The probability that the estimator is equal to the value of the estimated parameter is zero. Hence in practical applications we provide together with the point estimates their estimated standard errors. Given a distribution of random variable which has heavier tails or thinner tails than a normal distribution, then the confidence interval common in the literature will not be applicable. In this study, we obtained some results on the confidence procedure for the parameters of generalized normal distribution which is robust in any case of heavier or thinner than the normal distribution using pivotal quantities approach, and on the basis of a random sample of fixed size n. Some simulation studies and applications are also examined.