| Title:
|
Conditions for bimodality and multimodality of a mixture of two unimodal densities (English) |
| Author:
|
Došlá, Šárka |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
45 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
279-292 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Conditions for bimodality of mixtures of two unimodal distributions are investigated in some special cases. Based on general characterizations, explicit criteria for the parameters are derived for mixtures of two Cauchy, logistic, Student, gamma, log-normal, Gumbel and other distributions. (English) |
| Keyword:
|
bimodality |
| Keyword:
|
unimodality |
| Keyword:
|
multimodality |
| Keyword:
|
mixture of two unimodal distributions |
| MSC:
|
60E05 |
| MSC:
|
62E10 |
| idZBL:
|
Zbl 1165.62304 |
| idMR:
|
MR2518152 |
| . |
| Date available:
|
2010-06-02T18:31:26Z |
| Last updated:
|
2013-09-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140075 |
| . |
| Reference:
|
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| Reference:
|
[2] H. W. Block, Y. Li, and T. H. Savits: Mixtures of two normal distributions: Modality and failure rate.Statist. Probab. Lett. 74 (2005), 253–264. MR 2189464 |
| Reference:
|
[3] A. C. Cohen: Compound normal distribution (Advanced Problems and Solutions).Amer. Math. Monthly 63 (1956), 129. |
| Reference:
|
[4] Š. Došlá: Bimodální rozdělení (Bimodal Distributions).Master Thesis, Charles University, Prague 2006. |
| Reference:
|
[5] I. Eisenberger: Genesis of bimodal distributions.Technometrics 6 (1964), 357–363. MR 0184314 |
| Reference:
|
[6] F. Helguero: Sui Massimi Delle Curve Dimorfiche.Biometrika 3 (1904), 85–98. |
| Reference:
|
[7] J. H. B. Kemperman: Mixture with a limited number of modal intervals.Ann. Statist. 19 (1991), 2120–2144. MR 1135167 |
| Reference:
|
[8] T. M. Sellke and S. H. Sellke: Chebyshev inequalities for unimodal distributions.Amer. Statist. 51 (1997), 34–40. MR 1440938 |
| Reference:
|
[9] C. A. Robertson and J. G. Fryer: Some descriptive properties of normal mixtures.Skand. Aktuarietidskr. 52 (1969), 137–146. MR 0267674 |
| Reference:
|
[10] J. Wessels: Multimodality in a family of probability densities, with application to a linear mixture of two normal densities.Statist. Neerlandika 18 (1964), 267–282. |
| . |
