scholarly journals The ArcTan Lomax Distribution with Properties and Applications

2021 ◽  
pp. 117-125
Author(s):  
Arun Kumar Chaudhary ◽  
Vijay Kumar
Keyword(s):  
Survival Analysis ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Goodness Of Fit ◽  
Continuous Distribution ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Lomax Distribution ◽  
And Mathematics

Here, in this paper, a continuous distribution called ArcTan Lomax distribution with three-parameter has been introduced along with some relevant properties of statistics and mathematics pertaining to the distribution. With the help of three established estimations methods including maximum likelihood estimation (MLE), estimation of the presented distribution’s model parameters is done. Also with the help of a real set of data, the distribution’s goodness-of-fit is examined in contrast to some established models in survival analysis.

scholarly journals A New Generalization of the Lomax Distribution with Increasing, Decreasing, and Constant Failure Rate

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Pelumi E. Oguntunde ◽  
Mundher A. Khaleel ◽  
Mohammed T. Ahmed ◽  
Adebowale O. Adejumo ◽  
Oluwole A. Odetunmibi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Real Life ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Lomax Distribution ◽  
Life Data ◽  
Real Life Data ◽  
Method Of Maximum Likelihood ◽  
Better Than

Developing new compound distributions which are more flexible than the existing distributions have become the new trend in distribution theory. In this present study, the Lomax distribution was extended using the Gompertz family of distribution, its resulting densities and statistical properties were carefully derived, and the method of maximum likelihood estimation was proposed in estimating the model parameters. A simulation study to assess the performance of the parameters of Gompertz Lomax distribution was provided and an application to real life data was provided to assess the potentials of the newly derived distribution. Excerpt from the analysis indicates that the Gompertz Lomax distribution performed better than the Beta Lomax distribution, Weibull Lomax distribution, and Kumaraswamy Lomax distribution.

scholarly journals Half Logistic Exponential Extension Distribution with Properties and Applications

2020 ◽  
Vol 9 (3) ◽  
pp. 506-512
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Hazard Rate ◽  
Goodness Of Fit ◽  
Likelihood Estimation ◽  
Real Data ◽  
Model Parameters ◽  
Type I ◽  
Proposed Model ◽  
New Distribution

In this article, we have introduced a new distribution based on type I half logistic-G family and exponential extension as a base distribution known as Half Logistic Exponential Extension (HLEE) distribution. The statistical properties of this model are also explored, such as the behavior of probability density, hazard rate, and quantile functions are investigated. The Maximum likelihood estimation (MLE) method is used to estimate model parameters. For the potentiality of the proposed model we have compared the goodness of fit with some others models. We have proven the importance and flexibility of the new distribution in modeling with real data applications empirically.

scholarly journals Assessment of Homodyned K Distribution Modeling Ultrasonic Speckles from Scatterers with Varying Spatial Organizations

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Xiao Hu ◽  
Yufeng Zhang ◽  
Li Deng ◽  
Guanghui Cai ◽  
Qinghui Zhang ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Goodness Of Fit ◽  
Human Subjects ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Practical Applications ◽  
Distribution Modeling ◽  
Gamma Distributions ◽  
Carotid Arterial

Objective. This paper presents an assessment of physical meanings of parameter and goodness of fit for homodyned K (HK) distribution modeling ultrasonic speckles from scatterer distributions with wide-varying spatial organizations. Methods. A set of 3D scatterer phantoms based on gamma distributions is built to be implemented from the clustered to random to uniform scatterer distributions continuously. The model parameters are obtained by maximum likelihood estimation (MLE) from statistical histograms of the ultrasonic envelope data and then compared with those by the optimally fitting models chosen from three single distributions. Results show that the parameters of the HK distribution still present their respective physical meanings of independent contributions in the scatterer distributions. Moreover, the HK distribution presents better goodness of fit with a maximum relative MLE difference of 6.23% for random or clustered scatterers with a well-organized periodic structure. Experiments based on ultrasonic envelope data from common carotid arterial B-mode images of human subjects validate the modeling performance of HK distribution. Conclusion. We conclude that the HK model for ultrasonic speckles is a better choice for characterizing tissue with a wide variety of spatial organizations, especially the emphasis on the goodness of fit for the tissue in practical applications.

scholarly journals Joint Maximum Likelihood of Phylogeny and Ancestral States Is Not Consistent

2019 ◽  
Vol 36 (10) ◽  
pp. 2352-2357
Author(s):  
David A Shaw ◽  
Vu C Dinh ◽  
Frederick A Matsen
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Branch Length ◽  
Continuous Model ◽  
Model Parameters ◽  
Infinite Length ◽  
Computationally Efficient ◽  
Ancestral States ◽  
Joint Method

Abstract Maximum likelihood estimation in phylogenetics requires a means of handling unknown ancestral states. Classical maximum likelihood averages over these unknown intermediate states, leading to provably consistent estimation of the topology and continuous model parameters. Recently, a computationally efficient approach has been proposed to jointly maximize over these unknown states and phylogenetic parameters. Although this method of joint maximum likelihood estimation can obtain estimates more quickly, its properties as an estimator are not yet clear. In this article, we show that this method of jointly estimating phylogenetic parameters along with ancestral states is not consistent in general. We find a sizeable region of parameter space that generates data on a four-taxon tree for which this joint method estimates the internal branch length to be exactly zero, even in the limit of infinite-length sequences. More generally, we show that this joint method only estimates branch lengths correctly on a set of measure zero. We show empirically that branch length estimates are systematically biased downward, even for short branches.

scholarly journals Multivariate Hawkes processes: an application to financial data

2011 ◽  
Vol 48 (A) ◽  
pp. 367-378 ◽  
Author(s):  
Paul Embrechts ◽  
Thomas Liniger ◽  
Lu Lin
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Statistical Estimation ◽  
Goodness Of Fit ◽  
Likelihood Estimation ◽  
Financial Data ◽  
Data Sets ◽  
Hawkes Process ◽  
Science And Engineering ◽  
Hawkes Processes

A Hawkes process is also known under the name of a self-exciting point process and has numerous applications throughout science and engineering. We derive the statistical estimation (maximum likelihood estimation) and goodness-of-fit (mainly graphical) for multivariate Hawkes processes with possibly dependent marks. As an application, we analyze two data sets from finance.

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