A Novel Zero-Truncated Katz Distribution by the Lagrange Expansion of the Second Kind with Associated Inferences
In this article, the Lagrange expansion of the second kind is used to generate a novel zero-truncated Katz distribution; we refer to it as the Lagrangian zero-truncated Katz distribution (LZTKD). Notably, the zero-truncated Katz distribution is a special case of this distribution. Along with the clo...
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| Format: | Article |
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MDPI AG
2023-06-01
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| Series: | Analytics |
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| Online Access: | https://www.mdpi.com/2813-2203/2/2/26 |
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| author | Damodaran Santhamani Shibu Christophe Chesneau Mohanan Monisha Radhakumari Maya Muhammed Rasheed Irshad |
| author_facet | Damodaran Santhamani Shibu Christophe Chesneau Mohanan Monisha Radhakumari Maya Muhammed Rasheed Irshad |
| author_sort | Damodaran Santhamani Shibu |
| collection | DOAJ |
| description | In this article, the Lagrange expansion of the second kind is used to generate a novel zero-truncated Katz distribution; we refer to it as the Lagrangian zero-truncated Katz distribution (LZTKD). Notably, the zero-truncated Katz distribution is a special case of this distribution. Along with the closed form expression of all its statistical characteristics, the LZTKD is proven to provide an adequate model for both underdispersed and overdispersed zero-truncated count datasets. Specifically, we show that the associated hazard rate function has increasing, decreasing, bathtub, or upside-down bathtub shapes. Moreover, we demonstrate that the LZTKD belongs to the Lagrangian distribution of the first kind. Then, applications of the LZTKD in statistical scenarios are explored. The unknown parameters are estimated using the well-reputed method of the maximum likelihood. In addition, the generalized likelihood ratio test procedure is applied to test the significance of the additional parameter. In order to evaluate the performance of the maximum likelihood estimates, simulation studies are also conducted. The use of real-life datasets further highlights the relevance and applicability of the proposed model. |
| first_indexed | 2024-03-11T02:51:28Z |
| format | Article |
| id | doaj.art-1b2d354c519e49adb131b36a2767b418 |
| institution | Directory Open Access Journal |
| issn | 2813-2203 |
| language | English |
| last_indexed | 2024-03-11T02:51:28Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Analytics |
| spelling | doaj.art-1b2d354c519e49adb131b36a2767b4182023-11-18T08:57:30ZengMDPI AGAnalytics2813-22032023-06-012246348410.3390/analytics2020026A Novel Zero-Truncated Katz Distribution by the Lagrange Expansion of the Second Kind with Associated InferencesDamodaran Santhamani Shibu0Christophe Chesneau1Mohanan Monisha2Radhakumari Maya3Muhammed Rasheed Irshad4Department of Statistics, University College, Thiruvananthapuram 695 034, IndiaDepartment of Mathematics, Université de Caen Basse-Normandie, UFR de Sciences, F-14032 Caen, FranceDepartment of Statistics, University College, Thiruvananthapuram 695 034, IndiaDepartment of Statistics, University College, Thiruvananthapuram 695 034, IndiaDepartment of Statistics, Cochin University of Science and Technology, Cochin 682 022, IndiaIn this article, the Lagrange expansion of the second kind is used to generate a novel zero-truncated Katz distribution; we refer to it as the Lagrangian zero-truncated Katz distribution (LZTKD). Notably, the zero-truncated Katz distribution is a special case of this distribution. Along with the closed form expression of all its statistical characteristics, the LZTKD is proven to provide an adequate model for both underdispersed and overdispersed zero-truncated count datasets. Specifically, we show that the associated hazard rate function has increasing, decreasing, bathtub, or upside-down bathtub shapes. Moreover, we demonstrate that the LZTKD belongs to the Lagrangian distribution of the first kind. Then, applications of the LZTKD in statistical scenarios are explored. The unknown parameters are estimated using the well-reputed method of the maximum likelihood. In addition, the generalized likelihood ratio test procedure is applied to test the significance of the additional parameter. In order to evaluate the performance of the maximum likelihood estimates, simulation studies are also conducted. The use of real-life datasets further highlights the relevance and applicability of the proposed model.https://www.mdpi.com/2813-2203/2/2/26Lagrange expansion of the first kindLagrange expansion of the second kindzero-truncated Katz distributiondispersionmaximum likelihood estimationsimulation |
| spellingShingle | Damodaran Santhamani Shibu Christophe Chesneau Mohanan Monisha Radhakumari Maya Muhammed Rasheed Irshad A Novel Zero-Truncated Katz Distribution by the Lagrange Expansion of the Second Kind with Associated Inferences Analytics Lagrange expansion of the first kind Lagrange expansion of the second kind zero-truncated Katz distribution dispersion maximum likelihood estimation simulation |
| title | A Novel Zero-Truncated Katz Distribution by the Lagrange Expansion of the Second Kind with Associated Inferences |
| title_full | A Novel Zero-Truncated Katz Distribution by the Lagrange Expansion of the Second Kind with Associated Inferences |
| title_fullStr | A Novel Zero-Truncated Katz Distribution by the Lagrange Expansion of the Second Kind with Associated Inferences |
| title_full_unstemmed | A Novel Zero-Truncated Katz Distribution by the Lagrange Expansion of the Second Kind with Associated Inferences |
| title_short | A Novel Zero-Truncated Katz Distribution by the Lagrange Expansion of the Second Kind with Associated Inferences |
| title_sort | novel zero truncated katz distribution by the lagrange expansion of the second kind with associated inferences |
| topic | Lagrange expansion of the first kind Lagrange expansion of the second kind zero-truncated Katz distribution dispersion maximum likelihood estimation simulation |
| url | https://www.mdpi.com/2813-2203/2/2/26 |
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