An Extended Mixture Inverse Gaussian Distribution
Keywords:Mixture inverse Gaussian distribution, Length biased inverse Gaussian distribution, Birnbaum- Saunders distribution
This paper proposes an extend mixture inverse Gaussian (EMIG) distribution which is mixed between the inverse Gaussian distribution and the length biased inverse Gaussian (LBIG) distribution. The Birnbaum-Saunders (BS) distribution and LBIG distribution are presented as special cases of the EMIG distribution. The properties of this distribution are discussed which include the shapes of the probability density functions, distribution functions survival functions and hazard rate functions, mean and variance. The EMIG has two
parameters and it is shown that maximum likelihood estimation (MLE) can be obtained by solving equation. An application of the model to a real data set is analyzed using the new distribution, which shows that the EMIG distribution can be used quite effectively in analyzing real data by using Akaike’s information criterion (AIC) statistics and goodness of fit tests.
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