Alternative Means of Statistical Data Analysis: L-Moments and TL-Moments of Probability Distributions
Moments and cumulants are commonly used to characterize the probability distribution or observed data set. The use of the moment method of parameter estimation is also common in the construction of an appropriate parametric distribution for a certain data set. The moment method does not always produ...
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| Format: | Article |
| Language: | English |
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Czech Statistical Office
2014-06-01
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| Series: | Statistika: Statistics and Economy Journal |
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| Online Access: | http://www.czso.cz/csu/2014edicniplan.nsf/engc/01003BF6F2/$File/32019714q2077.pdf |
| _version_ | 1818010931941081088 |
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| author | Diana Bílková |
| author_facet | Diana Bílková |
| author_sort | Diana Bílková |
| collection | DOAJ |
| description | Moments and cumulants are commonly used to characterize the probability distribution or observed data set. The use of the moment method of parameter estimation is also common in the construction of an appropriate parametric distribution for a certain data set. The moment method does not always produce satisfactory results. It is difficult to determine exactly what information concerning the shape of the distribution is expressed by its moments of the third and higher order. In the case of small samples in particular, numerical values of sample moments can be very different from the corresponding values of theoretical moments of the relevant probability distribution from which the random sample comes. Parameter estimations of the probability distribution made by the moment method are oft en considerably less accurate than those obtained using other methods, particularly in the case of small samples. The present paper deals with an alternative approach to the construction of an appropriate parametric distribution for the considered data set using order statistics. |
| first_indexed | 2024-04-14T06:01:02Z |
| format | Article |
| id | doaj.art-9810c39347cc4668ab5fb4914cb81ad8 |
| institution | Directory Open Access Journal |
| issn | 1804-8765 1804-8765 |
| language | English |
| last_indexed | 2024-04-14T06:01:02Z |
| publishDate | 2014-06-01 |
| publisher | Czech Statistical Office |
| record_format | Article |
| series | Statistika: Statistics and Economy Journal |
| spelling | doaj.art-9810c39347cc4668ab5fb4914cb81ad82022-12-22T02:08:45ZengCzech Statistical OfficeStatistika: Statistics and Economy Journal1804-87651804-87652014-06-019427794Alternative Means of Statistical Data Analysis: L-Moments and TL-Moments of Probability DistributionsDiana Bílková0University of Economics, Prague, Czech RepublicMoments and cumulants are commonly used to characterize the probability distribution or observed data set. The use of the moment method of parameter estimation is also common in the construction of an appropriate parametric distribution for a certain data set. The moment method does not always produce satisfactory results. It is difficult to determine exactly what information concerning the shape of the distribution is expressed by its moments of the third and higher order. In the case of small samples in particular, numerical values of sample moments can be very different from the corresponding values of theoretical moments of the relevant probability distribution from which the random sample comes. Parameter estimations of the probability distribution made by the moment method are oft en considerably less accurate than those obtained using other methods, particularly in the case of small samples. The present paper deals with an alternative approach to the construction of an appropriate parametric distribution for the considered data set using order statistics.http://www.czso.cz/csu/2014edicniplan.nsf/engc/01003BF6F2/$File/32019714q2077.pdfMikrocensus L-moments and TL-moments of probability distributionsample L-moments and TL-momentsprobability density functiondistribution functionquantile functionorder statisticsincome distribution |
| spellingShingle | Diana Bílková Alternative Means of Statistical Data Analysis: L-Moments and TL-Moments of Probability Distributions Statistika: Statistics and Economy Journal Mikrocensus L-moments and TL-moments of probability distribution sample L-moments and TL-moments probability density function distribution function quantile function order statistics income distribution |
| title | Alternative Means of Statistical Data Analysis: L-Moments and TL-Moments of Probability Distributions |
| title_full | Alternative Means of Statistical Data Analysis: L-Moments and TL-Moments of Probability Distributions |
| title_fullStr | Alternative Means of Statistical Data Analysis: L-Moments and TL-Moments of Probability Distributions |
| title_full_unstemmed | Alternative Means of Statistical Data Analysis: L-Moments and TL-Moments of Probability Distributions |
| title_short | Alternative Means of Statistical Data Analysis: L-Moments and TL-Moments of Probability Distributions |
| title_sort | alternative means of statistical data analysis l moments and tl moments of probability distributions |
| topic | Mikrocensus L-moments and TL-moments of probability distribution sample L-moments and TL-moments probability density function distribution function quantile function order statistics income distribution |
| url | http://www.czso.cz/csu/2014edicniplan.nsf/engc/01003BF6F2/$File/32019714q2077.pdf |
| work_keys_str_mv | AT dianabilkova alternativemeansofstatisticaldataanalysislmomentsandtlmomentsofprobabilitydistributions |