On the non-existence of maximum likelihood estimates for the extended exponential power distribution and its generalizations

2015 ◽  
Vol 107 ◽  
pp. 111-114
Author(s):  
Samuel E. Tumlinson
Keyword(s):  
Maximum Likelihood ◽  
Power Distribution ◽  
Maximum Likelihood Estimates ◽  
Exponential Power Distribution ◽  
Exponential Power

scholarly journals The Location-Scale Mixture Exponential Power Distribution: A Bayesian and Maximum Likelihood Approach

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Z. Rahnamaei ◽  
N. Nematollahi ◽  
R. Farnoosh
Keyword(s):  
Maximum Likelihood ◽  
Power Distribution ◽  
Real Data ◽  
Scale Mixture ◽  
Exponential Power Distribution ◽  
Likelihood Approach ◽  
Slash Distribution ◽  
Exponential Power ◽  
Mean Square Errors ◽  
New Distribution

We introduce an alternative skew-slash distribution by using the scale mixture of the exponential power distribution. We derive the properties of this distribution and estimate its parameter by Maximum Likelihood and Bayesian methods. By a simulation study we compute the mentioned estimators and their mean square errors, and we provide an example on real data to demonstrate the modeling strength of the new distribution.

scholarly journals Asymmetric Bimodal Exponential Power Distribution on Real Line

2017 ◽  
Author(s):  
Mehmet Niyazi Çankaya
Keyword(s):  
Real Line ◽  
Power Distribution ◽  
Information Matrix ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Data Generation ◽  
Artificial Data ◽  
Exponential Power Distribution ◽  
Exponential Power ◽  
Two Parameters

The asymmetric bimodal exponential power (ABEP) distribution is an extension of the generalized gamma distribution to the real line via adding two parameters which fit the shape of peakedness in bimodality on real line. The special values of peakedness parameters of the distribution are combination of half Laplace and half normal distributions on real line. The distribution has two parameters fitting the height of bimodality, so capacity of bimodality is enhanced by using these parameters. Adding a skewness parameter is considered to model asymmetry in data. The location-scale form of this distribution is proposed. The Fisher information matrix of these parameters in ABEP is obtained explicitly. Properties of ABEP are examined. Real data examples are given to illustrate the modelling capacity of ABEP. The replicated artificial data from maximum likelihood estimates of parameters of ABEP and distributions having an algorithm for artificial data generation procedure are provided to test the similarity with real data.

scholarly journals Generalized Exponential Power Distribution with Application to Complete and Censored Data

2021 ◽  
pp. 34-55
Author(s):  
M. M. E. Abd El-Monsef ◽  
M. M. El-Awady
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Power Distribution ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Type I ◽  
Sample Type ◽  
Exponential Power Distribution ◽  
Exponential Power

The exponential power distribution (EP) is a lifetime model that can exhibit increasing and bathtub hazard rate function. This paper proposed a generalization of EP distribution, named generalized exponential power (GEP) distribution. Some properties of GEP distribution will be investigated. Recurrence relations for single moments of generalized ordered statistics from GEP distribution are established and used for characterizing the GEP distribution. Estimation of the model parameters are derived using maximum likelihood method based on complete sample, type I, type II and random censored samples. A simulation study is performed in order to examine the accuracy of the maximum likelihood estimators of the model parameters. Three applications to real data, two with censored data, are provided in order to show the superiority of the proposed model to other models.

scholarly journals Estimating parameters of linear regression with an exponential power distribution of errors by using a polynomial maximization method

2021 ◽  
Vol 1 (4 (109)) ◽  
pp. 64-73
Author(s):  
Serhii Zabolotnii ◽  
Vladyslav Khotunov ◽  
Anatolii Chepynoha ◽  
Olexandr Tkachenko
Keyword(s):  
Maximum Likelihood ◽  
Linear Regression ◽  
Power Distribution ◽  
Maximum Likelihood Method ◽  
Least Square Method ◽  
Least Square ◽  
Likelihood Method ◽  
Random Errors ◽  
Exponential Power Distribution ◽  
Exponential Power

This paper considers the application of a method for maximizing polynomials in order to find estimates of the parameters of a multifactorial linear regression provided the random errors of the regression model follow an exponential power distribution. The method used is conceptually close to a maximum likelihood method because it is based on the maximization of selective statistics in the neighborhood of the true values of the evaluated parameters. However, in contrast to the classical parametric approach, it employs a partial probabilistic description in the form of a limited number of statistics of higher orders. The adaptive algorithm of statistical estimation has been synthesized, which takes into consideration the properties of regression residues and makes it possible to find refined values for the estimates of the parameters of a linear multifactorial regression using the numerical Newton-Rafson iterative procedure. Based on the apparatus of the quantity of extracted information, the analytical expressions have been derived that make it possible to analyze the theoretical accuracy (asymptotic variances) of estimates for the method of maximizing polynomials depending on the magnitude of the exponential power distribution parameters. Statistical modeling was employed to perform a comparative analysis of the variance of estimates obtained using the method of maximizing polynomials with the accuracy of classical methods: the least squares and maximum likelihood. Regions of the greatest efficiency for each studied method have been constructed, depending on the magnitude of the parameter of the form of exponential power distribution and sample size. It has been shown that estimates from the polynomial maximization method may demonstrate a much lower variance compared to the estimates from a least-square method. And, in some cases (for flat-topped distributions and in the absence of a priori information), may exceed the estimates from the maximum likelihood method in terms of accuracy

scholarly journals Statistical Inferences and Applications of the Half Exponential Power Distribution

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Wenhao Gui
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Normal Distribution ◽  
Power Distribution ◽  
Exponential Power Distribution ◽  
Statistical Inferences ◽  
Proposed Model ◽  
Exponential Power ◽  
First Time

We investigate the statistical inferences and applications of the half exponential power distribution for the first time. The proposed model defined on the nonnegative reals extends the half normal distribution and is more flexible. The characterizations and properties involving moments and some measures based on moments of this distribution are derived. The inference aspects using methods of moment and maximum likelihood are presented. We also study the performance of the estimators using the Monte Carlo simulation. Finally, we illustrate it with two real applications.

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