Proportional inverse Gaussian distribution: A new tool for analysing continuous proportional data

Liu, Pengyi1; Tian, Guo-Liang2; Yuen, Kam Chuen3; Zhang, Chi4; Tang, Man-Lai5

2021-11-01

10.1111/anzs.12345

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS   影响因子和分区

1369-1473

1467-842X

Outcomes in the form of rates, fractions, proportions and percentages often appear in various fields. Existing beta and simplex distributions are frequently unable to exhibit satisfactory performances in fitting such continuous data. This paper aims to develop the normalised inverse Gaussian (N-IG) distribution proposed by Lijoi, Mena & Prunster (2005, Journal of the American Statistical Association, 100, 1278-1291) as a new tool for analysing continuous proportional data in (0,1) and renames the N-IG as proportional inverse Gaussian (PIG) distribution. Our main contributions include: (i) To overcome the difficulty of an integral in the PIG density function, we propose a novel minorisation-maximisation (MM) algorithm via the continuous version of Jensen's inequality to calculate the maximum likelihood estimates of the parameters in the PIG distribution; (ii) We also develop an MM algorithm aided by the gradient descent algorithm for the PIG regression model, which allows us to explore the relationship between a set of covariates with the mean parameter; (iii) Both the comparative studies and the real data analyses show that the PIG distribution is better when comparing with the beta and simplex distributions in terms of the AIC, the Cramer-von Mises and the Kolmogorov-Smirnov tests. In addition, bootstrap confidence intervals and testing hypothesis on the symmetry of the PIG density are also presented. Simulation studies are conducted and the hospital stay data of Barcelona in 1988 and 1990 are analysed to illustrate the proposed methods.

AIC continuous proportional data MM algorithm proportional inverse Gaussian distribution simplex distribution

SCI

英语

通讯

National Natural Science Foundation of China[11771199,12171225,11801380] ; Research Grants Council of the Hong Kong Special Administrative Region, China[HKU17306220] ; Research Grant Council of the Hong Kong Special Administrative Region["UGC/FDS14/P01/14","UGC/FDS14/P01/16"]

Mathematics

Statistics & Probability

WOS:000721479700001

WILEY

MATHEMATICS

Web of Science

1.Yunnan Univ Finance & Econ, Dept Stat, Kunming 650221, Yunnan, Peoples R China
2.Southern Univ Sci & Technol, Dept Stat & Data Sci, Shenzhen 518055, Guangdong, Peoples R China
3.Univ Hong Kong, Dept Stat & Actuarial Sci, Pokfulam Rd, Hong Kong, Peoples R China
4.Shenzhen Univ, Coll Econ, Shenzhen 518055, Guangdong, Peoples R China
5.Brunel Univ London, Coll Engn Design & Phys Sci, Dept Math, Kingston Lane, Uxbridge UB8 3PH, Middx, England

Liu, Pengyi,Tian, Guo-Liang,Yuen, Kam Chuen,et al. Proportional inverse Gaussian distribution: A new tool for analysing continuous proportional data[J]. AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS,2021.

Liu, Pengyi,Tian, Guo-Liang,Yuen, Kam Chuen,Zhang, Chi,&Tang, Man-Lai.(2021).Proportional inverse Gaussian distribution: A new tool for analysing continuous proportional data.AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS.

Liu, Pengyi,et al."Proportional inverse Gaussian distribution: A new tool for analysing continuous proportional data".AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS (2021).