Non-Linear Least Squares and Maximum Likelihood Estimation of Probability Density Function of Cross-Border Transmission Losses

2018 ◽  
Vol 33 (2) ◽  
pp. 2230-2238 ◽  
Author(s):  
Ivan Tolic ◽  
Kruno Milicevic ◽  
Nenad Suvak ◽  
Ivan Biondic
Keyword(s):  
Maximum Likelihood ◽  
Probability Density Function ◽  
Maximum Likelihood Estimation ◽  
Least Squares ◽  
Probability Density ◽  
Density Function ◽  
Likelihood Estimation ◽  
Transmission Losses ◽  
Linear Least Squares ◽  
Cross Border

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.

Advanced Topics

2019 ◽  
pp. 57-74
Author(s):  
Carey Witkov ◽  
Keith Zengel
Keyword(s):  
Maximum Likelihood ◽  
Probability Density Function ◽  
Maximum Likelihood Estimation ◽  
Probability Density ◽  
Likelihood Estimation ◽  
Nonlinear Problems ◽  
Probability Density Functions ◽  
Density Functions ◽  
P Values ◽  
Chi Squared

A variety of advanced topics are introduced to offer greater challenge for beginners and to answer thorny questions often asked by early researchers who are just starting to use chi-squared analysis. Topics covered include probability density functions, p-values, the derivation of the chi-squared probability density function and its uses, reduced chi-squared, the Poisson distribution, and advanced techniques for maximum likelihood estimation in cases where uncertainties are not Gaussian or the model is nonlinear. Problems are included (with solutions in an appendix).

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.

Maximum Likelihood Estimation and Non-Linear Least Squares Fitting Implementation in FPGA Devices for High Resolution Hodoscopy

2013 ◽  
Vol 60 (5) ◽  
pp. 3578-3584 ◽  
Author(s):  
Jose M. Blasco ◽  
Enrique Sanchis ◽  
Vicente Gonzalez ◽  
Jose D. Martin ◽  
Francisco J. Egea ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
High Resolution ◽  
Maximum Likelihood Estimation ◽  
Least Squares ◽  
Likelihood Estimation ◽  
Linear Least Squares ◽  
Least Squares Fitting ◽  
Non Linear

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.

Jaya algorithm in estimation of P[X > Y] for two parameter Weibull distribution

2022 ◽  
Vol 7 (2) ◽  
pp. 2820-2839
Author(s):  
Saurabh L. Raikar ◽  
◽  
Dr. Rajesh S. Prabhu Gaonkar ◽  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Real Life ◽  
Likelihood Estimation ◽  
Estimation Methods ◽  
Jaya Algorithm ◽  
Two Parameter

<abstract> <p>Jaya algorithm is a highly effective recent metaheuristic technique. This article presents a simple, precise, and faster method to estimate stress strength reliability for a two-parameter, Weibull distribution with common scale parameters but different shape parameters. The three most widely used estimation methods, namely the maximum likelihood estimation, least squares, and weighted least squares have been used, and their comparative analysis in estimating reliability has been presented. The simulation studies are carried out with different parameters and sample sizes to validate the proposed methodology. The technique is also applied to real-life data to demonstrate its implementation. The results show that the proposed methodology's reliability estimates are close to the actual values and proceeds closer as the sample size increases for all estimation methods. Jaya algorithm with maximum likelihood estimation outperforms the other methods regarding the bias and mean squared error.</p> </abstract>

Sign in / Sign up

Export Citation Format

Share Document