scholarly journals Effective estimation algorithm for parameters of multivariate Farlie–Gumbel–Morgenstern copula

2021 ◽  
Author(s):  
Shuhei Ota ◽  
Mitsuhiro Kimura
Keyword(s):  
Parameter Estimation ◽  
Data Analysis ◽  
Computational Complexity ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Asymptotic Normality ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Algorithm ◽  
Simulation Studies

AbstractThis paper focuses on the parameter estimation for the d-variate Farlie–Gumbel–Morgenstern (FGM) copula ($$d\ge 2$$ d ≥ 2 ), which has $$2^d-d-1$$ 2 d - d - 1 dependence parameters to be estimated; therefore, maximum likelihood estimation is not practical for a large d from the viewpoint of computational complexity. Besides, the restriction for the FGM copula’s parameters becomes increasingly complex as d becomes large, which makes parameter estimation difficult. We propose an effective estimation algorithm for the d-variate FGM copula by using the method of inference functions for margins under the restriction of the parameters. We then discuss its asymptotic normality as well as its performance determined through simulation studies. The proposed method is also applied to real data analysis of bearing reliability.

Topp–Leone Linear Exponential Distribution

2018 ◽  
Vol 33 (1) ◽  
pp. 31-43
Author(s):  
Bol A. M. Atem ◽  
Suleman Nasiru ◽  
Kwara Nantomah
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Simulation Studies ◽  
Finite Sample ◽  
Data Set ◽  
Finite Sample Properties ◽  
Linear Exponential Distribution

Abstract This article studies the properties of the Topp–Leone linear exponential distribution. The parameters of the new model are estimated using maximum likelihood estimation, and simulation studies are performed to examine the finite sample properties of the parameters. An application of the model is demonstrated using a real data set. Finally, a bivariate extension of the model is proposed.

scholarly journals Cubic Transformation of Exponential Weibull and its Statistical Properties

2020 ◽  
pp. 39-50
Author(s):  
Haiyue Wang ◽  
Zhenhua Bao
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Statistical Properties ◽  
Reasoning Process ◽  
The Family

In this paper, a cubic transformation exponential Weibull distribution is proposed by using the family of cubic transformation distributions introduced by Rahman et al.The reasoning process of the proposed cubic transformation exponential Weibull distribution is discussed in detail, and its statistical properties and parameter estimation are also discussed.Using real data, the maximum likelihood estimation is used to simulate. Through the comparison of fitting results, it is concluded that the cubic transformation exponential Weibull distribution proposed in this paper has stronger applicability.

scholarly journals Generalizations of Burr Type X Distribution with Applications

2020 ◽  
pp. 1-8
Author(s):  
Noor Akma Ibrahim ◽  
Mundher Abdullah Khaleel
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Density Function ◽  
Likelihood Estimation ◽  
Real Data ◽  
Data Sets ◽  
Lifetime Data ◽  
Simulation Studies ◽  
Cumulative Density Function ◽  
Two Parameters

We propose the generalizations of Burr Type X distribution with two parameters by using the methods of Beta-G, Gamma-G and Weibull-G families of distributions. We discuss maximum likelihood estimation of the model’s parameters. The performances of the parameter’s estimates are assessed via simulation studies under different sets of conditions. In the applications to real data sets, three sets of data are used whereby from the results we can deduce that these models can be used quite effectively in analysing lifetime data. Keywords: cumulative density function; lifetime data; maximum likelihood estimation

scholarly journals Maximum Likelihood Estimation for Three-Parameter Weibull Distribution Using Evolutionary Strategy

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Fan Yang ◽  
Hu Ren ◽  
Zhili Hu
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Evolutionary Strategy ◽  
Likelihood Method ◽  
Conventional Algorithm

The maximum likelihood estimation is a widely used approach to the parameter estimation. However, the conventional algorithm makes the estimation procedure of three-parameter Weibull distribution difficult. Therefore, this paper proposes an evolutionary strategy to explore the good solutions based on the maximum likelihood method. The maximizing process of likelihood function is converted to an optimization problem. The evolutionary algorithm is employed to obtain the optimal parameters for the likelihood function. Examples are presented to demonstrate the proposed method. The results show that the proposed method is suitable for the parameter estimation of the three-parameter Weibull distribution.

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