Abstract
MSNBurr and MSTBurr distribution have been developed as Neo-Normal distributions that represent a relaxation of normality. The difference between them is that the MSTBurr’s peak is below MSNBurr’s. In this paper, we propose a MSEPBurr distribution with its peak could be not only lower but also high-er than MSNBurr. Furthermore, we study several properties of MSEPBurr, such as mean, variance, skewness, kurtosis, and quantile. The MSEPBurr parameters are estimated by using the Bayesian approach with the BUGS language implementation for its computation. We employ simulation study and use existing data to illustrate the application of the regression model. In real data, we notice that MSEPBurr has similar performance with MSNBurr and MSTBurr that they outperform Normal and Student-t distribution in Australian athlete data because their skewness can accommodate long left tail excellently. However, their performance is less than the Student-t model in chemical reaction rate data because their skewness can not accommodate long right tail perfectly. Although in general their perfor-mance is the same, we observe that the MSEPBurr performs better than the MSNBurr and the MSTBurr in some simulated data.
Highlights
The Normal distribution is commonly used in statistical modeling
This paper has presented MSEPBurr distribution as a general form of MSNBurr distribution
The mean and variance of MSEPBurr are affected by v parameter, but not for the skewness and kurtosis which they are only influenced by the α parameter
Summary
The Normal distribution is commonly used in statistical modeling. the use of this distribution is sometimes incompatible with the available data. In contrast to Azzalini (1985), Fernandez and Steel (1998) proposed the Skew-Normal distribution that has a stable mode of the location parameter. The study of the skewed or symmetrical distribution has been carried out by Iriawan (2000) who developed the “Modified to be Stable as Normal from Burr”, hereinafter referred to MSNBurr distribution. It was derived from the modification of Burr type II distribution (Burr, 1942). Iriawan (2000) developed the “Modified to be Stable as t from Burr”, hereinafter referred to MSTBurr distribution with its peak could be below MSNBurr’s when their location and scale parameters are the same. We propose “Modified to be Stable Exponential Power from Burr”, referred to MSEPBurr distribution with its peak could be lower and higher than MSNBurr distribution
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