Double Inverse-Gaussian Distributions and Associated Inference

Abstract

In order to have more flexibility, several double distributions have been studied in the literature. In this paper, we propose a double inverse Gaussian distribution using random sign mixture transform and study its associated inferences. The maximum likelihood estimation is performed to estimate the parameters. Extensive simulation studies are carried out to examine the performance of the estimators and the corresponding confidence intervals of the parameters. A real data set example is presented to illustrate the procedure.

A Bimodal Extension of the Log-Normal Distribution on the Real Line with an Application to DNA Microarray Data

“…The data labelled as "SID 377353, ESTs [5':, 3':AA055048]" consist of the following 118 observations: 0.029, 0.062, 0.011, 0.009, 0.065, −0.128, 0.133, 0.116, 0.184, 0.111, −0.066, −0.049, 0.05, 0.137, 0.162, 0.173, 0.033, 0.107, 0. For the sake of comparing the bimodal DLN distribution with other bimodal distributions, we consider the double inverse Gaussian (DIG) distribution proposed in [16]. The PDF of the DIG distribution is…”

“…However, the words 'double' or 'reflection' are sometimes used to denote the distribution of the absolute value of a random variable. Some double continuous distributions based on the RST are: Double inverse Gaussian distribution [16].…”