scholarly journals Measuring Subclusters in Galaxy Clusters

1999 ◽  
Vol 186 ◽  
pp. 417-417
Author(s):  
Z.Y. Shao
Keyword(s):  
Maximum Likelihood ◽  
Radial Velocity ◽  
Galaxy Clusters ◽  
Maximum Likelihood Method ◽  
Velocity Space ◽  
Likelihood Method ◽  
Cluster Region ◽  
Distribution Parameters ◽  
Celestial Sphere ◽  
Image Position

We assume that there are Kc subclusters and Kf fields (foreground or background) in a cluster region. Then, the distribution of all galaxies in this region can be described as follow: where, nc and nf are normalized numbers of subcluster members and field galaxies. φc, φf, are their normalized distributions in radial velocity space. Both of them can be assumed as Gaussian. μc and μf are normalized distributions in the projected surface of the celestial sphere. For field galaxies, it's uniform, and for subcluster members, usually we use the King's approximate formulae. Distribution parameters and their uncertainties can be found by using the standard maximum likelihood method. And membership probabilities of the ith galaxy belonging to the cth subcluster can be calculated as Pc(i) = φc(i)/φp(i).

Zero-truncated Poisson-Lindley distribution

2021 ◽  
pp. 40-50
Author(s):  
Afida Nurul Hilma ◽  
Dian Lestari ◽  
Sindy Devila
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Lindley Distribution ◽  
Count Distribution ◽  
Distribution Parameters ◽  
Counting Distribution ◽  
Over Dispersion

In order to find a counting distribution that can handle the condition when the data has no zero-count. Distribution named Zero-truncated Poisson-Lindley distribution is developed. It can handle the condition when the data has no zero-count both in over-dispersion and under-dispersion. In this paper, characteristics of Zero-truncated Poisson-Lindley distribution are obtained and estimate distribution parameters using the maximum likelihood method. Then, the application of the model to real data is given.

Reliability Analysis of a Small Pneumatic Cylinder Life

2011 ◽  
Vol 110-116 ◽  
pp. 4240-4245
Author(s):  
Jun Zhao Zhang ◽  
Cong Ling Wang ◽  
Xue Fa Fang
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Distribution Model ◽  
Pneumatic Cylinder ◽  
Life Test ◽  
Life Distribution ◽  
Median Rank ◽  
Distribution Parameters

The reliability of the pneumatic cylinder was investigated by routine life test. The results show that the failures of the pneumatic cylinder can be described as a Weibull distribution and fatigue fracture of the aluminum end cap and the head of install bolt is the major failure for the pneumatic cylinder. The pneumatic cylinder life distribution parameters were estimated by the median rank method in combination with maximum likelihood method. The distribution model for the reliability of the pneumatic cylinder was also proposed here.

Application of differential evolution for wind speed distribution parameters estimation

2021 ◽  
pp. 0309524X2199996
Author(s):  
Rajesh Kumar ◽  
Arun Kumar
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Wind Speed ◽  
Weibull Distribution ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Speed Distribution ◽  
De Algorithm ◽  
Wind Speed Distribution ◽  
Distribution Parameters

Weibull distribution is an extensively used statistical distribution for analyzing wind speed and determining energy potential studies. Estimation of the wind speed distribution parameter is essential as it significantly affects the success of Weibull distribution application to wind energy. Various estimation methods viz. graphical method, moment method (MM), maximum likelihood method (ML), modified maximum likelihood method, and energy pattern factor method or power density method have been presented in various reported research studies for accurate estimation of distribution parameters. ML is the most preferred approach to study the parameter estimation. ML works on the principle of forming a likelihood function and maximizing the function for parameter estimation. ML generally uses the numerical based iterative method, such as Newton–Raphson. However, the iterative methods proposed in the literature are generally computationally intensive. In this paper, an efficient technique utilizing differential evolution (DE) algorithm to enhance the estimation accuracy of maximum likelihood estimation has been presented. The [Formula: see text] of GA-Weibull, SA-Weibull, and DE-Weibull is 0.958, 0.953, and 0.973 respectively, and value of RMSE of DE-Weibull 0.0083, GA-Weibull (0.0104), and SA-Weibull (0.0110), for the yearly wind speed data are obtained. The lowest root mean square error and larger regression value for both monthly and yearly wind speed data indicate that the DE-Weibull distribution has the best goodness of fit and advocate the DE algorithm for the parameter estimation.

scholarly journals Simplified Method of GED Distribution Parameters Estimation

2012 ◽  
Vol 10 (2) ◽  
pp. 35-49
Author(s):  
Jan Purczyński
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Simple Relation ◽  
Parameters Estimation ◽  
Likelihood Method ◽  
Test Statistic ◽  
Mathematical Functions ◽  
Simplified Method ◽  
Distribution Parameters ◽  
Estimation Of Distribution

Simplified Method of GED Distribution Parameters EstimationIn this paper a simplified method of estimating GED distribution parameters has been proposed. The method uses first, second and 0.5-th order absolute moments. Unlike in maximum likelihood method, which involves solving a set of equations including special mathematical functions, the solution is given in the form of a simple relation. Application of three different approximations of Euler's gamma function value results in three different sets of results for which the χ2test is conducted. As a final solution (estimation of distribution parameters) the set is chosen which yields the smallest value of the χ2test statistic. The method proposed in this paper yields the χ2test statistic value which does not exceed the value of statistic for a distribution with parameters obtained with the maximum likelihood method.

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