An extended normal distribution for reliability data analysis

摘要

Normal distribution which has only symmetric density function shape plays important role in statistics and probability theory. In this paper, we introduce a new flexible five-parameter extended normal distribution. Some characterizations of the new distribution which include quantile function, ordinary moments, median, entropy, order statistics are derived. The maximum likelihood estimation method is used to estimate the parameters of the new distribution. The potentials of the new distribution are illustrated by means of comparison with some distributions using two real-life data sets. The comparison which is based on goodness-of-fit statistics indicates that the new distribution provides a better fit than the other competing distributions.