scholarly journals The Burr X Fréchet Model for Extreme Values: Mathematical Properties, Classical Inference and Bayesian Analysis

2019 ◽  
pp. 797-818 ◽  
Author(s):  
Haitham Yousof ◽  
S. Jahanshahi ◽  
Vikas Kumar Sharma
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Extreme Values ◽  
Likelihood Estimation ◽  
Real Data ◽  
Mcmc Methods ◽  
Bayes Estimators ◽  
Mathematical Properties ◽  
Asymptotic Confidence Intervals ◽  
Classical Inference

In this paper, we investigate a new model based on Burr X and Fréchet distribution forextreme values and derive some of its properties. Maximum likelihood estimation alongwith asymptotic confidence intervals is considered for estimating the parameters of thedistribution. We demonstrate empirically the flexibility of the distribution in modelingvarious types of real data. Furthermore, we also provide Bayes estimators and highestposterior density intervals of the parameters of the distribution using Markov ChainMonte Carlo (MCMC) methods.

The Poisson Nadarajah–Haghighi Distribution: Properties and Applications to Lifetime Data

2019 ◽  
Vol 27 (01) ◽  
pp. 2050005
Author(s):  
Muhammad Mansoor ◽  
M. H. Tahir ◽  
Aymaan Alzaatreh ◽  
Gauss M. Cordeiro
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Survival Data ◽  
Maximum Likelihood Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Likelihood Method ◽  
Lifetime Data ◽  
Monte Carlo Simulation Study ◽  
Mathematical Properties

A new three-parameter compounded extended-exponential distribution “Poisson Nadarajah–Haghighi” is introduced and studied, which is quite flexible and can be used effectively in modeling survival data. It can have increasing, decreasing, upside-down bathtub and bathtub-shaped failure rate. A comprehensive account of the mathematical properties of the model is presented. We discuss maximum likelihood estimation for complete and censored data. The suitability of the maximum likelihood method to estimate its parameters is assessed by a Monte Carlo simulation study. Four empirical illustrations of the new model are presented to real data and the results are quite satisfactory.

Sparse Code Shrinkage: Denoising of Nongaussian Data by Maximum Likelihood Estimation

1999 ◽  
Vol 11 (7) ◽  
pp. 1739-1768 ◽  
Author(s):  
Aapo Hyvärinen
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Sparse Coding ◽  
Likelihood Estimation ◽  
Wavelet Representation ◽  
Mathematical Properties ◽  
Important Benefit ◽  
Redundancy Reduction ◽  
Natural Data ◽  
Wavelet Methods

Sparse coding is a method for finding a representation of data in which each of the components of the representation is only rarely significantly active. Such a representation is closely related to redundancy reduction and independent component analysis, and has some neurophysiological plausibility. In this article, we show how sparse coding can be used for denoising. Using maximum likelihood estimation of nongaussian variables corrupted by gaussian noise, we show how to apply a soft-thresholding (shrinkage) operator on the components of sparse coding so as to reduce noise. Our method is closely related to the method of wavelet shrinkage, but it has the important benefit over wavelet methods that the representation is determined solely by the statistical properties of the data. The wavelet representation, on the other hand, relies heavily on certain mathematical properties (like self-similarity) that may be only weakly related to the properties of natural data.

scholarly journals The Ristic-Balakrishnan odd log-logistic family of distributions: Properties and Applications

2020 ◽  
Vol 8 (1) ◽  
pp. 17-35
Author(s):  
Hamid Esmaeili ◽  
Fazlollah Lak ◽  
Emrah Altun
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Real Data ◽  
Model Parameters ◽  
Mathematical Properties ◽  
Proposed Model ◽  
The Family ◽  
Logistic Family ◽  
Family Of Distributions ◽  
Extra Parameter

This paper investigates general mathematical properties of a new generator of continuous distributions with two extra parameter called the Ristic-Balakrishnan odd log-logistic family of distributions. We present some special models and investigate the asymptotes. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Explicit expressions for the ordinary and incomplete moments, generating functions and order statistics, which hold for any baseline model, are determined. Further, we discuss the estimation of the model parameters by maximum likelihood and present a simulation study based on maximum likelihood estimation. A regression model based on proposed model was introduced. Finally, three applications to real data were provided to illustrate the potentiality of the family of distributions.

scholarly journals The Marshall-Olkin Extended Power Lomax Distribution with Applications

2020 ◽  
pp. 331-341
Author(s):  
JIJU GILLARIOSE ◽  
Lishamol Tomy
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Limiting Distributions ◽  
Lomax Distribution ◽  
New Distribution ◽  
Extended Power

In this article, we dened a new four-parameter model called Marshall-Olkin extended power Lomax distribution and studied its properties. Limiting distributions of sample maxima and sample minima are derived. The reliability of a system when both stress and strength follows the new distribution is discussed and associated characteristics are computed for simulated data. Finally, utilizing maximum likelihood estimation, the goodness of the distribution is tested for real data.

Analiza temperaturilor maxime și minime anuale în Chișinău

2019 ◽  
Author(s):  
Valentin Raileanu ◽  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Extreme Values ◽  
Extreme Value Distribution ◽  
Likelihood Estimation ◽  
Generalized Extreme Value Distribution ◽  
Return Periods ◽  
R Software ◽  
Data Format ◽  
Return Levels

The article briefly describes the fields of application of the theory of extreme values, including climatology. The data format and the analysis methods of the annual maxima and minima temperatures in Chisinau are presented. Free R software and the GUI in2extRemes graphical package are used. Estimating the parameters of the Generalized Extreme Value distribution and return levels vs return periods is done using the Maximum Likelihood Estimation (MLE) method.

Topp–Leone Linear Exponential Distribution

2018 ◽  
Vol 33 (1) ◽  
pp. 31-43
Author(s):  
Bol A. M. Atem ◽  
Suleman Nasiru ◽  
Kwara Nantomah
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Simulation Studies ◽  
Finite Sample ◽  
Data Set ◽  
Finite Sample Properties ◽  
Linear Exponential Distribution

Abstract This article studies the properties of the Topp–Leone linear exponential distribution. The parameters of the new model are estimated using maximum likelihood estimation, and simulation studies are performed to examine the finite sample properties of the parameters. An application of the model is demonstrated using a real data set. Finally, a bivariate extension of the model is proposed.

scholarly journals Transmuted Modified Inverse Rayleigh Distribution

2015 ◽  
Vol 44 (3) ◽  
pp. 17-29 ◽  
Author(s):  
Muhammad Shuaib Khan ◽  
Robert King
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Order Statistics ◽  
Generating Function ◽  
Likelihood Estimation ◽  
Moment Generating Function ◽  
Rayleigh Distribution ◽  
Mean Deviation ◽  
Lifetime Data ◽  
Mathematical Properties

We introduce the transmuted modified Inverse Rayleighdistribution by using quadratic rank transmutation map (QRTM), whichextends the modified Inverse Rayleigh distribution. A comprehensiveaccount of the mathematical properties of the transmuted modified InverseRayleigh distribution are discussed. We derive the quantile, moments,moment generating function, entropy, mean deviation, Bonferroni andLorenz curves, order statistics and maximum likelihood estimation Theusefulness of the new model is illustrated using real lifetime data.

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