Goodness-of-fit testing for the inverse Gaussian distribution based on new entropy estimation using ranked set sampling and double ranked set sampling
1 Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq 25113, Jordan
2 Department of Statistics, Quaid-i-Azam University, Islamabad, 45320, Pakistan
Environmental Systems Research 2012, 1:8 doi:10.1186/2193-2697-1-8Published: 15 September 2012
Entropy is a measure of uncertainty and dispersion associated with a random variable. Several goodness-of-fit tests based on entropy are available in literature and the entropy been widely used in many applications.
Goodness-of-fit test for the inverse Gaussian distribution is studied based on new entropy estimation using simple random sampling (SRS), ranked set sampling (RSS) and double ranked set sampling (DRSS) methods. The critical values of the new tests are obtained using Monte Carlo simulations. The power values of the suggested tests based on several alternative hypotheses using SRS, RSS, and DRSS are also presented. It is observed that the proposed tests are more powerful as compared to the test under SRS. Also, it turns out that the test based on DRSS is superior to the RSS test for all of the cases considered in this study.
Since the suggested goodness-of-fit tests for the inverse Gaussian distribution using DRSS are more efficient than that based on RSS, one may consider them using multistage RSS.