Abstract
We introduce a new class of the slash distribution using the epsilon half normal distribution. The newly defined model extends the slashed half normal distribution and has more kurtosis than the ordinary half normal distribution. We study the characterization and properties including moments and some measures based on moments of this distribution. A simulation is conducted to investigate asymptotically the bias properties of the estimators for the parameters. We illustrate its use on a real data set by using maximum likelihood estimation.
Highlights
The epsilon half normal distribution, proposed by Castro et al [1], is widely used for nonnegative data modeling, for instance, to consider the lifetime process under fatigue
We introduce a new class of the slash distribution using the epsilon half normal distribution
When 0, the epsilon half normal distribution reduces to the half normal distribution investigated in Castro et al [1] provided mathematical properties of the epsilon half normal distribution and discussed some inferential aspects related to the maximum likelihood estimation
Summary
The epsilon half normal distribution, proposed by Castro et al [1], is widely used for nonnegative data modeling, for instance, to consider the lifetime process under fatigue. Gómez et al [9] replaced standard normal random variable Z by an elliptical distribution and defined a new family of slash distributions They studied its general properties of the resulting families, including their moments. Wang et al [11] introduced the multivariate skew version of this distribution and examined its properties and inferences They substituted the standard normal random variable Z by a skew normal distribution studied in [12] to define a skew extension of the slash distribution. Epsilon half normal distribution EHN , is an extension of the half normal distribution, it is naturally to define a slash distribution based on it in which skewness and thick tailed situations may exist It leads to a new model on nonnegative measurements with more flexible asymmetry and kurtosis parameters.
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