### Content: Volume 2, Issue 1

### Article

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

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

^{2}Department 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

### Keywords

### 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. 3^{rd} ed., Prentice-Hall, Englewood Cliffs, N. J. | ||

[3] | Chatfield, C. (1995). The Analysis of Time Series. An Introduction. 5^{th} 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 Characterization of moments of pure diagonal bilinear process of order two and moving average process of order two, Unpublished Ph.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. 2^{nd} ed. Pearson Addision Wesley, New York. | ||

### Article

**Effects of Automated Teller Machine on the Performance of Nigerian Banks**

^{1}Department 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

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### References

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[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. | ||

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[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. | ||

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[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. | ||

### Article

**A Study on New Sequence of Functions Involving -Function**

^{1}Department of Mathematics, Anand International College of Engineering, Jaipur, India

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

^{3}Department 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

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### 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 T_{n}α^{,k}(x,r,p), Indian J. Math. 1974,16(1), 39-48. | ||

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[11] | Joshi, C. M. and Prajapat, M. L., The operator T_{a,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. | ||

### Article

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

^{1}Department of Mathematics, Usmanu Danfodio University, Sokoto, Nigeria

^{2}Department of Mathematical Sciences, Bayero University, Kano, Nigeria

^{3}Department 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

### Keywords

### 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. | ||

### Article

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

^{1}Department of Statistics, Central Bank of Nigeria, Owerri

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

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

^{4}Department 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

_{t}+0.6413y

_{t-1}-0.8840e

_{t-11 }-0.7308912e

_{t-12}+0.8268e

_{t}. 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.

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### 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. | ||

### Article

**Paradox Algorithm in Application of a Linear Transportation Problem**

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

^{2}Department of Statistics, Imo State University, Owerri Nigeria

^{3}Department of Statistics, Abia State Polytechnic, Aba Nigeria

^{4}Department 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

### Keywords

### 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). | ||

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[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. | ||

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[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. | ||

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[19] | Szwarc W. (1971): The transportation paradox, Nav. Res. Logist. Q.18:185-202. | ||

### Article

**Characterization of Distribution by Conditional Expectation of Lower Record Values**

^{1}Department 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

### Keywords

### 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). | ||

### Article

**Measuring the Uncertainty of Human Reasoning**

^{1}School 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

### Keywords

### References

[1] | Klir, G. J. & Folger, T. A., Fuzzy Sets, Uncertainty and Information, Prentice-Hall, London, 1988. | ||

[2] | Klir G. J., “Principles of uncertainty: What are they? Why do we need them?” Fuzzy Sets and Systems, 74, 15-31, 1995. | ||

[3] | Sen, Z., Fuzzy Logic and Hydrological Modelling, Taylor & Francis Group, CRC Press, 2010. | ||

[4] | Sen, Z., “Fuzzy philosophy of science and education”, Turkish Journal of Fuzzy Systems, 2 (2), 77-98, 2011. | ||

[5] | Shackle, G. L. S., Decision, Order and Time in Human Affairs, Cambridge University Press, Cambridge, 1961. | ||

[6] | Shannon, C. E., “A mathematical theory of communications”, Bell Systems Technical Journal, 27, 379-423 and 623-656, 1948. | ||

[7] | Voskoglou, M. Gr., Stochastic and fuzzy models in Mathematics Education, Artificial Intelligence and Management, Lambert Academic Publishing, Saarbrucken, Germany, 2011 (for more details look at http://amzn.com./3846528218). | ||

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