Abstract
The Skew-Reflected-Gompertz (SRG) distribution, introduced by Hosseinzadeh et al. (J. Comput. Appl. Math. (2019) 349, 132–141), produces two-piece asymmetric behavior of the Gompertz (GZ) distribution, which extends the positive to a whole dominion by an extra parameter. The SRG distribution also permits a better fit than its well-known classical competitors, namely the skew-normal and epsilon-skew-normal distributions, for data with a high presence of skewness. In this paper, we study information quantifiers such as Shannon and Rényi entropies, and Kullback–Leibler divergence in terms of exact expressions of GZ information measures. We find the asymptotic test useful to compare two SRG-distributed samples. Finally, as a real-world data example, we apply these results to South Pacific sea surface temperature records.
Highlights
The Skew-Reflected-Gompertz (SRG) distribution was recently introduced by [1] and corresponds to an extension of the Gompertz distribution [2], named after Benjamin Gompertz (1779–1865).It extends the positive dominion R+ to the whole of R by an extra parameter, ε, −1 < ε < 1, and produces two-piece asymmetric behavior of Gompertz (GZ) density
We have presented a methodology to compute the Shannon and the Rényi entropy and the Kullback–Leibler divergence for the family of Skew-Reflected-Gompertz distributions
Our methods consider the information quantifiers previously computed for the Gompertz distribution
Summary
The Skew-Reflected-Gompertz (SRG) distribution was recently introduced by [1] and corresponds to an extension of the Gompertz distribution [2], named after Benjamin Gompertz (1779–1865) It extends the positive dominion R+ to the whole of R by an extra parameter, ε, −1 < ε < 1, and produces two-piece asymmetric behavior of Gompertz (GZ) density. We build on the study of [3], which developed hypothesis testing for normality, i.e., if the shape parameter is close to zero They considered the Kullback–Leibler (KL) divergence in terms of moments and cumulants of the modified SN distribution. We introduced hypothesis testing developed by [12] for the SRG distribution, which is useful to compare two data sets with bimodal and asymmetric behavior such as SST
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