| Title:
|
Hypotheses testing with the two-parameter Pareto distribution on the basis of records in fuzzy environment (English) |
| Author:
|
Saeidi, Ali Reza |
| Author:
|
Akbari, Mohammad Ghasem |
| Author:
|
Doostparast, Mahdi |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
50 |
| Issue:
|
5 |
| Year:
|
2014 |
| Pages:
|
744-757 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In problems of testing statistical hypotheses, we may be confronted with fuzzy concepts. There are also situations in which the available data are record statistics such as weather and sports. In this paper, we consider the problem of testing fuzzy hypotheses on the basis of records. Pareto distribution is investigated in more details since it is used in applications including economic and life testing analysis. For illustrative proposes, a real data set on annual wage is analyzed using the results obtained. (English) |
| Keyword:
|
decision analysis |
| Keyword:
|
fuzzy hypotheses |
| Keyword:
|
pareto distribution |
| Keyword:
|
record data |
| Keyword:
|
testing hypotheses |
| MSC:
|
62A86 |
| MSC:
|
62F03 |
| MSC:
|
62F86 |
| idZBL:
|
Zbl 1308.62029 |
| idMR:
|
MR3301858 |
| DOI:
|
10.14736/kyb-2014-5-0744 |
| . |
| Date available:
|
2015-01-13T09:31:04Z |
| Last updated:
|
2016-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144104 |
| . |
| Reference:
|
[1] Akbari, M. G., Arefi, M.: Statistical nonparametric test based on the intuitionistic fuzzy data..J. Intell. Fuzzy Systems 25 (2013), 525-534. Zbl 1291.62109, MR 3079176 |
| Reference:
|
[2] Akbari, M. G., Rezaei, A.: An uniformly minimum variance unbiased point estimator using fuzzy observations..Austrian J. Statist. 36 (2007), 307-317. |
| Reference:
|
[3] Akbari, M. G., Rezaei, A.: Bootstrap statistical inference for the variance based on fuzzy data..Austrian J. Statist. 38 (2009), 121-130. |
| Reference:
|
[4] Akbari, M. G., Rezaei, A., Waghei, Y.: Statistical inference about the variance of fuzzy random variables..Sankhya 71-B (2009), 1-15. Zbl 1192.60010, MR 2639304 |
| Reference:
|
[5] Akbari, M. G., Rezaei, A.: Bootstrap testing fuzzy hypotheses and observations on fuzzy statistic..Expert Systems Appl. 37 (2010), 8, 5782-5787. |
| Reference:
|
[6] Arnold, B. C.: Pareto Distributions..International Co-operative Publishing House, Fairland 1983. Zbl 1151.91638, MR 0751409 |
| Reference:
|
[7] Arnold, B. C., Balakrishnan, N., Nagaraja, H. N.: Records..John Wiley and Sons, New York 1998. Zbl 0914.60007, MR 1628157 |
| Reference:
|
[8] Arnold, B. F.: An approach to fuzzy hypothesis testing..Metrika 44 (1996), 119-126. Zbl 0862.62019, MR 1414142, 10.1007/BF02614060 |
| Reference:
|
[9] Arnold, B. F.: Testing fuzzy hypotheses with crisp data..Fuzzy Sets and Systems 94 (1998), 323-333. Zbl 0940.62015, MR 1612278, 10.1016/S0165-0114(96)00258-8 |
| Reference:
|
[10] Buckley, J. J.: Fuzzy Probabilities: New Approach and Applications..Springer-Verlag, Berlin, Heidelberg 2005. Zbl 1060.60002, MR 1968858 |
| Reference:
|
[11] Buckley, J. J.: Fuzzy Probability and Statistics..Springer-Verlag, Berlin, Heidelberg 2006. Zbl 1095.62002 |
| Reference:
|
[12] Delgado, M., Verdegay, J. L., Vila, M. A.: Testing fuzzy hypotheses, a Bayesian approach..In: Approximate Reasoning in Expert Systems (M. M. Gupta, ed.) 1985, pp. 307-316. MR 0845354 |
| Reference:
|
[13] Doostparast, M., Akbari, M. G., Balakrishnan, N.: Bayesian analysis for the two-parameter Pareto distribution based on record values and times..J. Stat. Comput. Simul. 81 (2011), 11, 1393-1403. MR 2851259, 10.1080/00949655.2010.486762 |
| Reference:
|
[14] Doostparast, M., Balakrishnan, N.: Pareto record-based analysis..Statistics 47 (2013), 5, 1075-1089. MR 3175735, 10.1080/02331888.2012.694440 |
| Reference:
|
[15] Dyer, D.: Structural probability bounds for the strong Pareto laws..Canad. J. Statist. 9 (1981), 71-77. MR 0638387, 10.2307/3315297 |
| Reference:
|
[16] Filzmoser, P., Viertl, R.: Testing hypotheses with fuzzy data: the fuzzy $p-$value..Metrika 59 (2004), 21-29. Zbl 1052.62009, MR 2043430, 10.1007/s001840300269 |
| Reference:
|
[17] Gonzalez-Rodriguez, G., Montenegro, M., Colubi, A., Gil, M. A.: Bootstrap techniques and fuzzy random variables: Synergy in hypothesis testing with fuzzy data..Fuzzy Sets and Systems 157 (2006), 2608-2613. Zbl 1119.62037, MR 2328386 |
| Reference:
|
[18] Gulati, S., Padgett, W. J.: Smooth nonparametric estimation of the distribution and density functions from record-breaking data..Commun. Commun. Statist. - Theory and Methods 23 (1994), 1259-1274. Zbl 0825.62160, MR 1281210, 10.1080/03610929408831319 |
| Reference:
|
[19] Holena, M.: Fuzzy hypotheses for GUHA implications..Fuzzy Sets and Systems 98 (1998), 101-125. 10.1016/S0165-0114(96)00369-7 |
| Reference:
|
[20] Holena, M.: Fuzzy hypotheses testing in the framework of fuzzy logic..Fuzzy Sets and Systems 145 (2004), 229-252. Zbl 1050.68137, MR 2073999, 10.1016/S0165-0114(03)00208-2 |
| Reference:
|
[21] Körner, R.: An asymptotic $\alpha-$cut for the expectation of random fuzzy variables..J. Statist. Plann. Inferences 83 (2000), 331-346. MR 1748017, 10.1016/S0378-3758(99)00107-X |
| Reference:
|
[22] Montenegro, M., Colubi, A., Casals, M. R., Gil, M. A.: Asymptotic and bootstrap techniques for testing the expected value of a fuzzy random variable..Metrika 59 (2004), 31-49. Zbl 1052.62048, MR 2043431, 10.1007/s001840300270 |
| Reference:
|
[23] Parchami, A., Taheri, S. M., Mashinchi, M.: Fuzzy p-value in testing fuzzy hypotheses with crisp data..Statist. Papers 51 (2010), 1, 209-226. Zbl 1247.62105, MR 2556596, 10.1007/s00362-008-0133-4 |
| Reference:
|
[24] Samaniego, F. J., Whitaker, L. R.: On estimating population characteristics from record-breaking observations II: NonParametric results..Naval Res. Logist. 35 (1988), 221-236. Zbl 0656.62045, MR 0930966, 10.1002/1520-6750(198804)35:2<221::AID-NAV3220350207>3.0.CO;2-2 |
| Reference:
|
[25] Taheri, S. M., Arefi, M.: Testing fuzzy hypotheses based on fuzzy statistics..Soft Computing 13 (2009), 617-625. 10.1007/s00500-008-0339-3 |
| Reference:
|
[26] Taheri, S. M., Behboodian, J.: Neyman-Pearson lemma for fuzzy hypotheses testing..Metrika 49 (1999), 3-17. Zbl 1103.62021, MR 1713647, 10.1007/s001840050021 |
| Reference:
|
[27] Torabi, H., Behboodian, J., Taheri, S. M.: Neyman-Pearson Lemma for fuzzy hypotheses testing with vague data..Metrika 64 (2006), 289-304. Zbl 1103.62021, MR 2259229, 10.1007/s00184-006-0049-8 |
| Reference:
|
[28] Viertl, R.: Univariate statistical analysis with fuzzy data..Comput. Statist. Data Anal. 51 (2006), 133-147. Zbl 1157.62368, MR 2297592, 10.1016/j.csda.2006.04.002 |
| Reference:
|
[29] Yao, J. S., Wu, K.: Ranking fuzzy numbers based on decomposition principle and signed distance..Fuzzy Sets and Systems 11 (2000), 275-288. Zbl 1179.62031, MR 1788399, 10.1016/S0165-0114(98)00122-5 |
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