An Extension of the Truncated-Exponential Skew- Normal Distribution

In the paper, we present an extension of the truncated-exponential skew-normal (TESN) distribution. This distribution is defined as the quotient of two independent random variables whose distributions are the TESN distribution and the beta distribution with shape parameters q and 1, respectively. The resulting distribution has a more flexible coefficient of kurtosis. We studied the general probability density function (pdf) of this distribution, its survival and hazard functions, some of its properties, moments and inference by the maximum likelihood method. We carried out a simulation and applied the methodology to a real dataset.

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Using Iterative Reweighting Algorithm and Genetic Algorithm to Calculate The Estimation of The Parameters Of The Maximum Likelihood of The Skew Normal Distribution

Journal of Economics and Administrative Sciences ◽

10.33095/jeas.v27i127.2148 ◽

2021 ◽

Vol 27 (127) ◽

pp. 253-264

Author(s):

مرتضى علاء الخفاجي ◽

رباب عبد الرضا البكري

Keyword(s):

Genetic Algorithm ◽

Maximum Likelihood ◽

Normal Distribution ◽

Likelihood Estimation ◽

Real Data ◽

Likelihood Method ◽

Skew Normal Distribution ◽

Iterative Reweighting ◽

Non Linear Equation ◽

Skew Normal

Excessive skewness which occurs sometimes in the data is represented as an obstacle against normal distribution. So, recent studies have witnessed activity in studying the skew-normal distribution (SND) that matches the skewness data which is regarded as a special case of the normal distribution with additional skewness parameter (α), which gives more flexibility to the normal distribution. When estimating the parameters of (SND), we face the problem of the non-linear equation and by using the method of Maximum Likelihood estimation (ML) their solutions will be inaccurate and unreliable. To solve this problem, two methods can be used that are: the genetic algorithm (GA) and the iterative reweighting algorithm (IR) based on the Maximum Likelihood method. Monte Carlo simulation was used with different skewness levels and sample sizes, and the superiority of the results was compared. It was concluded that (SND) model estimation using (GA) is the best when the samples sizes are small and medium, while large samples indicate that the (IR) algorithm is the best. The study was also done using real data to find the parameter estimation and a comparison between the superiority of the results based on (AIC, BIC, Mse and Def) criteria.

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Slashed Exponentiated Rayleigh Distribution

Revista Colombiana de Estadística ◽

10.15446/rce.v38n2.51673 ◽

2015 ◽

Vol 38 (2) ◽

pp. 453-466 ◽

Cited By ~ 1

Author(s):

Hugo S. Salinas ◽

Yuri A. Iriarte ◽

Heleno Bolfarine

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Method ◽

Real Data ◽

Random Variable ◽

Rayleigh Distribution ◽

Likelihood Method ◽

Independent Random Variables ◽

Parameter Estimates ◽

Positive Data ◽

New Distribution

<p>In this paper we introduce a new distribution for modeling positive data with high kurtosis. This distribution can be seen as an extension of the exponentiated Rayleigh distribution. This extension builds on the quotient of two independent random variables, one exponentiated Rayleigh in the numerator and Beta(q,1) in the denominator with q>0. It is called the slashed exponentiated Rayleigh random variable. There is evidence that the distribution of this new variable can be more flexible in terms of modeling the kurtosis regarding the exponentiated Rayleigh distribution. The properties of this distribution are studied and the parameter estimates are calculated using the maximum likelihood method. An application with real data reveals good performance of this new distribution.</p>

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