scholarly journals Chaotic optimization algorithm based on the modified probability density function of Lozi map

2021 ◽  
Vol 39 (6) ◽  
pp. 9-22
Author(s):  
Rabah Bououden ◽  
Mohamed Salah Abdelouahab
Keyword(s):  
Global Optimization ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Optimization Algorithm ◽  
Chaotic Maps ◽  
New Technique ◽  
Random Numbers ◽  
Chaos Optimization ◽  
Design Variables

Chaos optimization algorithms (COAs) usually utilize different chaotic maps(logistic, tent, Hénon, Lozi,...) to generate the pseudo-random numbers mapped as the design variables for global optimization. In this paper we are going to propose new technique to improve the chaotic optimization algorithm by using some transformations to modify the density of the map instead of changing it.

Properties and methods of estimation for a bivariate exponentiated Fréchet distribution

2020 ◽  
Vol 70 (5) ◽  
pp. 1211-1230
Author(s):  
Abdus Saboor ◽  
Hassan S. Bakouch ◽  
Fernando A. Moala ◽  
Sheraz Hussain
Keyword(s):  
Maximum Likelihood ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Superior Performance ◽  
Estimation Methods ◽  
Conditional Probability Density ◽  
Data Set ◽  
Fréchet Distribution ◽  
Frechet Distribution

AbstractIn this paper, a bivariate extension of exponentiated Fréchet distribution is introduced, namely a bivariate exponentiated Fréchet (BvEF) distribution whose marginals are univariate exponentiated Fréchet distribution. Several properties of the proposed distribution are discussed, such as the joint survival function, joint probability density function, marginal probability density function, conditional probability density function, moments, marginal and bivariate moment generating functions. Moreover, the proposed distribution is obtained by the Marshall-Olkin survival copula. Estimation of the parameters is investigated by the maximum likelihood with the observed information matrix. In addition to the maximum likelihood estimation method, we consider the Bayesian inference and least square estimation and compare these three methodologies for the BvEF. A simulation study is carried out to compare the performance of the estimators by the presented estimation methods. The proposed bivariate distribution with other related bivariate distributions are fitted to a real-life paired data set. It is shown that, the BvEF distribution has a superior performance among the compared distributions using several tests of goodness–of–fit.

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