{"id":1171,"date":"2023-10-09T08:33:37","date_gmt":"2023-10-09T08:33:37","guid":{"rendered":"https:\/\/cvsc.upcebu.edu.ph\/?p=1171"},"modified":"2025-05-21T06:28:30","modified_gmt":"2025-05-21T06:28:30","slug":"on-the-zero-and-k-inflated-negative-binomial-distribution-with-applications","status":"publish","type":"post","link":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/2023\/10\/09\/on-the-zero-and-k-inflated-negative-binomial-distribution-with-applications\/","title":{"rendered":"ON THE ZERO AND k-INFLATED NEGATIVE BINOMIAL DISTRIBUTION WITH APPLICATIONS"},"content":{"rendered":"\n<p>Ian Jay A. Serra<\/p>\n\n\n\n<p>Daisy Lou L. Polistico<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/cvsc.upcebu.edu.ph\/wp-content\/uploads\/2023\/10\/Picture1-1.jpg\" alt=\"\" class=\"wp-image-1173\" style=\"width:274px;height:392px\" width=\"274\" height=\"392\" srcset=\"https:\/\/cvsc.upcebu.edu.ph\/wp-content\/uploads\/2023\/10\/Picture1-1.jpg 631w, https:\/\/cvsc.upcebu.edu.ph\/wp-content\/uploads\/2023\/10\/Picture1-1-210x300.jpg 210w\" sizes=\"(max-width: 274px) 100vw, 274px\" \/><\/figure>\n\n\n\n<p><strong>Abstract<\/strong><\/p>\n\n\n\n<p>In the literature, there are a significant number of studies on mixtures and compound probability distributions used for count data with inflated frequencies. This study extended some existing zero-inflated distributions, by considering the flexibility of peaks in the data with excessive counts other than zeros and handled an overdispersion in the data. Moreover, this study formulated a proposed zero- and&nbsp;<em>k<\/em>-inflated negative binomial (Z<em>k<\/em>INB) distribution which is a mixture of a multinomial logistic and negative binomial distribution. The multinomial logistic component captures the occurrence of excessive counts, at zero and at&nbsp;<em>k<\/em>&nbsp;&gt; 0, while the negative binomial component captures the counts that are assumed to follow a negative binomial distribution. The probability mass function (pmf) and the moment generating function (mgf ) of the distribution were derived in order to compute some vital structural properties of the formulated distribution, such as the mean and the variance. Examples showed &nbsp;that the formulated Z<em>k<\/em>INB seems to capture better distributions as compared with other existing distributions for inflated count data.<\/p>\n\n\n\n<p>Keywords:<\/p>\n\n\n\n<p>inflated count data, overdispersion, Z<em>k<\/em>INB distribution, excessive counts, negative binomial distribution, count distributions<\/p>\n\n\n\n<p>Link to the Article<\/p>\n\n\n\n<p><a href=\"https:\/\/pphmjopenaccess.com\/index.php\/aas\/article\/view\/209\">https:\/\/pphmjopenaccess.com\/index.php\/aas\/article\/view\/209<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ian Jay A. Serra Daisy Lou L. Polistico Abstract In the literature, there are a significant number of studies on mixtures and compound probability distributions used for count data with inflated frequencies. This study extended some existing zero-inflated distributions, by considering the flexibility of peaks in the data with excessive counts other than zeros and [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[7],"tags":[],"class_list":["post-1171","post","type-post","status-publish","format-standard","hentry","category-recent-publications"],"_links":{"self":[{"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/posts\/1171","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/comments?post=1171"}],"version-history":[{"count":1,"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/posts\/1171\/revisions"}],"predecessor-version":[{"id":1937,"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/posts\/1171\/revisions\/1937"}],"wp:attachment":[{"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/media?parent=1171"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/categories?post=1171"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/tags?post=1171"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}