REMARKS ON THE FORMULA FOR THE MOMENTS OF THE PÓLYA PROBABILITY DISTRIBUTION
ABSTRACT The probability distribution of a random variable can be characterized by some numbers called parameters of the distribution. The moments belong to the most frequently used parameters. We focus on the Pólya distribution because it is easy to obtain from it as special cases some very...
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| Format: | Article |
| Language: | English |
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Lodz University Press
2015-08-01
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| Series: | Acta Universitatis Lodziensis. Folia Oeconomica |
| Subjects: | |
| Online Access: | https://czasopisma.uni.lodz.pl/foe/article/view/581 |
| _version_ | 1819051010127036416 |
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| author | Tadeusz Gerstenkorn |
| author_facet | Tadeusz Gerstenkorn |
| author_sort | Tadeusz Gerstenkorn |
| collection | DOAJ |
| description | ABSTRACT
The probability distribution of a random variable can be characterized by some numbers called parameters of the distribution. The moments belong to the most frequently used parameters. We focus on the Pólya distribution because it is easy to obtain from it as special cases some very important in the statistics distributions, as binomial, negative binomial and Poisson (the last one in the limit procedure).
In 1972 G. Mühlbach gave very interesting formulae for the moments of the Pólya distribution. The author did not investigate the evaluation of the numerical efficacy of the formula for the moments. We will show that it is possible to demonstrate this formula in a simpler form, which has a practical significance and importance. |
| first_indexed | 2024-12-21T11:57:08Z |
| format | Article |
| id | doaj.art-109d602bf644433bab135be410a8cc2b |
| institution | Directory Open Access Journal |
| issn | 0208-6018 2353-7663 |
| language | English |
| last_indexed | 2024-12-21T11:57:08Z |
| publishDate | 2015-08-01 |
| publisher | Lodz University Press |
| record_format | Article |
| series | Acta Universitatis Lodziensis. Folia Oeconomica |
| spelling | doaj.art-109d602bf644433bab135be410a8cc2b2022-12-21T19:04:54ZengLodz University PressActa Universitatis Lodziensis. Folia Oeconomica0208-60182353-76632015-08-013314256REMARKS ON THE FORMULA FOR THE MOMENTS OF THE PÓLYA PROBABILITY DISTRIBUTIONTadeusz Gerstenkorn0Professor Emeritus, University of Łódź,ABSTRACT The probability distribution of a random variable can be characterized by some numbers called parameters of the distribution. The moments belong to the most frequently used parameters. We focus on the Pólya distribution because it is easy to obtain from it as special cases some very important in the statistics distributions, as binomial, negative binomial and Poisson (the last one in the limit procedure). In 1972 G. Mühlbach gave very interesting formulae for the moments of the Pólya distribution. The author did not investigate the evaluation of the numerical efficacy of the formula for the moments. We will show that it is possible to demonstrate this formula in a simpler form, which has a practical significance and importance.https://czasopisma.uni.lodz.pl/foe/article/view/581moments of the probability distribution, Pólya probability distribution |
| spellingShingle | Tadeusz Gerstenkorn REMARKS ON THE FORMULA FOR THE MOMENTS OF THE PÓLYA PROBABILITY DISTRIBUTION Acta Universitatis Lodziensis. Folia Oeconomica moments of the probability distribution, Pólya probability distribution |
| title | REMARKS ON THE FORMULA FOR THE MOMENTS OF THE PÓLYA PROBABILITY DISTRIBUTION |
| title_full | REMARKS ON THE FORMULA FOR THE MOMENTS OF THE PÓLYA PROBABILITY DISTRIBUTION |
| title_fullStr | REMARKS ON THE FORMULA FOR THE MOMENTS OF THE PÓLYA PROBABILITY DISTRIBUTION |
| title_full_unstemmed | REMARKS ON THE FORMULA FOR THE MOMENTS OF THE PÓLYA PROBABILITY DISTRIBUTION |
| title_short | REMARKS ON THE FORMULA FOR THE MOMENTS OF THE PÓLYA PROBABILITY DISTRIBUTION |
| title_sort | remarks on the formula for the moments of the polya probability distribution |
| topic | moments of the probability distribution, Pólya probability distribution |
| url | https://czasopisma.uni.lodz.pl/foe/article/view/581 |
| work_keys_str_mv | AT tadeuszgerstenkorn remarksontheformulaforthemomentsofthepolyaprobabilitydistribution |