The skew symmetric Laplace uniform distribution SSLUD({\mu}) is introduced in Lohot, R. K. and Dixit, V. U. (2024) using the skewing mechanism of Azzalini (1985). Here we derive the most powerful (MP) test for symmetry of the SSLUD({\mu}). Since the form of the test statistic is complicated and it is difficult to obtain its exact distribution, critical values and the power of MP test are obtained using simulation. Further, we construct a confidence interval (CI) for parameter {\mu} assuming asymptotic normality and empirical distribution of the maximum likelihood estimator of {\mu}. These two methods are compared based on the average length and coverage probability of the CI. Finally, the CI of the parameter {\mu} is constructed using data on the transformed daily percentage change in the price of NIFTY 50, an Indian stock market index given in Lohot, R. K. and Dixit, V. U. (2024).

翻译：偏斜对称拉普拉斯-均匀分布 SSLUD(μ) 由 Lohot, R. K. 与 Dixit, V. U. (2024) 基于 Azzalini (1985) 的偏斜机制引入。本文推导了 SSLUD(μ) 对称性的最有效检验。由于检验统计量的形式较为复杂，难以获得其精确分布，我们通过模拟方法获得了最有效检验的临界值与功效。进一步，在假设渐近正态性以及参数 μ 的最大似然估计量经验分布的基础上，构建了参数 μ 的置信区间。我们基于置信区间的平均长度与覆盖概率对这两种方法进行了比较。最后，利用 Lohot, R. K. 与 Dixit, V. U. (2024) 中给出的印度股市指数 NIFTY 50 价格日百分比变化率转换数据，构建了参数 μ 的置信区间。