Introducing a Family of Distributions by Using the Class of Normal Mean–Variance Mixture

In this study, we present a new family of asymmetric distributions by taking into consideration the multivariate normal mean–variance (NMV) mixture model. These models are created using one-parameter distributions consisting of two-component linear combinations of the gamma distribution such as the Suja, Rama, Akash and Lindley distributions. These distributions are referred to as the NMV mixture distributions. The object is to evaluate how the various distributions operate and assess how well the skewness and kurtosis of the distributions match different data sets. We also derive some asymptotic properties of the new distribution family. We estimate the parameters of the proposed models and obtain the asymptotic standard errors of these estimators using the generalization of the expectation–maximization (EM) algorithm. The advantage of the suggested distributions is demonstrated with real data sets and simulation studies.