Extended Inverse Gaussian Distribution: Properties and Application

doi:10.1007/s12204-019-2144-9

J Shanghai Jiaotong Univ Sci ›› 2020, Vol. 25 ›› Issue (2): 193-200.doi: 10.1007/s12204-019-2144-9

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Extended Inverse Gaussian Distribution: Properties and Application

LAI Junfeng (赖俊峰), JI Dandan (季丹丹), YAN Zaizai (闫在在)

(1. College of Science, Inner Mongolia University of Technology, Hohhot 010051, China; 2. College of Mathematics and Statistics, Chifeng University, Chifeng 024000, Inner Mongolia, China)
(1. College of Science, Inner Mongolia University of Technology, Hohhot 010051, China; 2. College of Mathematics and Statistics, Chifeng University, Chifeng 024000, Inner Mongolia, China)

Online:2020-04-01 Published:2020-04-01
Contact: YAN Zaizai (闫在在) E-mail:zz.yan@163.com

Abstract

Abstract: In this paper, a new distribution called the extended inverse Gaussian (EIG) distribution is introduced. By means of the method of T-X family, the new distribution is compounded by the inverse Gaussian (IG) and Weibull distributions. We study its fundamental properties, such as probability density function, hazard rate function, raw moments, moments generating function, skewness and kurtosis, and residual life. We also discuss the maximum likelihood estimators and asymptotic confident intervals of parameters in new distribution. Finally, the EIG distribution and several other competing distributions are fitted into an actual data set and it is shown that the EIG distribution has a superior performance among the compared distributions by making use of various goodness-of-fit tests.

Key words: reliability theory| inverse Gaussian distribution| hazard rate function

摘要： In this paper, a new distribution called the extended inverse Gaussian (EIG) distribution is introduced. By means of the method of T-X family, the new distribution is compounded by the inverse Gaussian (IG) and Weibull distributions. We study its fundamental properties, such as probability density function, hazard rate function, raw moments, moments generating function, skewness and kurtosis, and residual life. We also discuss the maximum likelihood estimators and asymptotic confident intervals of parameters in new distribution. Finally, the EIG distribution and several other competing distributions are fitted into an actual data set and it is shown that the EIG distribution has a superior performance among the compared distributions by making use of various goodness-of-fit tests.

关键词: reliability theory| inverse Gaussian distribution| hazard rate function

CLC Number:

O 213.2

LAI Junfeng (赖俊峰), JI Dandan (季丹丹), YAN Zaizai (闫在在). Extended Inverse Gaussian Distribution: Properties and Application[J]. J Shanghai Jiaotong Univ Sci, 2020, 25(2): 193-200.

References 16

[1]	GUPTA R D, KUNDU D. Exponentiated exponential family: An alternative to Gamma and Weibull distributions[J]. Biometrical Journal, 2001, 43(1): 117-130.
[2]	TAHIR M H, CORDEIRO G M, ALZAATREH A, et al. A new Weibull-Pareto distribution: Properties and applications [J]. Communications in Statistics: Simulation and Computation, 2016, 45(10): 3548-3567.
[3]	ALZAATREH A, GHOSH I. A study of the Gamma-Pareto (IV) distribution and its applications [J]. Communications in Statistics: Theory and Methods, 2016,45(3): 636-654.
[4]	ALZAATREH A, LEE C, FAMOYE F. A new method for generating families of continuous distributions [J].METRON, 2013, 71(1): 63-79.
[5]	TWEEDIE M C K. Statistical properties of inverse Gaussian distributions [J]. Annals of Mathematical Statistics, 1957, 28(3): 362-377.
[6]	MEHTA J S. Estimation in inverse Gaussian distribution [J]. Trabajos de Estadisticay de Investigacion Operativa, 1969, 20(1): 103-111.
[7]	FOLKS J L, CHHIKARA R S. The inverse Gaussian distribution and its statistical application: A review[J]. Journal of the Royal Statistical Society. Series B(Methodological ), 1978, 40(3): 263-289.
[8]	JOHNSON N L, KOTZ S, BALAKRISHNAN N. Continuous univariate distributions [M]. 2nd ed. New York:John Wiley & Sons, 1994.
[9]	JAIN R K, JAIN S. Inverse Gaussian distribution and its application to reliability [J]. Microelectronics Reliability,1996, 36(10): 1323-1335.
[10]	TAKAGI K, KUMAGAI S, MATSUNAGA I, et al.Application of inverse Gaussian distribution to occupational exposure data [J]. Annals of Occupational Hygiene,1997, 41(5): 505-514.
[11]	YANG Z L, LEE R T C. On the failure rate estimation of the inverse Gaussian distribution [J]. Journal of Statistical Computation and Simulation, 2001, 71(3):201-213.
[12]	SAW ??C, YONG J. Interval estimation for the exponential inverse Gaussian distribution [J]. Journal of Statistical Computation and Simulation, 2008, 78(4):339-349.
[13]	NADARAJAH S. An alternative inverse Gaussian distribution[J]. Mathematics and Computers in Simulation,2009, 79(5): 1721-1729.
[14]	GUO B C, WANG B X, XIE M. A study of process monitoring based on inverse Gaussian distribution [J].Computers and Industrial Engineering, 2014, 76(1):49-59.
[15]	GLASER R E. Bathtub and related failure rate characterizations [J]. Journal of the American Statistical Association, 1980, 75(371): 667-672.
[16]	HOSMER DW, LEMESHOWS, MAY S. Applied survival analysis: Regression modeling of time to event data [M]. New Jersey: John Wiley & Sons, 2008.

Extended Inverse Gaussian Distribution: Properties and Application

Extended Inverse Gaussian Distribution: Properties and Application

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