Identifiability of Finite Mixtures of Von Mises Distributions

Fraser, Martin D.; Hsu, Yu‐Sheng; Walker, Joseph J.

doi:10.1214/aos/1176345595

Cited by 25 publications

(14 citation statements)

References 8 publications

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“…The question of identifiability needs to be considered for consistent estimation of the parameters (Leroux 1992). Identifiability has been proved by Fraser et al (1981). If we assume that κ 1 = κ 2 = κ and restrict this parameter to a compact interval [ , 1/ ] for some small > 0, then the conditions for strong consistency and asymptotic normality of the maximum likelihood estimator (MLE) are satisfied (Leroux 1992;Bickel et al 1998).…”

Section: The Von Mises-hmm (Continued)mentioning

confidence: 99%

Hidden Markov models for circular and linear-circular time series

et al. 2006

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We introduce a new class of circular time series based on hidden Markov models. These are compared with existing models, their properties are outlined and issues relating to parameter estimation are discussed. The new models conveniently describe multi-modal circular time series as dependent mixtures of circular distributions. Two examples from biology and meteorology are used to illustrate the theory. Finally, we introduce a hidden Markov model for bivariate linear-circular time series and use it to describe larval movement of the fly Drosophila.

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Section: The Von Mises-hmm (Continued)mentioning

confidence: 99%

Hidden Markov models for circular and linear-circular time series

et al. 2006

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“…The distribution of the dihedral angle of methanol is still exceptionally symmetric and simple-in more complex molecules, dihedral angle distributions have typically several peaks of unequal height and a varying degree of skewness, placed at unequal angular intervals from each other. One could consider modeling such distributions with probability density distributions that are mixtures of several von Mises 16 or Gaussian distributions, and obtain the parameters of such mixtures using the maximum likelihood method. Another, and a more general, alternative is a direct Fourier series expansion of the probability density function f():…”

Section: Introductionmentioning

confidence: 99%

Statistical thermodynamics of internal rotation in a hindering potential of mean force obtained from computer simulations

et al. 2003

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A method of statistical estimation is applied to the problem of one-dimensional internal rotation in a hindering potential of mean force. The hindering potential, which may have a completely general shape, is expanded in a Fourier series, the coefficients of which are estimated by fitting an appropriate statistical-mechanical distribution to the random variable of internal rotation angle. The function of reduced moment of inertia of an internal rotation is averaged over the thermodynamic ensemble of atomic configurations of the molecule obtained in stochastic simulations. When quantum effects are not important, an accurate estimate of the absolute internal rotation entropy of a molecule with a single rotatable bond is obtained. When there is more than one rotatable bond, the "marginal" statistical-mechanical properties corresponding to a given internal rotational degree of freedom are reduced. The method is illustrated using Monte Carlo simulations of two public health relevant halocarbon molecules, each having a single internal-rotation degree of freedom, and a molecular dynamics simulation of an immunologically relevant polypeptide, in which several dihedral angles are analyzed.

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“…Here, we discussed the problem of identifiability of finite mixture of Gumbel distributions. Discussions of the identifiability of a mixtures may be found in several articles, including Teicher (1960Teicher ( , 1961Teicher ( , 1963Teicher ( , 1967, Yakowitz (1970), Al-Hussaini and Ahmad (1981), Fraser et al (1981), Ahmad (1982Ahmad ( , 1988, Ahmad and Abd-ElHakim (1990), and Kont (1983), among others.…”

Section: Identifiabilitymentioning

confidence: 99%

Estimation of a Discriminant Function Based on Small Sample Size from a Mixture of Two Gumbel Distributions

Ahmad¹,

Jaheen²,

Modhesh³

2010

Communications in Statistics - Simulation and Computation

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The identifiability of finite mixture of Gumbel distributions is proved. A procedure is presented for finding maximum likelihood estimates for the four parameters of a mixture of two Gumbel distributions, using classified and unclassified observations. A nonlinear discriminant function for a mixture of two Gumbel distributions is derived and estimated based on small sample size. Throughout simulation experiments, the performance of the corresponding estimated nonlinear discriminant function is investigated.

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Identifiability of Finite Mixtures of Von Mises Distributions

Cited by 25 publications

References 8 publications

Hidden Markov models for circular and linear-circular time series

Hidden Markov models for circular and linear-circular time series

Statistical thermodynamics of internal rotation in a hindering potential of mean force obtained from computer simulations

Estimation of a Discriminant Function Based on Small Sample Size from a Mixture of Two Gumbel Distributions

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