We introduce the beta generalized normal distribution which is obtained by compounding the beta and generalized normal [Nadarajah, S., A generalized normal distribution, \emph{Journal of Applied Statistics}. 32, 685--694, 2005] distributions. The new model includes as sub-models the beta normal, beta Laplace, normal, and Laplace distributions. The shape of the new distribution is quite flexible, specially the skewness and the tail weights, due to two additional parameters. We obtain general expansions for the moments. The estimation of the parameters is investigated by maximum likelihood. We also proposed a random number generator for the new distribution. Actual synthetic aperture radar were analyzed and modeled after the new distribution. Results could outperform the $\mathcal{G}^0$, $\mathcal{K}$, and $\Gamma$ distributions in several scenarios.
翻译：我们引入了乙型普通正常分布,这是通过补充乙型和普遍正常[Nadarajah, S., 普遍正常分布,\emph{Journal of Application Statistics}. 32, 685-694, 2005] 分布获得的。新模型包括了乙型正常分配、 乙型拉帕特、 正常分配和 Laplace 分布等子模型。新分布的形状非常灵活, 特别是由于另外两个参数, 偏斜和尾部重量。 我们获得了瞬间的一般扩展。 对参数的估计以最大的可能性进行调查。 我们还为新分布提出了随机数字生成器。 在新分布之后, 实际合成孔径雷达进行了分析并建模。 结果可能在若干情况下超过$mathcal{G ⁇ 0, $\mathcal{K} 和$\Gamma$的分布。
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