zbMATH — the first resource for mathematics

Conditions for bimodality and multimodality of a mixture of two unimodal densities. (English) Zbl 1165.62304
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.

62E10 Characterization and structure theory of statistical distributions
60E05 Probability distributions: general theory
Full Text: EuDML Link
[1] J. Behboodian: On the modes of a mixture of two normal distribution. Technometrics 12 (1970), 131-139. · Zbl 0195.20304
[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. · Zbl 1076.62102
[3] A. C. Cohen: Compound normal distribution (Advanced Problems and Solutions). Amer. Math. Monthly 63 (1956), 129.
[4] Š. Došlá: Bimodální rozdělení (Bimodal Distributions). Master Thesis, Charles University, Prague 2006.
[5] I. Eisenberger: Genesis of bimodal distributions. Technometrics 6 (1964), 357-363.
[6] F. Helguero: Sui Massimi Delle Curve Dimorfiche. Biometrika 3 (1904), 85-98.
[7] J. H. B. Kemperman: Mixture with a limited number of modal intervals. Ann. Statist. 19 (1991), 2120-2144. · Zbl 0756.62008
[8] T. M. Sellke and S. H. Sellke: Chebyshev inequalities for unimodal distributions. Amer. Statist. 51 (1997), 34-40.
[9] C. A. Robertson and J. G. Fryer: Some descriptive properties of normal mixtures. Skand. Aktuarietidskr. 52 (1969), 137-146. · Zbl 0205.46603
[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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.