A fuzzy bootstrap test for the mean with Dp,q-distance
In this paper, we consider the problem of testing a simple hypothesis about the mean of a fuzzy random variable. For this purpose, we take a distance between the sample mean and the mean in the null hypothesis as a test statistic. An asymptotic test about the fuzzy mean is obtained by using a centra...
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| Veröffentlicht in: | Fuzzy information and engineering 2011-12, Vol.3 (4), p.351-358 |
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| creator | Sadeghpour-Gildeh, Bahram Rahimpour, Sedigheh |
| description | In this paper, we consider the problem of testing a simple hypothesis about the mean of a fuzzy random variable. For this purpose, we take a distance between the sample mean and the mean in the null hypothesis as a test statistic. An asymptotic test about the fuzzy mean is obtained by using a central limit theorem. The asymptotical distribution is
ω
2
-distribution. The
ω
2
-distribution is only known for special cases, thus we have considered random
LR
-fuzzy numbers. In the fuzzy concept, in addition to the existence of several versions of the central limit theorem, there is another practical disadvantage: The limit law is, in most cases, difficult to handle. Therefore, the central limit theorem for fuzzy random variable does not seem to be a very useful tool to make inferences on the mean of fuzzy random variable. Thus we use the bootstrap technique. Finally, by means of a simulation study, we show that the bootstrap method is a powerful tool in the statistical hypothesis testing about the mean of fuzzy random variables. |
| doi_str_mv | 10.1007/s12543-011-0090-9 |
| format | Article |
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ω
2
-distribution. The
ω
2
-distribution is only known for special cases, thus we have considered random
LR
-fuzzy numbers. In the fuzzy concept, in addition to the existence of several versions of the central limit theorem, there is another practical disadvantage: The limit law is, in most cases, difficult to handle. Therefore, the central limit theorem for fuzzy random variable does not seem to be a very useful tool to make inferences on the mean of fuzzy random variable. Thus we use the bootstrap technique. Finally, by means of a simulation study, we show that the bootstrap method is a powerful tool in the statistical hypothesis testing about the mean of fuzzy random variables.</description><identifier>ISSN: 1616-8658</identifier><identifier>EISSN: 1616-8666</identifier><identifier>DOI: 10.1007/s12543-011-0090-9</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer-Verlag</publisher><subject>Asymptotic properties ; Computational Intelligence ; Engineering ; Existence theorems ; Hypotheses ; Null hypothesis ; Original Article ; Random variables ; Regression analysis ; Statistical analysis ; Statistical methods</subject><ispartof>Fuzzy information and engineering, 2011-12, Vol.3 (4), p.351-358</ispartof><rights>Springer-Verlag Berlin Heidelberg and Fuzzy Information and Engineering Branch of the Operations Research Society of China 2011</rights><rights>2011 Taylor and Francis Group, LLC</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-p199t-a3c801487df0060b2a06dcdf53f1d6d3e7486e27debf38111fb12f86ba874e223</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><creatorcontrib>Sadeghpour-Gildeh, Bahram</creatorcontrib><creatorcontrib>Rahimpour, Sedigheh</creatorcontrib><title>A fuzzy bootstrap test for the mean with Dp,q-distance</title><title>Fuzzy information and engineering</title><addtitle>Fuzzy Inf. Eng</addtitle><description>In this paper, we consider the problem of testing a simple hypothesis about the mean of a fuzzy random variable. For this purpose, we take a distance between the sample mean and the mean in the null hypothesis as a test statistic. An asymptotic test about the fuzzy mean is obtained by using a central limit theorem. The asymptotical distribution is
ω
2
-distribution. The
ω
2
-distribution is only known for special cases, thus we have considered random
LR
-fuzzy numbers. In the fuzzy concept, in addition to the existence of several versions of the central limit theorem, there is another practical disadvantage: The limit law is, in most cases, difficult to handle. Therefore, the central limit theorem for fuzzy random variable does not seem to be a very useful tool to make inferences on the mean of fuzzy random variable. Thus we use the bootstrap technique. Finally, by means of a simulation study, we show that the bootstrap method is a powerful tool in the statistical hypothesis testing about the mean of fuzzy random variables.</description><subject>Asymptotic properties</subject><subject>Computational Intelligence</subject><subject>Engineering</subject><subject>Existence theorems</subject><subject>Hypotheses</subject><subject>Null hypothesis</subject><subject>Original Article</subject><subject>Random variables</subject><subject>Regression analysis</subject><subject>Statistical analysis</subject><subject>Statistical methods</subject><issn>1616-8658</issn><issn>1616-8666</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpFkE1LAzEQhoMoWGp_gLeAV6MzyW6SPZb6CQUveg7ZTWK36O42SRH7692yonOZOTzM-_IQcolwgwDqNiEvC8EAkQFUwKoTMkOJkmkp5enfXepzskhpC-MILLXQMyKXNOwPh29a931OOdqBZp8yDX2keePpp7cd_Wrzht4N1zvm2pRt1_gLchbsR_KL3z0nbw_3r6sntn55fF4t12zAqsrMikYDFlq5ACCh5haka1woRUAnnfCq0NJz5XwdhEbEUCMPWtZWq8JzLubkavo7xH63H4uZbb-P3RhpOIdCo1ZYjhSfqDTEtnv38Z9CMEdFZlJkRkXmqMhU4gfIlleg</recordid><startdate>20111201</startdate><enddate>20111201</enddate><creator>Sadeghpour-Gildeh, Bahram</creator><creator>Rahimpour, Sedigheh</creator><general>Springer-Verlag</general><general>Taylor & Francis Group</general><scope/></search><sort><creationdate>20111201</creationdate><title>A fuzzy bootstrap test for the mean with Dp,q-distance</title><author>Sadeghpour-Gildeh, Bahram ; Rahimpour, Sedigheh</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p199t-a3c801487df0060b2a06dcdf53f1d6d3e7486e27debf38111fb12f86ba874e223</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Asymptotic properties</topic><topic>Computational Intelligence</topic><topic>Engineering</topic><topic>Existence theorems</topic><topic>Hypotheses</topic><topic>Null hypothesis</topic><topic>Original Article</topic><topic>Random variables</topic><topic>Regression analysis</topic><topic>Statistical analysis</topic><topic>Statistical methods</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sadeghpour-Gildeh, Bahram</creatorcontrib><creatorcontrib>Rahimpour, Sedigheh</creatorcontrib><jtitle>Fuzzy information and engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Sadeghpour-Gildeh, Bahram</au><au>Rahimpour, Sedigheh</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A fuzzy bootstrap test for the mean with Dp,q-distance</atitle><jtitle>Fuzzy information and engineering</jtitle><stitle>Fuzzy Inf. Eng</stitle><date>2011-12-01</date><risdate>2011</risdate><volume>3</volume><issue>4</issue><spage>351</spage><epage>358</epage><pages>351-358</pages><issn>1616-8658</issn><eissn>1616-8666</eissn><abstract>In this paper, we consider the problem of testing a simple hypothesis about the mean of a fuzzy random variable. For this purpose, we take a distance between the sample mean and the mean in the null hypothesis as a test statistic. An asymptotic test about the fuzzy mean is obtained by using a central limit theorem. The asymptotical distribution is
ω
2
-distribution. The
ω
2
-distribution is only known for special cases, thus we have considered random
LR
-fuzzy numbers. In the fuzzy concept, in addition to the existence of several versions of the central limit theorem, there is another practical disadvantage: The limit law is, in most cases, difficult to handle. Therefore, the central limit theorem for fuzzy random variable does not seem to be a very useful tool to make inferences on the mean of fuzzy random variable. Thus we use the bootstrap technique. Finally, by means of a simulation study, we show that the bootstrap method is a powerful tool in the statistical hypothesis testing about the mean of fuzzy random variables.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer-Verlag</pub><doi>10.1007/s12543-011-0090-9</doi><tpages>8</tpages><oa>free_for_read</oa></addata></record> |
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| source | EZB-FREE-00999 freely available EZB journals |
| subjects | Asymptotic properties Computational Intelligence Engineering Existence theorems Hypotheses Null hypothesis Original Article Random variables Regression analysis Statistical analysis Statistical methods |
| title | A fuzzy bootstrap test for the mean with Dp,q-distance |
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