Large Sample Comparison of Parameter Estimates in Gamma Raindrop Distributions
Raindrop size distributions have been characterized through the gamma family. Over the years, quite a few estimates of these gamma parameters have been proposed. The natural question for the practitioner, then, is what estimation procedure should be used. We provide guidance in answering this questi...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-03-01
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| Series: | Atmosphere |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-4433/11/4/333 |
| _version_ | 1797626427264204800 |
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| author | Roger W. Johnson Donna V. Kliche |
| author_facet | Roger W. Johnson Donna V. Kliche |
| author_sort | Roger W. Johnson |
| collection | DOAJ |
| description | Raindrop size distributions have been characterized through the gamma family. Over the years, quite a few estimates of these gamma parameters have been proposed. The natural question for the practitioner, then, is what estimation procedure should be used. We provide guidance in answering this question when a large sample size (>2000 drops) of accurately measured drops is available. Seven estimation procedures from the literature: five method of moments procedures, maximum likelihood, and a pseudo maximum likelihood procedure, were examined. We show that the two maximum likelihood procedures provide the best precision (lowest variance) in estimating the gamma parameters. Method of moments procedures involving higher-order moments, on the other hand, give rise to poor precision (high variance) in estimating these parameters. A technique called the delta method assisted in our comparison of these various estimation procedures. |
| first_indexed | 2024-03-11T10:10:13Z |
| format | Article |
| id | doaj.art-c3ee43e244794a73a16ad4228bc1047c |
| institution | Directory Open Access Journal |
| issn | 2073-4433 |
| language | English |
| last_indexed | 2024-03-11T10:10:13Z |
| publishDate | 2020-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Atmosphere |
| spelling | doaj.art-c3ee43e244794a73a16ad4228bc1047c2023-11-16T14:36:24ZengMDPI AGAtmosphere2073-44332020-03-0111433310.3390/atmos11040333Large Sample Comparison of Parameter Estimates in Gamma Raindrop DistributionsRoger W. Johnson0Donna V. Kliche1Department of Mathematics, South Dakota School of Mines & Technology, Rapid City, SD 57701, USAAtmospheric and Environmental Sciences, South Dakota School of Mines & Technology, Rapid City, SD 57701, USARaindrop size distributions have been characterized through the gamma family. Over the years, quite a few estimates of these gamma parameters have been proposed. The natural question for the practitioner, then, is what estimation procedure should be used. We provide guidance in answering this question when a large sample size (>2000 drops) of accurately measured drops is available. Seven estimation procedures from the literature: five method of moments procedures, maximum likelihood, and a pseudo maximum likelihood procedure, were examined. We show that the two maximum likelihood procedures provide the best precision (lowest variance) in estimating the gamma parameters. Method of moments procedures involving higher-order moments, on the other hand, give rise to poor precision (high variance) in estimating these parameters. A technique called the delta method assisted in our comparison of these various estimation procedures.https://www.mdpi.com/2073-4433/11/4/333raindrop size distributiongamma distributionmethod of momentsmaximum likelihooddelta methodsimulation |
| spellingShingle | Roger W. Johnson Donna V. Kliche Large Sample Comparison of Parameter Estimates in Gamma Raindrop Distributions Atmosphere raindrop size distribution gamma distribution method of moments maximum likelihood delta method simulation |
| title | Large Sample Comparison of Parameter Estimates in Gamma Raindrop Distributions |
| title_full | Large Sample Comparison of Parameter Estimates in Gamma Raindrop Distributions |
| title_fullStr | Large Sample Comparison of Parameter Estimates in Gamma Raindrop Distributions |
| title_full_unstemmed | Large Sample Comparison of Parameter Estimates in Gamma Raindrop Distributions |
| title_short | Large Sample Comparison of Parameter Estimates in Gamma Raindrop Distributions |
| title_sort | large sample comparison of parameter estimates in gamma raindrop distributions |
| topic | raindrop size distribution gamma distribution method of moments maximum likelihood delta method simulation |
| url | https://www.mdpi.com/2073-4433/11/4/333 |
| work_keys_str_mv | AT rogerwjohnson largesamplecomparisonofparameterestimatesingammaraindropdistributions AT donnavkliche largesamplecomparisonofparameterestimatesingammaraindropdistributions |