The modes of a mixture of two normal distributions

• Autorzy: Sitek G.
• Języki publikacji: EN

Abstrakty

EN

Mixture distributions arise naturally where a statistical population contains two or more subpopulations. Finite mixture distributions refer to composite distributions constructed by mixing a number K of component distributions. The first account of mixture data being analyzed was documented by Pearson in 1894. We consider the distribution of a mixture of two normal distributions and investigate the conditions for which the distribution is bimodal. This paper presents a procedure for answering the question of whether a mixture of two normal distributions which five known parameters µ1, µ2, σ1, σ2, p is unimodal or not. For finding the modes, a simple iterative procedure is given. This article presents the possibility of estimation of modes using biaverage.

Słowa kluczowe

EN

mixture of normal distributions; bimodal distributions; biaverage

PL

mieszanina rozkładów normalnych; rozkład dwumodalny

• Wydawca: Wydawnictwo Politechniki Śląskiej
• Czasopismo: Silesian Journal of Pure and Applied Mathematics
• Rocznik: 2016
• Tom: Vol. 6, iss. 1
• Strony: 59--67
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Sitek G.

• Department of Statistics, University of Economics in Katowice, Poland

Bibliografia

• 1. Antoniewicz R.: About Average and Mean. Publisher University of Economics, Wrocl aw 2005 (in Polish).
• 2. Antoniewicz R., Misztal A.: Biaverage. Statist. Rev. 47, no. 3-4 (2001), 269– 274 (in Polish).
• 3. Behboodian J.: On the modes of a mixture of two normal distributions. Technometrics 12, no. 1 (1970), 131–139.
• 4. Eisenberger I.: Genesis of bimodal distributions. Technometrics 6, no. 4 (1964), 357–363.
• 5. Lindsay B.G.: Mixture Models: Theory, Geometry and Applications. Institute of Mathematical Statistics, Hayward 1995.
• 6. Murphy A.: One cause? Many causes? The argument from the bimodal distribution. J. Chronic Diseases 6, no. 4 (1964), 301–324.