A New Method for Maximum Likelihood Parameter Estimation of Gamma-Gamma Distribution

Kazeminia, Mahdi; Mehrjoo, Mehri

doi:10.1109/jlt.2013.2246858

Cited by 15 publications

(5 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(16). It is, however, noted that the ML estimate for the parameters of the Gamma-Gamma distribution has no closed form and, thus, alternative approaches such as method of moments (MOM) (Wang and Cheng, 2010) and numerical approximation (Kazeminia and Mehrjoo, 2013) are required. Exploring joint estimators for the parameters of the Gamma-Gamma distribution is beyond the scope of this study and will be conducted in our future work.…”

Section: Estimating Parameters Of Component Gamma Distributionsmentioning

confidence: 99%

Compound Gamma representation for modeling travel time variability in a traffic network

Kim

Mahmassani

2015

Transportation Research Part B: Methodological

View full text Add to dashboard Cite

a b s t r a c tThis paper proposes a compound probability distribution approach for capturing both vehicle-to-vehicle and day-to-day variability in modeling travel time reliability in a network. Starting from the observation that standard deviation and mean of distance-normalized travel time in a network are highly positively correlated and their relationship is well characterized by a linear function, this study assumes multiplicative error structures to describe data with such characteristics and derives a compound distribution to model travel delay per unit distance as a surrogate for travel time. The proposed Gamma-Gamma model arises when (within-day) vehicle-to-vehicle travel delay per unit distance is distributed according to a Gamma distribution, with mean that itself fluctuates from day to day following another Gamma distribution. The study calibrates the model parameters and validates the underlying assumptions using both simulated and actual vehicle trajectory data. The GammaGamma distribution shows good fits to travel delay observations when compared to the (simple) Gamma and Lognormal distributions. The main advantage of the GammaGamma model is its ability to recognize different variability dimensions reflected in travel time data and clear physical meanings of its parameters in connection with vehicle-to-vehicle and day-to-day variability. Based on the linearity assumption for the relationship between mean and standard deviation, two shape parameters of the GammaGamma model are linked to the coefficient of variation of travel delay in vehicle-to-vehicle and day-to-day distributions, respectively, and can be directly estimated from the slope of the associated mean-standard deviation plots. An extension of the basic model form was also introduced to address potential deviations from this linearity assumption. The extended Gamma-Gamma model can account for time-of-day variations in mean-standard deviation relationships-such as hysteresis patterns observed in mean and day-to-day variation in travel time-and incorporate such dynamics in travel time distribution modeling. In summary, the model provides a systematic way of quantifying, comparing, and assessing different types of variability, which is important in understanding travel time characteristics and evaluating various transportation measures that affect reliability.

show abstract

Section: Estimating Parameters Of Component Gamma Distributionsmentioning

confidence: 99%

Compound Gamma representation for modeling travel time variability in a traffic network

Kim

Mahmassani

2015

Transportation Research Part B: Methodological

View full text Add to dashboard Cite

show abstract

“…For the derivation of the Gamma pdf, the Maximum Likelihood Parameter Estimation (MLPE) method in Reference [20] is taken into account. Lastly, for the BPSK modulation equivalent, BER can be expressed as Reference [21] (Q function is considered in the integral).…”

Section: Ber Calculation In Frequency Selective Fading Mimo Orientationsmentioning

confidence: 99%

Reduced Complexity BER Calculations in Large Scale Spatial Multiplexing Multi-User MIMO Orientations in Frequency Selective Fading Environments

Gkonis

Kaklamani

2019

Electronics

View full text Add to dashboard Cite

In this article, a computationally-efficient approach is presented for Bit Error Rate (BER) calculations in multi-user Multiple Input Multiple Output (MIMO) frequency selective fading environments, operating in spatial multiplexing transmission mode. To this end, theoretical expressions for the equivalent Signal to Interference plus Noise Ratio (SINR) per active user and transmission mode, as well as mean BER, are derived. The key idea is that all parameters related to BER calculations can be expressed as sums of identically distributed random variables (RVs). Hence, computational burden can be reduced, since summation formulas take into account the parameters of a standalone RV along with the correlation of an arbitrary pair of RVs. As results indicate, the proposed approach can accurately estimate mean BER in multiuser MIMO orientations with increased reception diversity order, for arbitrary number of transmit/receive antennas, a modulation scheme, and a number of resolvable multi-path components.

show abstract

“…Because GaGLM is a model with two equations (4) being respectively parameterized for α and β , the estimation procedure VOLUME 4, 2016 could be relatively complex. In statistics, several expectationmaximization (EM) type algorithms have been developed for the Gamma distribution inference, where β was assumed to be a latent variable [12]. However, those algorithms were developed by fixing β as constant.…”

Section: Introductionmentioning

confidence: 99%

Consistency and Asymptotic Normality of the Maximum Likelihood Estimator in GaGLM

Wang

Qin

2022

IEEE Access

View full text Add to dashboard Cite

The Gamma distribution based generalized linear model (GaGLM) is a kind of statistical model feasible for the positive value of a non-stationary stochastic system, in which the location and the scale are regressed by the corresponding explanatory variables. This paper theoretically investigates the asymptotic properties of maximum likelihood estimates (MLE) of GaGLM, which can benefit the further interval estimates, hypothesis tests and stochastic control design. First, the score function and the Fisher information matrix for GaGLM are derived. Then, the Lyapunov condition is derived to ensure the asymptotic normality of the score function normalized by the Fisher information matrix. Based on this condition, the asymptotic normality of the MLE of GaGLM is proven. Finally, a numerical example is given to testify the asymptotic properties obtained in the research. The numerical results indicate that the MLE of GaGLM converged to a normal distribution as the number of sample measurements increased.INDEX TERMS Gamma distribution, Gamma regression, consistency and asymptotic normality, central limit theorem, maximum likelihood estimator.

show abstract

A New Method for Maximum Likelihood Parameter Estimation of Gamma-Gamma Distribution

Cited by 15 publications

References 20 publications

Compound Gamma representation for modeling travel time variability in a traffic network

Compound Gamma representation for modeling travel time variability in a traffic network

Reduced Complexity BER Calculations in Large Scale Spatial Multiplexing Multi-User MIMO Orientations in Frequency Selective Fading Environments

Consistency and Asymptotic Normality of the Maximum Likelihood Estimator in GaGLM

Contact Info

Product

Resources

About