The unit-inverse Gaussian distribution: A new alternative to two-parameter distributions on the unit interval

• Published in: Communications in statistics. Theory and methods Vol. 48; no. 14; pp. 3423 - 3438
• Main Authors: Ghitany, M. E., Mazucheli, J., Menezes, A. F. B., Alqallaf, F.
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 18-07-2019; Taylor & Francis Ltd
• Subjects: Beta distribution; equilibrium distribution; inverse Gaussian distribution; Inverse Gaussian probability distribution; Iterative methods; length biased distribution; maximum likelihood estimation; Method of moments; method of moments estimation; Parameter estimation; weighted distribution
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2018.1476717

A new two-parameter distribution over the unit interval, called the Unit-Inverse Gaussian distribution, is introduced and studied in detail. The proposed distribution shares many properties with other known distributions on the unit interval, such as Beta, Johnson S
B
, Unit-Gamma, and Kumaraswamy distributions. Estimation of the parameters of the proposed distribution are obtained by transforming the data to the inverse Gaussian distribution. Unlike most distributions on the unit interval, the maximum likelihood or method of moments estimators of the parameters of the proposed distribution are expressed in simple closed forms which do not need iterative methods to compute. Application of the proposed distribution to a real data set shows better fit than many known two-parameter distributions on the unit interval.