A Computer Program for Pharmacokinetics Based on Maximum Likelihood Estimation Using the Gamma Distribution with a Probability Density Function: Comparison with the Normal Distribution.

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.

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

IEEE Transactions on Power Systems ◽

10.1109/tpwrs.2017.2738319 ◽

2018 ◽

Vol 33 (2) ◽

pp. 2230-2238 ◽

Cited By ~ 9

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

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Statistical analysis based on quaternion normal random variables

Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie ◽

10.4102/satnt.v4i3.1042 ◽

1985 ◽

Vol 4 (3) ◽

pp. 120-127 ◽

Cited By ~ 1

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.

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Wakeby Distribution and the Maximum Likelihood Estimation Algorithm in Which Probability Density Function Is Not Explicitly Expressed

Communications for Statistical Applications and Methods ◽

10.5351/ckss.2005.12.2.443 ◽

2005 ◽

Vol 12 (2) ◽

pp. 443-451

Author(s):

Jeong-Soo Park

Keyword(s):

Maximum Likelihood ◽

Probability Density Function ◽

Maximum Likelihood Estimation ◽

Probability Density ◽

Density Function ◽

Likelihood Estimation ◽

Estimation Algorithm ◽

Wakeby Distribution

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Advanced Topics

Chi-Squared Data Analysis and Model Testing for Beginners ◽

10.1093/oso/9780198847144.003.0007 ◽

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).

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Properties and methods of estimation for a bivariate exponentiated Fréchet distribution

Mathematica Slovaca ◽

10.1515/ms-2017-0426 ◽

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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