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Goodness of fit for the inverse Gaussian distribution
Author(s) -
O'Reilly Federico J.,
Rueda RaÚL
Publication year - 1992
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315609
Subject(s) - mathematics , goodness of fit , statistics , empirical distribution function , asymptotic distribution , inverse gaussian distribution , f distribution , statistic , estimator , ratio distribution , test statistic , gaussian , monte carlo method , distribution (mathematics) , kolmogorov–smirnov test , inverse , statistical hypothesis testing , probability distribution , mathematical analysis , physics , geometry , quantum mechanics
For testing the fit of the inverse Gaussian distribution with unknown parameters, the empirical distribution‐function statistic A 2 is studied. Two procedures are followed in constructing the test statistic; they yield the same asymptotic distribution. In the first procedure the parameters in the distribution function are directly estimated, and in the second the distribution function is estimated by its Rao‐Blackwell distribution estimator. A table is given for the asymptotic critical points of A 2 . These are shown to depend only on the ratio of the unknown parameters. An analysis is provided of the effect of estimating the ratio to enter the table for A 2 . This analysis enables the proposal of the complete operating procedure, which is sustained by a Monte Carlo study.