The Method of Maximum Likelihood

Data Analysis ◽  
1999 ◽  
pp. 187-211 ◽  
Author(s):  
Siegmund Brandt
Keyword(s):  
Maximum Likelihood ◽  
Method Of Maximum Likelihood

scholarly journals Box-Cox Gamma-G Family of Distributions: Theory and Applications

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1801
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Ibrahim Elbatal ◽  
Christophe Chesneau ◽  
Farrukh Jamal
Keyword(s):  
Maximum Likelihood ◽  
Statistical Model ◽  
Cauchy Distribution ◽  
Natural Generalization ◽  
Power Parameter ◽  
New Class ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
Box Cox Transformation ◽  
Family Of Distributions

This paper is devoted to a new class of distributions called the Box-Cox gamma-G family. It is a natural generalization of the useful Ristić–Balakrishnan-G family of distributions, containing a wide variety of power gamma-G distributions, including the odd gamma-G distributions. The key tool for this generalization is the use of the Box-Cox transformation involving a tuning power parameter. Diverse mathematical properties of interest are derived. Then a specific member with three parameters based on the half-Cauchy distribution is studied and considered as a statistical model. The method of maximum likelihood is used to estimate the related parameters, along with a simulation study illustrating the theoretical convergence of the estimators. Finally, two different real datasets are analyzed to show the fitting power of the new model compared to other appropriate models.

scholarly journals Velocity Dispersion and Luminosity Function of Planetary Nebulae in the Nuclear Bulge of M31

1983 ◽  
Vol 103 ◽  
pp. 543-543
Author(s):  
D. G. Lawrie ◽  
H. C. Ford
Keyword(s):  
Maximum Likelihood ◽  
Radial Velocity ◽  
Luminosity Function ◽  
Velocity Dispersion ◽  
Planetary Nebulae ◽  
Image Intensifier ◽  
Interference Filter ◽  
Radial Velocities ◽  
Method Of Maximum Likelihood ◽  
Heliocentric Velocity

We used a sequence of velocity-modulated photographs to find and measure the radial velocities of faint planetary nebulae in the center of M31. The photographs were made with a Velocity Modulating Camera (VMC) which consists of a temperature-tuned 2.1 Å (FWHM) (O III) λ 5007 interference filter, a cooled, two-stage image intensifier, and a calibrating photomultiplier. The camera was mounted at the Cassegrain focus of the Shane 3 m telescope at Lick Observatory. We identified 19 new planetary nebulae, bringing the total number of known planetaries within 250 pc of M31's nucleus to 45. From the plate series, we derived radial velocities and relative brightnesses from 32 of the nebulae and placed radial velocity limits on the remaining nebulae in the field. By applying the method of maximum likelihood to the observed radial velocity distribution, we derive a mean heliocentric velocity of −309 (±25) km s−1 and a velocity dispersion of 155 (±22) km s−1 for the planetary nebulae.

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