scholarly journals Maximum likelihood estimation of the GLS model with unknown parameters in the disturbance covariance matrix

1978 ◽  
Vol 7 (3) ◽  
pp. 281-312 ◽  
Author(s):  
Jan R. Magnus
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Covariance Matrix ◽  
Likelihood Estimation ◽  
Unknown Parameters

scholarly journals New class of Lindley distributions: properties and applications

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Duha Hamed ◽  
Ahmad Alzaghal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Data Sets ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Lindley Distribution ◽  
New Class

AbstractA new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

scholarly journals A Study on Properties and Applications of a Lomax Gompertz-Makeham Distribution

2019 ◽  
pp. 1-27
Author(s):  
Innocent Boyle Eraikhuemen ◽  
Terna Godfrey Ieren ◽  
Tajan Mashingil Mabur ◽  
Mohammed Sa’ad ◽  
Samson Kuje ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Probability Distributions ◽  
Real Life ◽  
Likelihood Estimation ◽  
The Other ◽  
Unknown Parameters ◽  
Method Of Maximum Likelihood ◽  
Compound Model ◽  
New Distribution

The article presents an extension of the Gompertz-Makeham distribution using the Lomax generator of probability distributions. This generalization of the Gompertz-Makeham distribution provides a more skewed and flexible compound model called Lomax Gompertz-Makeham distribution. The paper derives and discusses some Mathematical and Statistical properties of the new distribution. The unknown parameters of the new model are estimated via the method of maximum likelihood estimation. In conclusion, the new distribution is applied to two real life datasets together with two other related models to check its flexibility or performance and the results indicate that the proposed extension is more flexible compared to the other two distributions considered in the paper based on the two datasets used.

scholarly journals Statistical analysis based on quaternion normal random variables

1985 ◽  
Vol 4 (3) ◽  
pp. 120-127 ◽  
Author(s):  
H. M. Rautenbach ◽  
J. J. J. Roux
Keyword(s):  
Statistical Analysis ◽  
Maximum Likelihood ◽  
Probability Density Function ◽  
Maximum Likelihood Estimation ◽  
Normal Distribution ◽  
Probability Density ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Unknown Parameters ◽  
Quaternion Case

The quaternion normal distribution is derived and a number of characteristics are highlighted. The maximum likelihood estimation procedure in the quaternion case is examined and the conclusion is reached that the estimation procedure is simplified if the unknown parameters of the associated real probability density function are estimated. The quaternion estimator is then obtained by regarding these estimators as the components of the quaternion estimator. By means of a example attention is given to a test criterium which can be used in the quaternion model.

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