Conditions for bimodality and multimodality of a mixture of two unimodal densities

Šárka Došlá

Kybernetika (2009)

  • Volume: 45, Issue: 2, page 279-292
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Došlá, Šárka. "Conditions for bimodality and multimodality of a mixture of two unimodal densities." Kybernetika 45.2 (2009): 279-292. <http://eudml.org/doc/37733>.

@article{Došlá2009,
abstract = {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.},
author = {Došlá, Šárka},
journal = {Kybernetika},
keywords = {bimodality; unimodality; multimodality; mixture of two unimodal distributions; bimodality; unimodality; multimodality; mixture of two unimodal distributions},
language = {eng},
number = {2},
pages = {279-292},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Conditions for bimodality and multimodality of a mixture of two unimodal densities},
url = {http://eudml.org/doc/37733},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Došlá, Šárka
TI - Conditions for bimodality and multimodality of a mixture of two unimodal densities
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 2
SP - 279
EP - 292
AB - 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.
LA - eng
KW - bimodality; unimodality; multimodality; mixture of two unimodal distributions; bimodality; unimodality; multimodality; mixture of two unimodal distributions
UR - http://eudml.org/doc/37733
ER -

References

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  1. On the modes of a mixture of two normal distribution, Technometrics 12 (1970), 131–139. 
  2. Mixtures of two normal distributions: Modality and failure rate, Statist. Probab. Lett. 74 (2005), 253–264. MR2189464
  3. Compound normal distribution (Advanced Problems and Solutions), Amer. Math. Monthly 63 (1956), 129. 
  4. Bimodální rozdělení (Bimodal Distributions), Master Thesis, Charles University, Prague 2006. 
  5. Genesis of bimodal distributions, Technometrics 6 (1964), 357–363. MR0184314
  6. Sui Massimi Delle Curve Dimorfiche, Biometrika 3 (1904), 85–98. 
  7. Mixture with a limited number of modal intervals, Ann. Statist. 19 (1991), 2120–2144. MR1135167
  8. Chebyshev inequalities for unimodal distributions, Amer. Statist. 51 (1997), 34–40. MR1440938
  9. Some descriptive properties of normal mixtures, Skand. Aktuarietidskr. 52 (1969), 137–146. MR0267674
  10. Multimodality in a family of probability densities, with application to a linear mixture of two normal densities, Statist. Neerlandika 18 (1964), 267–282. 

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