<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Huiming Zhang</style></author><author><style face="normal" font="default" size="100%">Kai Tan</style></author><author><style face="normal" font="default" size="100%">Li Bo</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">COM-negative binomial distribution: modeling overdispersion and ultrahigh zero-inflated count data</style></title><secondary-title><style face="normal" font="default" size="100%">Frontiers of Mathematics in China</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://link.springer.com/article/10.1007%2Fs11464-018-0714-z</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">13</style></volume><pages><style face="normal" font="default" size="100%"> 967–998</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;&lt;span&gt;We focus on the COM-type negative binomial distribution with three parameters, which belongs to COM-type (&lt;/span&gt;&lt;em class=&quot;EmphasisTypeItalic &quot;&gt;a&lt;/em&gt;&lt;span&gt;,&amp;nbsp;&lt;/span&gt;&lt;em class=&quot;EmphasisTypeItalic &quot;&gt;b&lt;/em&gt;&lt;span&gt;, 0) class distributions and family of equilibrium distributions of arbitrary birth-death process. Besides, we show abundant distributional properties such as overdispersion and underdispersion, log-concavity, log-convexity (infinite divisibility), pseudo compound Poisson, stochastic ordering, and asymptotic approximation. Some characterizations including sum of equicorrelated geometrically distributed random variables, conditional distribution, limit distribution of COM-negative hypergeometric distribution, and Stein’s identity are given for theoretical properties. COM-negative binomial distribution was applied to overdispersion and ultrahigh zero-inflated data sets. With the aid of ratio regression, we employ maximum likelihood method to estimate the parameters and the goodness-of-fit are evaluated by the discrete Kolmogorov-Smirnov test.&lt;/span&gt;&lt;/p&gt;</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue></record></records></xml>