Maximum Likelihood Estimation Using Probability Density Functions of Order Statistics

2016 ◽  
pp. 75-85
Author(s):  
Andrew G. Glen
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Probability Density ◽  
Order Statistics ◽  
Likelihood Estimation ◽  
Probability Density Functions ◽  
Density Functions

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 On the Performance of Transmuted Logistic Distribution: Statistical Properties and Application

2019 ◽  
Vol 1 (3) ◽  
pp. 34-42
Author(s):  
Adeyinka Femi Samuel
Keyword(s):  
Biological Sciences ◽  
Probability Density ◽  
Order Statistics ◽  
Likelihood Estimation ◽  
Moment Generating Function ◽  
Probability Density Functions ◽  
Logistic Distribution ◽  
Density Functions ◽  
Maximum Order ◽  
Method Of Maximum Likelihood

In this article we transmute the logistic distribution using quadratic rank transmutation map to develop a transmuted logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its parent model to enhance more flexibility in the analysis of data in various disciplines such as biological sciences, actuarial science, finance and insurance. The mathematical properties such as moment generating function, quantile, median and characteristic function of this distribution are discussed. The probability density functions of the minimum and maximum order statistics of the transmuted logistic distribution are established and the relationships between the probability density functions of the minimum and maximum order statistics of the parent model and the probability density function of the transmuted logistic distribution are considered. The parameter estimation is done by the method of maximum likelihood estimation. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using it to fit relevant data. The study is concluded by demonstrating that the transmuted logistic distribution performs better than its parent model. 

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 Compositional Data Modeling through Dirichlet Innovations

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2477
Author(s):  
Seitebaleng Makgai ◽  
Andriette Bekker ◽  
Mohammad Arashi
Keyword(s):  
Maximum Likelihood ◽  
Probability Density ◽  
Gamma Distribution ◽  
Compositional Data ◽  
Dirichlet Distribution ◽  
Real Data ◽  
Probability Density Functions ◽  
Density Functions ◽  
Data Sets ◽  
Method Of Maximum Likelihood

The Dirichlet distribution is a well-known candidate in modeling compositional data sets. However, in the presence of outliers, the Dirichlet distribution fails to model such data sets, making other model extensions necessary. In this paper, the Kummer–Dirichlet distribution and the gamma distribution are coupled, using the beta-generating technique. This development results in the proposal of the Kummer–Dirichlet gamma distribution, which presents greater flexibility in modeling compositional data sets. Some general properties, such as the probability density functions and the moments are presented for this new candidate. The method of maximum likelihood is applied in the estimation of the parameters. The usefulness of this model is demonstrated through the application of synthetic and real data sets, where outliers are present.

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