen, Norway. [19] Szwarc W. (1971): The transportation paradox, Nav. Res. Logist. Q.18:185-202.
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### Article

Characterization of Distribution by Conditional Expectation of Lower Record Values

1Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh, India

American Journal of Applied Mathematics and Statistics. 2014, 2(1), 7-9
DOI: 10.12691/ajams-2-1-2
Copyright © 2013 Science and Education Publishing

Cite this paper:
M. I. Khan, M. Faizan. Characterization of Distribution by Conditional Expectation of Lower Record Values. American Journal of Applied Mathematics and Statistics. 2014; 2(1):7-9. doi: 10.12691/ajams-2-1-2.

Correspondence to: M.  I. Khan, Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh, India. Email: izhar.stats@gmail.com

### Abstract

It is widely known that the problem of characterizing a distribution an important problem which has recently attracted the attention of many researchers. Thus various characterizations have been established in many directions. In this paper, a general form of continuous probability distribution is characterized through conditional expectation of contrast of lower record statistics, conditioned on a non-adjacent record statistics and some of its deductions are also discussed.

### References

 [1] K.N. Chandler (1952). The distribution and frequency of record values. Journal of Royal Society. B14, 220-228. [2] Glick, N. (1978). Breaking record and breaking boards. American Mathematical Monthly, 85, 2-26. [3] Ahsanullah, M. (1995). Record Statistics. Nova Science Publishers, New York. [4] Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. (1998). Record . Johan Wiley and Sons, New York. [5] Ahsanullah, M. (2004). Record Values-Theory and Applications.University Press of America, New York.
 [6] Ahsanullah, M. and Raqab, M. Z. (2006). Bounds and Characterizations of Record Statistics. Nova Science Publishers, Hauppauge, New York. [7] Malinowska, I. and Szynal, D. (2008). On characterization of certain dis-tributions of kth lower (upper) record values. Applied Mathematics Computation, 202, 338-347. [8] Shawky, A. I. and Bakoban, R. A. (2008). Characterization from exponentiated gamma distributions based on record values. Journal of Statistical Theory and Applications, 7, 263-277. [9] Shawky, A. I. and Bakoban, R. A. (2009). Conditional expectation of certain distributions of record values. International Journal of Mathematical Analysis, 3 (17), 829-838. [10] Shawky, A. I. and Abu-Zinadah, H. H. (2006). General recurrence relations and characterizations of certain distributions based on record values. Journal of Approximation Theory and Applications, 2, 149-159. [11] Shawky, A. I. and Abu-Zinadah, H. H. (2008a). Characterization of the exponentiated Pareto distribution based on record values. Applied Mathematical Sciences, 2, 1283-1290. [12] Shawky, A. I. and Abu-Zinadah, H. H. (2008b). General recurrence relations and characterizations of certain distributions based on record statistics. Journal of Statistical Theory and Applications, 7, 93-117. [13] Wu, J.W. and Lee, W. C. (2001): On characterizations of generalized extreme values, power function, generalized Pareto and classical Pareto distributions by conditional expectation of record values. Statistical Papers, 42, 225-242. [14] Faizan, M. and Khan, M. I.(2011). A characterization of continuous distributions through lower record statistics. ProabStat Forum, 4, 39-43. [15] Nadarajah, S., Teimouri, M. and Shih, S.H. (2012). Characterizations of the Weibull and Uniform distributions using record values. Brazilian Journal of Probability and Statistics. (To appear).
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### Article

Measuring the Uncertainty of Human Reasoning

1School of Technological Applications, Graduate Technological Educational Institute (T. E. I.) of Western Greece, Patras, Greece

American Journal of Applied Mathematics and Statistics. 2014, 2(1), 1-6
DOI: 10.12691/ajams-2-1-1
Copyright © 2013 Science and Education Publishing

Cite this paper:
Michael Gr. Voskoglou. Measuring the Uncertainty of Human Reasoning. American Journal of Applied Mathematics and Statistics. 2014; 2(1):1-6. doi: 10.12691/ajams-2-1-1.

Correspondence to: Michael  Gr. Voskoglou, School of Technological Applications, Graduate Technological Educational Institute (T. E. I.) of Western Greece, Patras, Greece. Email:

### Abstract

Human reasoning is characterized by a degree of fuzziness and uncertainty. In the present paper we develop a fuzzy model for a better description of the reasoning process and we use the fuzzy systems’ total possibilistic uncertainty as well as the classical ’s entropy (properly modified for use in fuzzy environments) in measuring the individuals’ reasoning skills. Classroom experiments are also provided illustrating our results in practice.

### References

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 2014, Volume 2