Double-looped maximum likelihood estimation for the parameters of the generalized gamma distribution

Yılmaz, Hülya; Sazak, Hakan Savaş

doi:10.1016/j.matcom.2013.12.001

Cited by 9 publications

(3 citation statements)

References 24 publications

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“…This topic was dealt with in many papers (cf. the results in [2,36,52,67] and the list of references therein) but since almost all of the proposed methods are quite complex, this topic is still an open area, that needs to be better studied.…”

Section: Grazing Limit and The Fokker-planck Equationmentioning

confidence: 99%

Kinetic Modeling of Alcohol Consumption

Dimarco

Toscani

2019

J Stat Phys

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In most countries, alcohol consumption distributions have been shown to possess universal features. Their unimodal right-skewed shape is usually modeled in terms of the Lognormal distribution, which is easy to fit, test, and modify. However, empirical distributions often deviate considerably from the Lognormal model, and both Gamma and Weibull distributions appear to better describe the survey data. In this paper we explain the appearance of these distributions by means of classical methods of kinetic theory of multi-agent systems. The microscopic variation of alcohol consumption of agents around a universal social accepted value of consumption, is built up introducing as main criterion for consumption a suitable value function in the spirit of the prospect theory of Kahneman and Twersky. The mathematical properties of the value function then determine the unique macroscopic equilibrium which results to be a generalized Gamma distribution. The modeling of the microscopic kinetic interaction allows to clarify the meaning of the various parameters characterizing the generalized Gamma equilibrium. Alcohol consumption and Empirical distribution and Generalized Gamma distribution and Log-Normal distribution and Weibull distribution and Kinetic models and Fokker-Planck equations.

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Section: Grazing Limit and The Fokker-planck Equationmentioning

confidence: 99%

Kinetic Modeling of Alcohol Consumption

Dimarco

Toscani

2019

J Stat Phys

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“…The localization algorithm of sound source azimuth needed to undertake choosing according to the array structure and adopt different localization algorithms will have different positioning precisions and computing speeds, accompanied by the algorithm of the computation size and position precision of algorithm. Based on the location method of arrival delay, there is a maximum likelihood method based on search [39][40][41] and geometric localization algorithm [31][32][33]: the search method has a large amount of calculations and does not apply to real-time systems; if the sound source geometric localization algorithm is adopted, the algorithm has high positioning accuracy and the arrival delay itself has strong anti-interference, which can reduce the influence of the attenuation and interference of the actual sound propagation process on the accuracy of the sound source omnidirectional positioning calibration. 3 Complexity 3.1.…”

Section: Sound Source Geometric Localization Algorithmmentioning

confidence: 99%

Sound Source Omnidirectional Positioning Calibration Method Based on Microphone Observation Angle

Yang

Xing

2018

Complexity

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To get source azimuth from microphone observation angle of view in a complex real environment, this article, on the basis of the analysis of geometric positioning method, established a seven-element microphone array model and proposed a sound source omnidirectional positioning calibration method based on microphone observation angle. By using a seven-element array to invert the position and angle of a sound source, the relative time delay value of a pair of microphones on the vertical axis of the coordinate system is used to determine the elevation angle polarity and realize the omnidirectional sound source positioning. The array parameters, sound velocity, array size, horizontal deflection angle, elevation angle, and sound source are analyzed, and the error method is proposed. The sound source data was measured using the microphone array perspective, and a new Cartesian coordinate system was established based on the observation angle of view for omnidirectional positioning calibration of the sound source. The simulation results show that the position error of the method is about 0.01% and the angle error is about 0.005%, with high calibration accuracy. The actual measurement results show that this method can effectively calibrate the sound source azimuth, the error rate of the source coordinates is around 10%, the horizontal declination angle error is less than 5%, and the elevation angle error is less than 8%. Appropriately increasing the spacing of the array will have a better calibration effect in an actual complex experimental environment.

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“…An estimation method called the maximum likelihood with goodness-of-fit test was used to evaluate the parameter of the probability density function associated with the joint trace length data. It is more efficient than the method of moments with goodness-of-fit test technique, especially for small and moderate sample sizes (Bai et al 1991;Rajan et al 2014;Yilmaz and Sazak 2014). The KS test was adopted to determine the optimum measured trace length probability distribution for each fracture set.…”

Section: Introductionmentioning

confidence: 99%