1 Introduction The proposed distribution referred to as an Extended Inverse Gaussian Model (EIG) has density function where
An Extended Inverse Gaussian Model Iman Mabrouk Statistical and
Actuarial Sciences Department The University of Western Ontario
Supervised by: Dr. Serge Provost Outline Introduction Parameter
Effect Some Statistical Functions Numerical Examples 1 Introduction
The proposed distribution referred to as an Extended Inverse
Gaussian Model (EIG) has density function where The EIG model is a
generalization of a distribution introduced by Jrgensen (1982)
whose density function is where is a Generalization of the Inverse
Gaussian model (GIG) where the density of Inverse Gaussian model is
Reduced Models 1)A reduced model called the Reduced Extended
Inverse Gaussian(REIG) is obtained by omitting. The density
function of REIG model is Reduced Models 2)Omitting yields a
Reparameterized Generalized Gamma model (RGG) where the density of
the generalized gamma model is and it can be obtained from by
letting 2 Parameter Effect 2.1 The Extended Inverse Gaussian Model
(EIG) 2)1 2.2 The Reduced Extended Inverse Gaussian Model (REIG) 3
Some Statistical Functions 3.1 The Extended Gaussian Model (EIG)
3.2 The Reduced Extended Inverse Gaussian Model (REIG) 4 Numerical
Examples 4.1 Goodness-of-fit statistics 4.2 Maximum Flood Levels
4.3 Snowfall Precipitations i.The Anderson-Darling statistic where
and the are the ordered observations. ii.The Cramr-von Mises
statistic 4.1 Goodness-of-fit statistics: Maximum Flood Levels in
millions of cubic feet per second for the Susquehanna River at
Harrisburg, Pennsylvania over 20 four- year periods. 4.2 Maximum
Flood Levels Estimates of the Parameters and Goodness- of-Fit
Statistics for the Flood Data Maximum Likelihood Estimates Weibull
Gamma Inverse Gaussian Lognormal (-.898,.269) RGG GIG REIG EIG The
EIG model and its reduced version provide a better fit than that
resulting from the other models The EIG and REIG models fit the
data nearly equally well in this case. Note that The sample size is
small Only scant data is available in the tails of the distribution
Notes CDF (solid line) and empirical CDF (dots) for the flood data
set using EIG model Snow precipitation in centimeters over 63
consecutive years in the city of Buffalo. 4.3 Snowfall Data
Estimates of the Parameters and Goodness- of-Fit Statistics for the
Snowfall Data Inverse Gaussian Lognormal (-.898,.269) REIG Gamma
GIG Weibull RGG EIG Maximum Likelihood Estimates CDF (solid line)
and empirical CDF (dots) for the snowfall data set using EIG Model
The Extended Inverse Gaussian model provides more flexibility for
fitting various types of data sets Conclusion References
1.D'Agostino, R. B. and Stephens, M. A. (1986). Goodness-of-fit
Techniques. CRC Press, Boca Raton. 2.Dumonceaux, R., Antle, C.
(1973). Discrimination between the log-normal and the Weibull
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Hartigan, J. Kiefer, and K. Krickeberg, Springer-Verlag, New York.
4. Mathai, A.M. and Saxena, R.K. (1978). The H-function with
applications in statistics and other discplines. Wiley, New York.
5.Seshadri, V. (1993). The Inverse Gaussian Distribution: A Case
Study in Exponential Families. Oxford Science Publication,
Oxford.
