Easily Changeable Kurtosis Distribution
The goal of this paper is to introduce the easily changeable kurtosis (ECK) distribution. The uniform distribution appears as a special cases of the ECK distribution. The new distribution tends to the normal distribution. Properties of the ECK distribution such as PDF, CDF, modes, inflection points...
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| Format: | Article |
| Language: | English |
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Austrian Statistical Society
2023-07-01
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| Series: | Austrian Journal of Statistics |
| Online Access: | https://www.ajs.or.at/index.php/ajs/article/view/1434 |
| _version_ | 1797777547822366720 |
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| author | Piotr Sulewski |
| author_facet | Piotr Sulewski |
| author_sort | Piotr Sulewski |
| collection | DOAJ |
| description |
The goal of this paper is to introduce the easily changeable kurtosis (ECK) distribution. The uniform distribution appears as a special cases of the ECK distribution. The new distribution tends to the normal distribution. Properties of the ECK distribution such as PDF, CDF, modes, inflection points, quantiles, moments, moment generating function, Moors’ measure, moments of order statistics, random number generator and the Fisher Information Matrix are derived. The unknown parameters of the ECK distribution are estimated by the maximum likelihood method. The Shannon, Renyi and Tsallis entropies are calculated. Illustrative examples of applicability and flexibility of the ECK distribution are given. The most important R codes are presented in the Appendix.
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| first_indexed | 2024-03-12T23:06:26Z |
| format | Article |
| id | doaj.art-3435bd3ba2f74eafa97318771cffe0db |
| institution | Directory Open Access Journal |
| issn | 1026-597X |
| language | English |
| last_indexed | 2024-03-12T23:06:26Z |
| publishDate | 2023-07-01 |
| publisher | Austrian Statistical Society |
| record_format | Article |
| series | Austrian Journal of Statistics |
| spelling | doaj.art-3435bd3ba2f74eafa97318771cffe0db2023-07-18T17:35:58ZengAustrian Statistical SocietyAustrian Journal of Statistics1026-597X2023-07-0152310.17713/ajs.v52i3.1434Easily Changeable Kurtosis DistributionPiotr Sulewski0Pomeranin University The goal of this paper is to introduce the easily changeable kurtosis (ECK) distribution. The uniform distribution appears as a special cases of the ECK distribution. The new distribution tends to the normal distribution. Properties of the ECK distribution such as PDF, CDF, modes, inflection points, quantiles, moments, moment generating function, Moors’ measure, moments of order statistics, random number generator and the Fisher Information Matrix are derived. The unknown parameters of the ECK distribution are estimated by the maximum likelihood method. The Shannon, Renyi and Tsallis entropies are calculated. Illustrative examples of applicability and flexibility of the ECK distribution are given. The most important R codes are presented in the Appendix. https://www.ajs.or.at/index.php/ajs/article/view/1434 |
| spellingShingle | Piotr Sulewski Easily Changeable Kurtosis Distribution Austrian Journal of Statistics |
| title | Easily Changeable Kurtosis Distribution |
| title_full | Easily Changeable Kurtosis Distribution |
| title_fullStr | Easily Changeable Kurtosis Distribution |
| title_full_unstemmed | Easily Changeable Kurtosis Distribution |
| title_short | Easily Changeable Kurtosis Distribution |
| title_sort | easily changeable kurtosis distribution |
| url | https://www.ajs.or.at/index.php/ajs/article/view/1434 |
| work_keys_str_mv | AT piotrsulewski easilychangeablekurtosisdistribution |