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.

scholarly journals Numerical simulation of the two-locus Wright-Fisher stochastic differential equation with application to approximating transition probability densities

2020 ◽  
Author(s):  
Zhangyi He ◽  
Mark Beaumont ◽  
Feng Yu
Keyword(s):  
Differential Equation ◽  
Natural Selection ◽  
Probability Density Function ◽  
Stochastic Differential Equation ◽  
Probability Density ◽  
Density Function ◽  
Genetic Recombination ◽  
Transition Probability ◽  
Superior Performance ◽  
Transition Probability Density

AbstractOver the past decade there has been an increasing focus on the application of the Wright-Fisher diffusion to the inference of natural selection from genetic time series. A key ingredient for modelling the trajectory of gene frequencies through the Wright-Fisher diffusion is its transition probability density function. Recent advances in DNA sequencing techniques have made it possible to monitor genomes in great detail over time, which presents opportunities for investigating natural selection while accounting for genetic recombination and local linkage. However, most existing methods for computing the transition probability density function of the Wright-Fisher diffusion are only applicable to one-locus problems. To address two-locus problems, in this work we propose a novel numerical scheme for the Wright-Fisher stochastic differential equation of population dynamics under natural selection at two linked loci. Our key innovation is that we reformulate the stochastic differential equation in a closed form that is amenable to simulation, which enables us to avoid boundary issues and reduce computational costs. We also propose an adaptive importance sampling approach based on the proposal introduced by Fearnhead (2008) for computing the transition probability density of the Wright-Fisher diffusion between any two observed states. We show through extensive simulation studies that our approach can achieve comparable performance to the method of Fearnhead (2008) but can avoid manually tuning the parameter ρ to deliver superior performance for different observed states.

Maximum-likelihood maximum-entropy constrained probability density function estimation for prediction of rare events

AIChE Journal ◽  
2014 ◽  
Vol 60 (3) ◽  
pp. 1013-1026 ◽  
Author(s):  
Taha Mohseni Ahooyi ◽  
Masoud Soroush ◽  
Jeffrey E. Arbogast ◽  
Warren D. Seider ◽  
Ulku G. Oktem
Keyword(s):  
Maximum Likelihood ◽  
Probability Density Function ◽  
Probability Density ◽  
Maximum Entropy ◽  
Density Function ◽  
Rare Events ◽  
Function Estimation ◽  
Density Function Estimation

scholarly journals Maximum-likelihood estimation of the parameters of a four-parameter class of probability distributions

1988 ◽  
Vol 31 (2) ◽  
pp. 271-283 ◽  
Author(s):  
Siegfried H. Lehnigk
Keyword(s):  
Maximum Likelihood ◽  
Probability Density Function ◽  
Maximum Likelihood Estimation ◽  
Probability Density ◽  
Density Function ◽  
Probability Distributions ◽  
Likelihood Estimation ◽  
Initial Shape ◽  
Definition Of ◽  
Image Position

We shall concern ourselves with the class of continuous, four-parameter, one-sided probability distributions which can be characterized by the probability density function (pdf) classIt depends on the four parameters: shift c ∈ R, scale b > 0, initial shape p < 1, and terminal shape β > 0. For p ≦ 0, the definition of f(x) can be completed by setting f(c) = β/bΓ(β−1)>0 if p = 0, and f(c) = 0 if p < 0. For 0 < p < 1, f(x) remains undefined at x = c; f(x)↑ + ∞ as x↓c.

scholarly journals Bivariate Burr Type III Distribution: Estimation and Prediction

2021 ◽  
pp. 16-36
Author(s):  
A. A. M. Mahmoud ◽  
R. M. Refaey ◽  
G. R. AL-Dayian ◽  
A. A. EL-Helbawy
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Real Life ◽  
Bivariate Distribution ◽  
Cumulative Distribution ◽  
Data Set ◽  
Squared Error Loss Function ◽  
Type Iii ◽  
Estimation And Prediction

In this paper, a bivariate Burr Type III distribution is constructed and some of its statistical properties such as bivariate probability density function and its marginal, joint cumulative distribution and its marginal, reliability and hazard rate functions are studied. The joint probability density function and the joint cumulative distribution are given in closed forms. The joint expectation of this distribution is proposed. The maximum likelihood estimation and prediction for a future observation are derived. Also, Bayesian estimation and prediction are considered under squared error loss function. The performance of the proposed bivariate distribution is examined using a simulation study. Finally, a data set is analyzed under the proposed distribution to illustrate its flexibility for real-life application.

An Efficient Approach for Incremental Association Rule Mining through Histogram Matching Technique

2012 ◽  
Vol 2 (2) ◽  
pp. 29-42 ◽  
Author(s):  
Ajay Kumar ◽  
Shishir Kumar ◽  
Sakshi Saxena
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Association Rule ◽  
Clustering Algorithm ◽  
Synthetic Data ◽  
Rule Mining ◽  
Data Set ◽  
Matching Technique ◽  
Burst Data

The objective of the work being presented is to propose an approach for obtaining appropriate association rules when the data set is being incrementally updated. During this process raw data is clustered by K-mean Clustering Algorithm and appropriate rules are generated for each cluster. Further, a histogram and probability density function are also generated for each cluster. When Burst data set is coming to the system, initially the histogram and probability density function of this new data set are obtained. The new data set has to be added to the cluster whose histogram and probability density functions are almost similar. The proposed method is evaluated and explained on synthetic data.

scholarly journals Deep-Based Conditional Probability Density Function Forecasting of Residential Loads

2020 ◽  
Vol 11 (4) ◽  
pp. 3646-3657 ◽  
Author(s):  
Mousa Afrasiabi ◽  
Mohammad Mohammadi ◽  
Mohammad Rastegar ◽  
Lina Stankovic ◽  
Shahabodin Afrasiabi ◽  
...  
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Conditional Probability ◽  
Conditional Probability Density ◽  
Conditional Probability Density Function
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