scholarly journals Asymmetric Bimodal Exponential Power Distribution on the Real Line

Entropy ◽  
2018 ◽  
Vol 20 (1) ◽  
pp. 23 ◽  
Author(s):  
Mehmet Çankaya
Keyword(s):  
Real Line ◽  
Power Distribution ◽  
Exponential Power Distribution ◽  
The Real ◽  
Exponential Power

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.

A Note On Order Statistics from Exponential Power Distribution

2017 ◽  
Vol 6 (1-2) ◽  
pp. 138
Author(s):  
Soyinka Ajibola Taiwo ◽  
Olosunde A Akin
Keyword(s):  
Probability Density Function ◽  
Order Statistics ◽  
Power Distribution ◽  
Shape Parameter ◽  
Laplace Distribution ◽  
Tail Region ◽  
Exponential Power Distribution ◽  
Exponential Power ◽  
First Moment ◽  
Probability Density Function Pdf

 In this paper, we derived probability density function (pdf) for the order statistics from eponential power distribution (EPD). The distribution is flexible at the tail region, because of the presence of shape parameter, which regulates the thickness of the tail. The first moment of the obtained distribution of the order statistics from EPD is presented as well as other measures of central tendencies. This results generalized the results on order statistics from the Laplace distribution and also the results obtained by Arnold, Balakrishnan and Nagaraja on order statistics from normal distribution.

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.

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