Abstract
In this paper, we consider skew-normal distributions for constructing new a distribution which allows us to model proportions and rates with zero/one inflation as an alternative to the inflated beta distributions. The new distribution is a mixture between a Bernoulli distribution for explaining the zero/one excess and a censored skew-normal distribution for the continuous variable. The maximum likelihood method is used for parameter estimation. Observed and expected Fisher information matrices are derived to conduct likelihood-based inference in this new type skew-normal distribution. Given the flexibility of the new distributions, we are able to show, in real data scenarios, the good performance of our proposal.
Highlights
The recent statistical literature has experienced an intense research activity on skew distributions.It is due to the fact that many data sets are not fitted well with the normal distribution because of asymmetry and/or kurtosis excess [1]
By using skew-normal distributions, we have proposed a new family of distributions which are an alternative to the beta distribution when an excess zeros and/or one inflation is present
The parameters of the distributions were estimated by the maximum likelihood method
Summary
The recent statistical literature has experienced an intense research activity on skew distributions. As an alternative to not transform the data in the case of random variables with positive support, asymmetry to the right, and presence of LDL/UDL, the Birnbaum-Saunders, log-normal (LN), and log-SN (LSN) distributions can be used [30,32,33,34,35,36]. All the numerical calculations were performed by using the R software [38]
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