Logarithmic concavity of the inverse incomplete beta function with respect to parameter
The beta distribution is a two-parameter family of probability distributions whose distribution function is the (regularised) incomplete beta function. In this paper, the inverse incomplete beta function is studied analytically as univariate function of the first parameter. Monotonicity, limit resul...
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| creator | Askitis, Dimitris |
| description | The beta distribution is a two-parameter family of probability distributions
whose distribution function is the (regularised) incomplete beta function. In
this paper, the inverse incomplete beta function is studied analytically as
univariate function of the first parameter. Monotonicity, limit results and
convexity properties are provided. In particular, logarithmic concavity of the
inverse incomplete beta function is established. In addition, we provide
monotonicity results on inverses of a larger class of parametrised
distributions that may be of independent interest. |
| doi_str_mv | 10.48550/arxiv.1710.09708 |
| format | Article |
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whose distribution function is the (regularised) incomplete beta function. In
this paper, the inverse incomplete beta function is studied analytically as
univariate function of the first parameter. Monotonicity, limit results and
convexity properties are provided. In particular, logarithmic concavity of the
inverse incomplete beta function is established. In addition, we provide
monotonicity results on inverses of a larger class of parametrised
distributions that may be of independent interest.</description><identifier>DOI: 10.48550/arxiv.1710.09708</identifier><language>eng</language><subject>Mathematics - Classical Analysis and ODEs</subject><creationdate>2017-10</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,778,883</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1710.09708$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1710.09708$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Askitis, Dimitris</creatorcontrib><title>Logarithmic concavity of the inverse incomplete beta function with respect to parameter</title><description>The beta distribution is a two-parameter family of probability distributions
whose distribution function is the (regularised) incomplete beta function. In
this paper, the inverse incomplete beta function is studied analytically as
univariate function of the first parameter. Monotonicity, limit results and
convexity properties are provided. In particular, logarithmic concavity of the
inverse incomplete beta function is established. In addition, we provide
monotonicity results on inverses of a larger class of parametrised
distributions that may be of independent interest.</description><subject>Mathematics - Classical Analysis and ODEs</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8tqwzAURLXpoqT9gK6qH3Aqoei1DKEvMHQT6NJcSVeJILaMrLrN39dJuzowzAwcQh44W2-MlOwJyk-a11wvAbOamVvy2eYDlFSPffLU58HDnOqZ5kjrEWkaZizThT734wkrUocVaPwafE15oN_LkhacRvSV1kxHKNAvtXJHbiKcJrz_54rsX573u7em_Xh9323bBpQ2jWXBOOeZ8Bt0UknPUWkIwVrULiorokAVOQTDrAzIDAJzWkbuBMaonViRx7_bq1k3ltRDOXcXw-5qKH4BuY1OhA</recordid><startdate>20171026</startdate><enddate>20171026</enddate><creator>Askitis, Dimitris</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20171026</creationdate><title>Logarithmic concavity of the inverse incomplete beta function with respect to parameter</title><author>Askitis, Dimitris</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a678-90d8bbc03c4eb565c1e67add99e7bf693f3e6f1ad8095de08ea0b75f1b3eff7b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Mathematics - Classical Analysis and ODEs</topic><toplevel>online_resources</toplevel><creatorcontrib>Askitis, Dimitris</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Askitis, Dimitris</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Logarithmic concavity of the inverse incomplete beta function with respect to parameter</atitle><date>2017-10-26</date><risdate>2017</risdate><abstract>The beta distribution is a two-parameter family of probability distributions
whose distribution function is the (regularised) incomplete beta function. In
this paper, the inverse incomplete beta function is studied analytically as
univariate function of the first parameter. Monotonicity, limit results and
convexity properties are provided. In particular, logarithmic concavity of the
inverse incomplete beta function is established. In addition, we provide
monotonicity results on inverses of a larger class of parametrised
distributions that may be of independent interest.</abstract><doi>10.48550/arxiv.1710.09708</doi><oa>free_for_read</oa></addata></record> |
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| source | arXiv.org |
| subjects | Mathematics - Classical Analysis and ODEs |
| title | Logarithmic concavity of the inverse incomplete beta function with respect to parameter |
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